Electromagnetic Fields in Complex Mediums

A thesis submitted for the degree of

Doctor of Science

in

Electronics Engineering

by

Akhlesh Lakhtakia, B.Tech, M.S., Ph.D.

to

Banaras Hindu University

2006

CANDIDATE’S DECLARATION

I, Akhlesh Lakhtakia, declare that this thesis, entitled “Electromagnetic Fields in

Complex Mediums,” submitted for the award of the degree of Doctor of Science of this

University, has not been submitted for the award of any degree or diploma of this or any

other University.

Date: .......................................................... ..........................................................

Place: Varanasi Akhlesh Lakhtakia

CERTIFICATE

This is to certify that this thesis entitled “Electromagnetic Fields in Complex Medi-

ums” has been submitted by Akhlesh Lakhtakia for the award of the degree of Doctor of

Science of Banaras Hindu University.

......................................................................... .......................................................................................................

(Signature of the Advisor) (Signature of the Head of the Department/

Coordinator of the School)Pradip Kumar Jain, Professor

...........................................................................................

(Signature of the Chairman of the FRC)

TABLE OF CONTENTS

Acknowledgments xix

Extended Abstract 1

1. Introduction 1

2. Macroscopic Maxwell Postulates 2

3. Time-harmonic Maxwell Postulates 5

4. Constitutive Relations 6

4.1 Linear dielectric materials 7

4.2 Linear bianisotropic materials 8

4.3 Nonlinear bianisotropic materials 11

5. Complex-mediums Electromagnetics 12

6. Scope of My Research from 2001 to 2005 15

7. Sculptured Thin Films (STFs) 17

Plane-wave response of chiral STFs 20

Optical applications of chiral STFs 21

Pulse propagation in chiral STFs 24

8. Homogenization of Composite Materials 26

Linear materials 26

Nonlinear materials 28

9. Negative-phase-velocity Propagation 29

i

NPV propagation in materials 30

NPV propagation in outer space 32

10. Related Topic in Nanotechnology 33

11. Fundamental Issues in CME 35

12. Concluding Remarks 36

13. References 37

List of Publications 41

Publications on Sculptured Thin Films

A1. A. Lakhtakia, Sculptured thin films: accomplishments and emerging uses,

Mater Sci Engg C 19 (2002), 427-434. 57

A2. A. Lakhtakia and R. Messier, The past, the present, and the future of

sculptured thin films, Introduction to complex mediums for optics and

electromagnetics (W.S. Weiglhofer and A. Lakhtakia, eds), SPIE Press,

Bellingham, WA, USA, 2003, pp. 447-478. 65

A3. A. Lakhtakia and R. Messier, Sculptured thin films, Nanometer structures:

Theory, modeling, and simulation (A. Lakhtakia, ed), SPIE Press,

Bellingham, WA, USA, 2004, pp. 5-44. 70

A4. A. Lakhtakia and R. Messier, Sculptured thin films: Nanoengineered

morphology and optics, SPIE Press, Bellingham, WA, USA, 2005. 74

A5. J.A. Sherwin and A. Lakhtakia, Nominal model for structure-property

relations of chiral dielectric sculptured thin films, Math. Comput. Model. 34

(2001), 1499-1514; corrections: 35 (2002), 1355-1363. 81

A6. J.A. Sherwin, A. Lakhtakia, and I.J. Hodgkinson, On calibration

ii

of a nominal structure-property relationship model for chiral sculptured

thin films by axial transmittance measurements, Opt Commun 209

(2002), 369-375. 106

A7. J.A. Sherwin and A. Lakhtakia, Nominal model for the optical response

of a chiral sculptured thin film infiltrated with an isotropic chiral fluid,

Opt Commun 214 (2002), 231-245. 113

A8. J.A. Sherwin and A. Lakhtakia, Nominal model for the optical response

of a chiral sculptured thin film infiltrated by an isotropic chiral

fluid—oblique incidence, Opt Commun 222 (2003), 305-329. 128

A9. F. Chiadini and A. Lakhtakia, Gaussian model for refractive indexes

of columnar thin films and Bragg multilayers, Opt Commun 231

(2004), 257-261. 153

A10. F. Chiadini and A. Lakhtakia, Extension of Hodgkinson s model for

optical characterization of columnar thin films, Microw Opt Technol

Lett 42 (2004), 72-73. 158

A11. A. Lakhtakia, Microscopic model for elastostatic and elastodynamic

excitation of chiral sculptured thin films, J Compos Mater 36 (2002),

1277-1298. 160

A12. A. Lakhtakia and J.B. Geddes III, Nanotechnology for optics is a phase-

length-time sandwich, Opt Engg 43 (2004), 2410-2417. 182

A13. M.W. Horn, M.D. Pickett, R. Messier, and A. Lakhtakia, Blending

of nanoscale and microscale in uniform large-area sculptured thin-film

architectures, Nanotechnology 15 (2004), 303-310. 190

A14. M.W. Horn, M.D. Pickett, R. Messier, and A. Lakhtakia, Selective

growth of sculptured nanowires on microlithographic substrates,

iii

J Vac Sci Technol B 22 (2004), 3426-3430. 198

A15. S. Pursel, M.W. Horn, M.C. Demirel, and A. Lakhtakia, Growth

of sculptured polymer submicronwire assemblies by vapor deposition,

Polymer 46 (2005), 9544-9548. 203

A16. M.W. McCall and A. Lakhtakia, Development and assessment of coupled

wave theory of axial propagation in thin-film helicoidal bi-anisotropic media.

Part 2: dichroisms, ellipticity transformation and optical rotation,

J Modern Opt 48 (2001), 143-158. 208

A17. A. Lakhtakia and M.W. McCall, Simple expressions for Bragg reflection

from axially excited chiral sculptured thin films,

J Modern Opt 49 (2002), 1525-1535. 224

A18. M.W. McCall and A. Lakhtakia, Explicit expressions for spectral

remittances of axially excited chiral sculptured thin films, J Modern Opt 51

(2004), 111-127. 235

A19. M.W. McCall and A. Lakhtakia, Analysis of plane-wave light normally

incident to an axially excited structurally chiral half-space, J Modern Opt 52

(2005), 541-550. 252

A20. A. Lakhtakia, Pseudo-isotropic and maximum-bandwidth points for

axially excited chiral sculptured thin films, Microw Opt Technol Lett 34

(2002), 367-371. 262

A21. A. Lakhtakia and J.T. Moyer, Post- versus pre-resonance characteristics

of axially excited chiral sculptured thin films, Optik 113 (2002), 97-99. 267

A22. J.A. Polo, Jr. and A. Lakhtakia, Numerical implementation of exact

analytical solution for oblique propagation in a cholesteric liquid crystal,

Microw Opt Technol Lett 35 (2002), 397-400; correction: 44 (2005), 205. 270

iv

A23. J.A. Polo, Jr. and A. Lakhtakia, Comparison of two methods for oblique

propagation in helicoidal bianisotropic mediums, Opt Commun 230 (2004),

369-386. 275

A24. A. Lakhtakia and I.J. Hodgkinson, Resonances in the Bragg regimes

of axially excited, chiral sculptured thin films, Microw Opt Technol Lett 32

(2002), 43-46. 293

A25. A. Lakhtakia, Truncation of angular spread of Bragg zones by total

reflection, and Goos-Hanchen shifts exhibited by chiral sculptured thin films,

AEU Int J Electron Commun 56 (2002), 169-176; corrections: 57 (2003), 79. 297

A26. M.D. Pickett and A. Lakhtakia, On gyrotropic chiral sculptured

thin films for magneto-optics, Optik 113 (2002), 367-371. 306

A27. M.D. Pickett, A. Lakhtakia and J.A. Polo, Jr., Spectral responses

of gyrotropic chiral sculptured thin films to obliquely incident plane waves,

Optik 115 (2004), 393-398. 311

A28. M.W. McCall and A. Lakhtakia, Integrated optical polarization filtration

via chiral sculptured-thin-film technology, J Modern Opt 48 (2001), 2179-2184. 317

A29. A. Lakhtakia and M.W. McCall, Circular polarization filters, Encyclopedia

of optical engineering, Vol. 1 (R. Driggers, ed), Marcel Dekker, New York,

NY, USA, 2003, pp. 230-236. 323

A30. A. Lakhtakia, Axial excitation of tightly interlaced chiral sculptured thin

films: “averaged” circular Bragg phenomenon, Optik 112 (2001), 119-124. 330

A31. A. Lakhtakia, Stepwise chirping of chiral sculptured thin films for Bragg

bandwidth enhancement, Microw Opt Technol Lett 28 (2001), 323-326. 336

A32. F. Chiadini and A. Lakhtakia, Design of wideband circular-polarization

v

filters made of chiral sculptured thin films, Microw Opt Technol Lett 42

(2004), 135-138. 340

A33. A. Lakhtakia, Enhancement of optical activity of chiral sculptured

thin films by suitable infiltration of void regions, Optik 112 (2001),

145-148; correction: 112 (2001), 544. 344

A34. A. Lakhtakia and M.W. Horn, Bragg-regime engineering by columnar

thinning of chiral sculptured thin films, Optik 114 (2003), 556-560. 349

A35. F. Wang, A. Lakhtakia, and R. Messier, Towards piezoelectrically

tunable chiral sculptured thin film lasers, Sens Actuat A: Phys 102

(2002), 31-35. 354

A36. F. Wang, A. Lakhtakia, and R. Messier, On piezoelectric control of the

optical response of sculptured thin films, J Modern Opt 49 (2003), 239-249. 359

A37. M.W. McCall and A. Lakhtakia, Coupling of a surface grating to a

structurally chiral volume grating, Electromagnetics 23 (2003), 1-26. 370

A38. J.P. McIlroy, M.W. McCall, A. Lakhtakia, and I.J. Hodgkinson,

Strong coupling of a surface-relief dielectric grating to a structurally chiral

volume grating, Optik 116 (2005), 311-324. 396

A39. I.J. Hodgkinson, Q.h. Wu, L. De Silva, M. Arnold, M.W. McCall,

and A. Lakhtakia, Supermodes of chiral photonic filters with combined twist

and layer defects, Phys Rev Lett 91 (2003), 223903. 410

A40. I.J. Hodgkinson, Q.h. Wu, M. Arnold, M.W. McCall, and A. Lakhtakia,

Chiral mirror and optical resonator designs for circularly polarized light:

suppression of cross-polarized reflectances and transmittances, Opt Commun 210

(2002), 202-211. 414

vi

A41. F. Wang and A. Lakhtakia, Optical crossover phenomenon due to a central

90◦-twist defect in a chiral sculptured thin film or chiral liquid crystal,

Proc R Soc Lond A 461 (2005), 2985-3004. 425

A42. F. Wang and A. Lakhtakia, Defect modes in multisection helical photonic

crystals, Opt Exp 13 (2005), 7319-7335. 445

A43. F. Wang and A. Lakhtakia, Specular and nonspecular, thickness-dependent,

spectral holes in a slanted chiral sculptured thin film with a central twist

defect, Opt Commun 215 (2003), 79-92. 462

A44. F. Wang and A. Lakhtakia, Third method for generation of spectral holes

in chiral sculptured thin films, Opt Commun 250 (2005), 105-110. 476

A45. A. Lakhtakia, M.W. McCall, J.A. Sherwin, Q.H. Wu, and I.J. Hodgkinson,

Sculptured-thin-film spectral holes for optical sensing of fluids,

Opt Commun 194 (2001), 33-46. 482

A46. A. Lakhtakia, On bioluminescent emission from chiral sculptured thin films,

Opt Commun 188 (2001), 313-320. 496

A47. A. Lakhtakia, Local inclination angle: a key structural factor in emission

from chiral sculptured thin films, Opt Commun 202 (2002),

103-112; correction: 203 (2002), 447. 504

A48. A. Lakhtakia, On radiation from canonical source configurations in

structurally chiral materials, Microw Opt Technol Lett 37 (2003), 37-40. 514

A49. E.E. Steltz and A. Lakhtakia, Theory of second-harmonic-generated

radiation from chiral sculptured thin films for bio-sensing, Opt Commun 216

(2003), 139-150. 518

A50. A. Lakhtakia and J. Xu, An essential difference between dielectric mirrors

vii

and chiral mirrors, Microw Opt Technol Lett 47 (2005), 63-64. 530

A51. E. Ertekin and A. Lakhtakia, Optical interconnects realizable with

thin-film helicoidal bianisotropic mediums, Proc R Soc Lond A 457

(2001), 817-836. 532

A52. I. Hodgkinson, Q.h. Wu, L. De Silva, M. Arnold, A. Lakhtakia,

and M. McCall, Structurally perturbed chiral Bragg reflectors for elliptically

polarized light, Opt Lett 30 (2005), 2629-2631. 552

A53. J.A. Polo, Jr. and A. Lakhtakia, Sculptured nematic thin films with

periodically modulated tilt angle as rugate filters, Opt Commun 251

(2005), 10-22. 555

A54. J.A. Polo, Jr. and A. Lakhtakia, Tilt-modulated chiral sculptured thin

films: an alternative to quarter-wave stacks, Opt Commun 242 (2004), 13-21. 568

A55. F. Wang, A. Lakhtakia and R. Messier, Coupling of Rayleigh-Wood

anomalies and the circular Bragg phenomenon in slanted chiral sculptured

thin films, Eur Phys J Appl Phys 20 (2002), 91-103; corrections: 24 (2003), 91. 577

A56. F. Wang and A. Lakhtakia, Lateral shifts of optical beams on reflection

by slanted chiral sculptured thin films, Opt Commun 235 (2004), 107-132. 592

A57. A. Lakhtakia and M.W. McCall, Response of chiral sculptured thin films

to dipolar sources, AEU Int J Electron Commun 57 (2003), 23-32. 618

A58. F. Wang and A. Lakhtakia, Response of slanted chiral sculptured thin films

to dipolar sources, Opt Commun 235 (2004), 133-151. 628

A59. J.B. Geddes III and A. Lakhtakia, Reflection and transmission of optical

narrow-extent pulses by axially excited chiral sculptured thin films, Eur Phys J

Appl Phys 13 (2001), 3-14; corrections: 16 (2001), 247. 647

viii

A60. J.B. Geddes III and A. Lakhtakia, Time–domain simulation of the

circular Bragg phenomenon exhibited by axially excited chiral sculptured thin

films, Eur Phys J Appl Phys 14 (2001), 97-105; corrections: 16 (2001), 247. 660

A61. J.B. Geddes III and A. Lakhtakia, Pulse-coded information transmission

across an axially excited chiral sculptured thin film in the Bragg regime,

Microw Opt Technol Lett 28 (2001), 59-62. 670

A62. J.B. Geddes III and A. Lakhtakia, Videopulse bleeding in axially

excited chiral sculptured thin films in the Bragg regime, Eur Phys J

Appl Phys 17 (2002), 21-24. 674

A63. J. Wang, A. Lakhtakia, and J.B. Geddes III, Multiple Bragg regimes

exhibited by a chiral sculptured thin film half-space on axial excitation,

Optik 113 (2002), 213-221. 678

A64. J.B. Geddes III and A. Lakhtakia, Effects of carrier phase on reflection

of optical narrow-extent pulses from axially excited chiral sculptured thin

films, Opt Commun 225 (2003), 141-150. 687

A65. J.B. Geddes III and A. Lakhtakia, Numerical investigation of reflection,

refraction, and diffraction of pulsed optical beams by chiral sculptured thin

films, Opt Commun 252 (2005), 307-320. 697

Publications on Homogenization of Composite Materials

B1. B. Michel, A. Lakhtakia, W.S. Weiglhofer, and T.G. Mackay, Incremental

and differential Maxwell Garnett formalisms for bianisotropic composites,

Compos Sci Technol 61 (2001), 13-18. 711

B2. B.M. Ross and A. Lakhtakia, Bruggeman approach for isotropic

chiral mixtures revisited, Microw Opt Technol Lett 44 (2005), 524-527. 717

ix

B3. T.G. Mackay and A. Lakhtakia, A limitation of the Bruggeman formalism

for homogenization, Opt Commun 234 (2004), 35-42. 721

B4. J.A. Sherwin and A. Lakhtakia, Bragg-Pippard formalism for bianisotropic

particulate composites, Microw Opt Technol Lett 33 (2002), 40-44. 729

B5. A. Lakhtakia and T.G. Mackay, Size-dependent Bruggeman approach for

dielectric-magnetic composite materials, AEU Int J Electron Commun 59

(2005), 348-351. 734

B6. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Ellipsoidal topology,

orientation diversity and correlation length in bianisotropic composite

mediums, AEU Int J Electron Commun 55 (2001), 243-251. 738

B7. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Homogenisation of

similarly oriented, metallic, ellipsoidal inclusions using the bilocally

approximated strong-property-fluctuation theory, Opt Commun 197 (2001),

89-95. 747

B8. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Third-order

implementation and convergence of the strong-property-fluctuation theory in

electromagnetic homogenization, Phys Rev E 64 (2001), 066616. 754

B9. T.G. Mackay and A. Lakhtakia, Enhanced group velocity in metamaterials,

J Phys A: Math Gen 37 (2004), L19-L24. 763

B10. T.G. Mackay and A. Lakhtakia, Anisotropic enhancement of group

velocity in a homogenized dielectric composite medium, J Opt A: Pure Appl Opt 7

(2005), 669-674. 769

B11. T.G. Mackay and A. Lakhtakia, Voigt wave propagation in biaxial

composite materials, J Opt A: Pure Appl Phys 5 (2003), 91-95. 775

x

B12. T.G. Mackay and A. Lakhtakia, Correlation length facilitates Voigt wave

propagation, Waves Random Media 14 (2004), L1-L11. 780

B13. T.G. Mackay and A. Lakhtakia, Negative phase velocity in isotropic

dielectric-magnetic media via homogenization, Microw Opt Technol Lett 47

(2005), 313-315. 791

B14. M.N. Lakhtakia and A. Lakhtakia, Anisotropic composite materials

with intensity-dependent permittivity tensor: The Bruggeman approach,

Electromagnetics 21 (2001), 129-137. 794

B15. A. Lakhtakia, Application of strong permittivity fluctuation theory

for isotropic, cubically nonlinear, composite mediums, Opt Commun 192

(2001), 145-151. 803

B16. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Homogenisation of

isotropic, cubically nonlinear, composite mediums by the strong-property-

fluctuation theory: Third-order considerations, Opt Commun 204

(2002), 219-228. 810

B17. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, The strong-property-

fluctuation theory for cubically nonlinear, isotropic chiral composite mediums,

Electromagnetics 23 (2003), 455-479. 820

Publications on Negative-Phase-Velocity Propagation

C1. A. Lakhtakia, M.W. McCall, and W.S. Weiglhofer, Brief overview of recent

developments on negative phase-velocity mediums (alias left-handed materials),

AEU Int J Electron Commun 56 (2002), 407-410. 845

C2. A. Lakhtakia, M.W. McCall, and W.S. Weiglhofer, Negative phase-velocity

mediums, Introduction to complex mediums for optics and electromagnetics

(W.S. Weiglhofer and A. Lakhtakia, eds), SPIE, Bellingham, WA, USA, 2003,

xi

pp. 347-363. 849

C3. M.W. McCall, A. Lakhtakia, and W.S. Weiglhofer, The negative index of

refraction demystified, Eur J Phys 23 (2002), 353-359. 853

C4. A. Lakhtakia, An electromagnetic trinity from “negative permittivity”

and “negative permeability”, Int J Infrared Millim Waves 22 (2001), 1731- 1734;

correctly reprinted: 23 (2002), 813-818. 860

C5. A. Lakhtakia, On perfect lenses and nihility, Int J Infrared Millim

Waves 23 (2002), 339-343. 866

C6. A. Lakhtakia and J.A. Sherwin, Orthorhombic materials and perfect lenses,

Int J Infrared Millim Waves 24 (2003), 19-23. 871

C7. J. Wang and A. Lakhtakia, On reflection from a half-space with negative real

permittivity and permeability, Microw Opt Technol Lett 33 (2002), 465-467. 876

C8. R.A. Depine and A. Lakhtakia, A new condition to identify isotropic

dielectric- magnetic materials displaying negative phase velocity, Microw Opt

Technol Lett 41 (2004), 315-316. 879

C9. A. Lakhtakia and T.G. Mackay, Infinite phase velocity as the boundary

between negative and positive phase velocities, Microw Opt Technol

Lett 41 (2004), 165-166. 881

C10. J. Gerardin and A. Lakhtakia, Negative index of refraction and distributed

Bragg reflectors, Microw Opt Technol Lett 34 (2002), 409-411. 883

C11. J. Gerardin and A. Lakhtakia, Spectral response of Cantor multilayers

made of materials with negative refractive index, Phys Lett A 301

(2002), 377-381. 886

C12. A. Lakhtakia and C.M. Krowne, Restricted equivalence of paired

xii

epsilon-negative and mu-negative layers to a negative phase-velocity material

(alias left-handed material), Optik 114 (2003), 305-307. 891

C13. A. Lakhtakia, On planewave remittances and Goos-Hanchen shifts of

planar slabs with negative real permittivity and permeability, Electromagnetics 23

(2003), 71-75. 894

C14. A. Lakhtakia, Positive and negative Goos-Hanchen shifts and negative

phase-velocity mediums (alias left-handed materials), AEU Int J Electron

Commun 58 (2004), 229-231. 899

C15. T.G. Mackay and A. Lakhtakia, Plane waves with negative phase velocity

in Faraday chiral mediums, Phys Rev E 69 (2004), 026602. 902

C16. T.G. Mackay and A. Lakhtakia, Negative phase velocity in a material

with simultaneous mirror-conjugated and racemic chirality characteristics,

New J Phys 7 (2005), 165. 911

C17. A. Lakhtakia, Reversed circular dichroism of isotropic chiral mediums

with negative real permeability and permittivity, Microw Opt Technol Lett 33

(2002), 96-97. 927

C18. A. Lakhtakia, Reversal of circular Bragg phenomenon in ferrocholesteric

materials with negative real permittivities and permeabilities, Adv Mater 14

(2002), 447-449. 929

C19. A. Lakhtakia, Handedness reversal of circular Bragg phenomenon due to

negative real permittivity and permeability, Opt Exp 11 (2003), 716-722. 932

C20. A. Lakhtakia and M.W. McCall, Counterposed phase velocity and energy-

transport velocity vectors in a dielectric-magnetic uniaxial medium, Optik 115

(2004), 28-30. 939

xiii

C21. R.A. Depine and A. Lakhtakia, Diffraction gratings of isotropic

negative-phase velocity materials, Optik 116 (2005), 31-43. 942

C22. R.A. Depine and A. Lakhtakia, Perturbative approach for diffraction due

to a periodically corrugated boundary between vacuum and a negative phase-

velocity material, Opt Commun 233 (2004), 277-282. 955

C23. R.A. Depine and A. Lakhtakia, Plane-wave diffraction at the periodically

corrugated boundary of vacuum and a negative-phase-velocity material,

Phys Rev E 69 (2004), 057602. 961

C24. R.A. Depine, A. Lakhtakia, and D. R. Smith, Enhanced diffraction by a

rectangular grating made of a negative phase-velocity (or negative index)

material, Phys Lett A 337 (2005), 155-160. 965

C25. R.A. Depine and A. Lakhtakia, Diffraction by a grating made of a uniaxial

dielectric-magnetic medium exhibiting negative refraction, New J Phys 7

(2005), 158. 971

C26. T.G. Mackay and A. Lakhtakia, Negative phase velocity in a uniformly

moving, homogeneous, isotropic, dielectric-magnetic medium, J Phys A:

Math Gen 37 (2004), 5697-5711. 994

C27. A. Lakhtakia and T.G. Mackay, Towards gravitationally assisted negative

refraction by vacuum, J Phys A: Math Gen 37 (2004), L505-L510; correction: 37

(2004), 12093; comment: 38 (2005), 2543-2544; reply: 38 (2005), 2545-2546. 1009

C28. A. Lakhtakia, T.G. Mackay, and S. Setiawan, Global and local

perspectives of gravitationally assisted negative-phase-velocity propagation of

electromagnetic waves in vacuum, Phys Lett A 336 (2005), 89-96. 1020

C29. T.G. Mackay, A. Lakhtakia, and S. Setiawan, Gravitation and

electromagnetic wave propagation with negative phase velocity, New J Phys 7

xiv

(2005), 75. 1028

C30. T.G. Mackay, S. Setiawan, and A. Lakhtakia, Negative phase velocity of

electromagnetic waves and the cosmological constant, Eur Phys J C Direct (2005),

doi:10.1140/epjcd/s2005-01-001-9. 1042

C31. T.G. Mackay, A. Lakhtakia, and Sandi Setiawan, Electromagnetic waves

with negative phase velocity in Schwarzschild-de Sitter spacetime, Europhys

Lett 71 (2005), 925-931. 1046

C32. T.G. Mackay, A. Lakhtakia and Sandi Setiawan, Electromagnetic

negative-phase-velocity propagation in the ergosphere of a rotating black

hole, New J Phys 7 (2005), 171. 1053

C33. S. Setiawan, T.G. Mackay, and A. Lakhtakia, A comparison of

superradiance and negative phase velocity phenomenons in the ergosphere of a

rotating black hole, Phys Lett A 341 (2005), 15-21. 1068

Publications on Related Topics in Nanotechnology

D1. G.Ya. Slepyan, N.A. Krapivin, S.A. Maksimenko, A. Lakhtakia

and O.M. Yevtushenko, Scattering of electromagnetic waves by a semi-infinite

carbon nanotube, AEU Int J Electron Commun 55 (2001), 273-280. 1074

D2. G.Ya. Slepyan, S.A. Maksimenko, A. Lakhtakia, and O.M. Yevtushenko,

Electromagnetic response of carbon nanotubes and nanotube ropes,

Syn Metals 124 (2001), 121-123. 1082

D3. F. Wang, M.W. Horn, and A. Lakhtakia, Rigorous electromagnetic

modeling of near-field phase-shifting contact lithography, Microelectron

Engg 71 (2004), 34-53. 1085

D4. F. Wang, K.E. Weaver, A. Lakhtakia, and M.W. Horn, On contact

xv

lithography of high-aspect-ratio features with incoherent broadband ultraviolet

illumination, Microelectron Engg 77 (2005), 55-57. 1105

D5. F. Wang, K.E. Weaver, A. Lakhtakia, and M.W. Horn, Electromagnetic

modeling of near-field phase-shifting contact lithography with broadband

ultraviolet illumination, Optik 116 (2005), 1-9. 1108

D6. A. Gomez, A. Lakhtakia, M.A. Solano, and A. Vegas, Parallel-plate waveguides

with Kronig-Penney morphology as photonic band-gap filters, Microw Opt

Technol Lett 36 (2003), 4-8; correctly reprinted: 38 (2003), 511-514. 1117

D7. A. Gomez, M.A. Solano, A. Lakhtakia, and A. Vegas, Circular waveguides

with Kronig-Penney morphology as electromagnetic band-gap filters,

Microw Opt Technol Lett 37 (2003), 316-321. 1121

D8. M.A. Solano, A. Gomez, A. Lakhtakia, and A. Vegas, Rigorous analysis

of guided wave propagation of dielectric electromagnetic band-gaps in a

rectangular waveguide, Int J Electron 92 (2005), 117-130. 1127

D9. A. Gomez, A. Vegas, M.A. Solano, and A. Lakhtakia, On one- and two-

dimensional electromagnetic band gap structures in rectangular waveguides

at microwave frequencies, Electromagnetics 25 (2005), 437-460. 1141

D10. I.L. Lyubchanskii, N.N. Dadoenkova, M.I. Lyubchankskii, E.A. Shapovalov,

A. Lakhtakia, and Th. Rasing, Spectra of bigyrotropic magnetic photonic

crystals, Phys Stat Sol (a) 201 (2004), 3338-3344. 1165

D11. I.L. Lyubchanskii, N.N. Dadoenkova, M.I. Lyubchankskii, E.A. Shapovalov,

A. Lakhtakia, and Th. Rasing, One-dimensional bigyrotropic magnetic

photonic crystals, Appl Phys Lett 85 (2004), 5932-5934. 1172

Publications on Fundamental Issues in Complex-Mediums Electromagnetics

xvi

E1. A. Lakhtakia and R.A. Depine, On Onsager relations and linear

electromagnetic materials, AEU Int J Electron Commun 59 (2005), 101-104. 1175

E2. A. Lakhtakia, On the genesis of Post constraint in modern electromagnetism,

Optik 115 (2004), 151-158. 1179

E3. A. Lakhtakia, Conjugation symmetry in linear electromagnetism in

extension of materials with negative real permittivity and permeability scalars,

Microw Opt Technol Lett 40 (2004), 160-161. 1187

E4. A. Lakhtakia, Beltrami field phasors are eigenvectors of 6×6 linear

constitutive dyadics, Microw Opt Technol Lett 30 (2001), 127-128. 1189

E5. A. Lakhtakia, Conditions for circularly polarized plane wave propagation

in a linear bianisotropic medium, Electromagnetics 22 (2002), 123-127. 1191

E6. A. Lakhtakia, A representation theorem involving fractional derivatives

for linear homogeneous chiral mediums, Microw Opt Technol Lett 28

(2001), 385-386. 1196

E7. J. Gerardin and A. Lakhtakia, Conditions for Voigt wave propagation

in linear, homogeneous, dielectric mediums, Optik 112 (2001), 493-495. 1198

Personal Profile 1201

xvii

ACKNOWLEDGMENTS

I thank Prof. Pradip Kumar Jain for his invaluable advice and support in negotiating

the enrollment process as well as for actual assistance in the submission of this thesis. He

is a true friend and colleague, on whose steadfastness I can always count on.

Without the patient efforts of Prof. S. K. Balasubramaniam for many years, my

dream of obtaining a terminal degree from the same institution that gave me my first

degree would not have come true. Thank you, Sir.

Throughout my research career, I have had the good fortune of working with dedicated

students and highly motivated colleagues. I take this opportunity to tender my warmest

thanks and applaud them for putting up with my difficult working habits and finicky

character.

Finally, I thank my wife, Mercedes, who is not only the spice of my life but also the

rock to which my personal and professional lives are firmly tethered.

xix

EXTENDED ABSTRACT

1 Introduction

The essence of electromagnetism comprises four partial differential equations called the

Maxwell equations. At microscopic length scales, these equations involve two vector

fields along with two source densities, of which one is a scalar and the other is a vector.

As these equations were born of experience with electromagnetic phenomenons [1], they

are more appropriately named as the Maxwell postulates . The two vector fields are the

primitive fields of electromagnetism. At macroscopic length scales, spatial averaging of

the Maxwell postulates leads to the macroscopic Maxwell postulates. The four equations

remain almost intact in form, except that averaged source densities are decomposed into

two parts. Whereas one of the two parts can be externally applied, the other indicates the

existence of matter. The matter-indicating part is combined with the averaged primitive

fields to create two induction fields in two of the four Maxwell postulates. The familiar

form of the macroscopic Maxwell postulates thus involves two primitive fields and two

induction fields, in addition to two source densities.

A set of equations is necessary to relate the macroscopic induction fields to the macro-

scopic primitive fields. These are called the constitutive relations, whose delineation has

occupied much of the last 150 years [2, 3], but continues to remain a topic of great interest

to engineers, scientists, and mathematicians [4, 5]. These relations are conjured from elec-

tromagnetic as well as nonelectromagnetic considerations, but must be consistent with

the structure of the Maxwell postulates [6].

Most of my research over the past two decades has been on electromagnetic field in

materials described with complex constitutive relations. In this Extended Abstract of

a selection of my publications spanning the years 2001 to 2005, I begin by sketching a

1

journey from the (microscopic) Maxwell postulates to the macroscopic Maxwell postu-

lates, then go on to describe the concept and variety of constitutive relations, describe the

emergence and the characteristics of complex-mediums electromagnetics (CME) during

the late 1980s and the early 1990s, and finally present my CME research published in the

2001-2005 period.

2 Macroscopic Maxwell postulates

Electromagnetism is a microscopic science, even though it is mostly used in its macro-

scopic form. It was certainly a macroscopic science when Maxwell unified the equations of

Coulomb, Gauss, Faraday, and Ampere, added a displacement current to Ampere’s equa-

tion, and produced the four equations to which his name is attached. These equations

were remarkable in that they unified optics with electromagnetism, and were brilliantly

vindicated by Hertz’s discovery of electromagnetic wave propagation in air [7].

Although Maxwell had abandoned a mechanical basis for electromagnetism during the

early 1860s, and even used terms like molecular vortices, his conception of electromag-

netism was macroscopic [8]. By the end of the 19th century, that conception had been

drastically altered [2]. Hall’s successful explanation of the eponymous effect, the postu-

lation of the electron by Stoney and its subsequent discovery by Thomson, and Larmor’s

theory of the electron—all three developments precipitated that alteration. It was soon

codified by Lorentz and Heaviside, so that the 20th century dawned with the acquisition

of a microphysical basis by electromagnetism. Maxwell’s equations remained unaltered

in form at macroscopic length scales, but their genesis now lay in the fields engendered by

microscopic charge quantums. The subsequent emergence of quantum mechanics around

1930 did not change the form of the macroscopic equations either, although the notion of a

field lost its determinism and an inherent uncertainty was recognized in the measurements

of key variables.

2

The microscopic fields are just two: the electric field e (r, t) and the magnetic field

b (r, t).1 These fields vary extremely rapidly as functions of position r and time t. Their

sources are the microscopic charge density c (r, t) and the microscopic current density

j (r, t), where

c (r, t) =∑

ℓ

qℓ δ [r − rℓ(t)] , (1)

j (r, t) =∑

ℓ

qℓvℓ δ [r − rℓ(t)] ; (2)

δ(·) is the Dirac delta function, while rℓ(t) and vℓ(t) are the position and the velocity

of the point charge qℓ. All of the foregoing fields and sources appear in the Maxwell

postulates

∇ • e (r, t) = ǫ−10

c (r, t) , (3)

∇× b (r, t) − ǫ0µ0

∂

∂te (r, t) = µ0 j (r, t) , (4)

∇ • b (r, t) = 0 , (5)

∇× e (r, t) +∂

∂tb (r, t) = 0 , (6)

which are microscopic. Here and hereafter, ǫ0 = 8.854 × 10−12 F m−1 and µ0 = 4π ×

10−7 H m−1 are the permittivity and the permeability of free space (i.e., classical vacuum

in the absence of a gravitational field), respectively. The first two postulates are inhomo-

geneous differential equations as they contain source terms on their right sides, while the

last two are homogeneous differential equations.

Macroscopic measurement devices average over (relatively) large spatial and temporal

intervals. Therefore, spatiotemporal averaging of the microscopic quantities appears nec-

essary in order to deduce the macroscopic Maxwell postulates from Eqs. (3)–(6). Actually,

only spatial averaging is necessary [9, Sec. 6.6], because it implies temporal averaging

due to the finite magnitude of the universal maximum speed (ǫ0µ0)−1/2. Denoting the

1The lower-case roman letter signifies that the quantity is microscopic, while the tilde ˜ indicates

dependence on time.

3

macroscopic charge and current densities, respectively, by ρ (r, t) and J (r, t), we obtain

the macroscopic Maxwell postulates:

∇ • E (r, t) = ǫ−10

ρ (r, t) , (7)

∇× B (r, t) − ǫ0µ0

∂

∂tE (r, t) = µ0 J (r, t) , (8)

∇ • B (r, t) = 0 , (9)

∇× E (r, t) +∂

∂tB (r, t) = 0 . (10)

These equations involve the macroscopic primitive fields E (r, t) and B (r, t) as the spa-

tial averages of e (r, t) and b (r, t), respectively. From Eqs. (7) and (8), a macroscopic

continuity equation for the source densities can be derived as

∇ • J (r, t) +∂

∂tρ (r, t) = 0 . (11)

Equations (7)–(10) are not the familiar form of the macroscopic Maxwell postulates,

even though they hold in free space as well as in matter. The familiar form emerges after

the recognition that matter contains, in general, both free charges and bound charges.

Free and bound source densities can be separated as

ρ (r, t) = ρso (r, t) −∇ • P (r, t) , (12)

J (r, t) = Jso (r, t) +∂

∂tP (r, t) + ∇× M (r, t) . (13)

This decomposition is consistent with Eq. (11), provided the free source densities obey

the reduced continuity equation

∇ • Jso (r, t) +∂

∂tρso (r, t) = 0 . (14)

The free source densities represent “true” sources, which can be externally impressed.

Whereas Jso (r, t) is the source current density, ρso (r, t) is the source charge density.

Bound source densities represent matter in its macroscopic form and are, in turn,

quantified by the polarization P (r, t) and the magnetization M (r, t). Both P (r, t) and

4

M (r, t) are nonunique to the following extent: Suppose A (r, t) is some arbitrary vector

function. Then P (r, t) and M (r, t) can be replaced by P (r, t)−∇×A (r, t) and M (r, t)+

(∂/∂t) A (r, t), respectively, in Eqs. (12) and (13) without affecting the left sides of either

equation.

Polarization and magnetization are subsumed in the definitions of the electric induc-

tion D (r, t) and the magnetic induction H (r, t) as follows:

D (r, t) = ǫ0 E (r, t) + P (r, t) , (15)

H (r, t) = µ−10

B (r, t) − M (r, t) . (16)

Then, Eqs. (7)–(10) metamorphose into the following familiar form of the macroscopic

Maxwell postulates:

∇ • D (r, t) = ρso (r, t) , (17)

∇× H (r, t) −∂

∂tD (r, t) = Jso (r, t) , (18)

∇ • B (r, t) = 0 , (19)

∇× E (r, t) +∂

∂tB (r, t) = 0 . (20)

3 Time-harmonic Maxwell postulates

All fields and sources (or source densities)—whether microscopic or macroscopic—are

real-valued . But most electromagnetics research is carried out with time-harmonic fields.

In the standard procedure, the temporal Fourier transform defined as

Z (r, t) =1

2π

∫ ∞

−∞

Z (r, ω) e−iωt dω (21)

5

permits the mutation of Eqs. (17)–(20) into

∇ • D (r, ω) = ρso (r, ω) , (22)

∇× H (r, ω) + iωD (r, ω) = Jso (r, ω) , (23)

∇ • B (r, ω) = 0 , (24)

∇× E (r, ω) − iωB (r, ω) = 0 , (25)

which are the time-harmonic macroscopic Maxwell postulates. The quantities E (r, ω),

etc., are complex-valued functions of the angular frequency ω, and are called phasors in

the electrical engineering literature.

4 Constitutive relations

Equations (22)–(25) require more information in order to be solvable. This additional

information comes in the form of constitutive relations which, being medium-specific,

describe the electromagnetic response properties of a medium.

The simplest medium for electromagnetic fields to exist in is free space. In this

medium, the electric and magnetic field phasors are related very simply thus:

D (r, ω) = ǫ0 E (r, ω) , (26)

B (r, ω) = µ0 H (r, ω) . (27)

This medium is linear, isotropic, and homogeneous. It is also the medium in which

the constitutive properties—represented by ǫ0 and µ0—are not functions of the angular

frequency ω; hence, the medium is nondispersive. Finally, both ǫ0 and µ0 are real-valued

scalars, so that free space is nondissipative.

6

4.1 Linear dielectric materials

Every other medium must be of the material kind. The simple isotropic dielectric

medium—the staple of undergraduate textbooks on electromagnetism—is linear, homo-

geneous, and isotropic; its constitutive relations are as follows:

D (r, ω) = ǫ0 ǫr(ω)E (r, ω) , (28)

B (r, ω) = µ0 H (r, ω) . (29)

The scalar ǫr is called the relative permittivity, and its dependence on ω denotes dispersion

with respect to frequency. In general, ǫr is complex-valued due to dissipation. Both

dissipation and dispersion come hand-in-hand due to causality, i.e.,

ǫr(t) − δ(t) = 0 , t ≤ 0 , (30)

where ǫr(t) and ǫr(ω) are connected by Eq. (21) defining the Fourier transform. Causality

for time-harmonic fields is captured by the Kramers-Kronig relations [9, Sec. 7.10]

Re [ǫr(ω)] − 1 =1

πP

∫ ∞

−∞

Im [ǫr(ω′)]

ω′ − ωdω′ , (31)

Im [ǫr(ω)] = −1

πP

∫ ∞

−∞

Re [ǫr(ω′)] − 1

ω′ − ωdω′ , (32)

where Re (·) and Im (·) are the real and imaginary parts of a complex-valued quantity,

and P indicates a principal value operation. Let us note that Re [ǫr(ω)] is even in ω, but

Im [ǫr(ω)] is odd. The square root of ǫr is called the complex refractive index in optics

literature. Nonhomogeneity can be incorporated by using ǫr (r, ω) on the right side of

Eq. (28).

Crystals such as calcite are modeled in optics as linear and homogeneous dielectric

materials, but they are anisotropic. Their constitutive relations are written as follows:

D (r, ω) = ǫ0 ǫr(ω) • E (r, ω) , (33)

B (r, ω) = µ0 H (r, ω) . (34)

7

The quantity ǫr

is called the relative permittivity matrix. Therefore, Eq. (33) may be

written as

Dx (r, ω)

Dy (r, ω)

Dz (r, ω)

= ǫ0

ǫ(xx)r (ω) ǫ

(xy)r (ω) ǫ

(xz)r (ω)

ǫ(yx)r (ω) ǫ

(yy)r (ω) ǫ

(yz)r (ω)

ǫ(zx)r (ω) ǫ

(zy)r (ω) ǫ

(zz)r (ω)

Ex (r, ω)

Ey (r, ω)

Ez (r, ω)

(35)

in matrix notation. The nine components of ǫr

are complex-valued scalars, in general.

Crystallographic structure leads to many symmetries for ǫr, detailed expositions of which

are available elsewhere [10]. Gyrotropy is indicated by the antisymmetric parts of ǫr

[6].

All components of ǫr−I (with I as the identity matrix) must satisfy the Kramers-Kronig

relations (31) and (32), because

ǫr(t) − δ(t) I = 0 , t ≤ 0 . (36)

Nonhomogeneity can be incorporated by replacing ǫr(ω) by ǫ

r(r, ω).

4.2 Linear bianisotropic materials

The constitutive relations of linear dielectric-magnetic materials are only slightly different

from those of their nonmagnetic counterparts. Thus,

D (r, ω) = ǫ0 ǫr(r, ω) • E (r, ω) , (37)

B (r, ω) = µ0 µr(r, ω) • H (r, ω) , (38)

where µr(r, ω) is the relative permeability matrix. Its properties are similar to those of

ǫr(r, ω) in Sec. 4.1; but the physical origin is very different, of course [11].

Even more general linear constitutive properties are possible, and are indeed sanc-

tioned by the Lorentz invariance of the Maxwell postulates. Thus, the constitutive rela-

tions of a general linear medium may be stated as follows [3, 12]:

D (r, ω) = ǫ0

[

ǫr(r, ω) • E (r, ω) + α

r(r, ω) • H (r, ω)

]

, (39)

B (r, ω) = µ0

[

βr(r, ω) • E (r, ω) + µ

r(r, ω) • H (r, ω)

]

. (40)

8

Accordingly, two more constitutive matrixes are possible: the magnetoelectric matrixes

αr(r, ω) and β

r(r, ω). Anisotropic magnetoelectric properties are generally found in

a host of materials at very low frequencies and very low temperatures [13]. Isotropic

magnetoelectric properties are displayed, also by a host of materials, but in the near-

infrared, visible, and ultraviolet regimes [14].

Equations (39) and (40) contain four constitutive 3×3 matrixes. Thus, linear bian-

isotropic constitutive relations contain 36 complex-valued scalars to describe a material—

but not quite. Equation (18) has a redundancy in relation to (20) because B (r, t) is the

actual magnetic field, not H (r, t). The redundancy is eliminated by the Post constraint

Trace{

µr(r, ω) •

[

ǫ0 αr(r, ω) + µ0 β

r(r, ω)

]}

= 0 , (41)

which comes into play whenever magnetoelectric properties are considered [3, 15]. Thus,

there are only 35 independent complex-valued scalars in Eqs. (39) and (40).

Other symmetries can enter, depending on the material in consideration. For instance,

many materials display a property called reciprocity [16] entailing the conditions

ǫr(r, ω) = ǫT

r(r, ω)

µr(r, ω) = µT

r(r, ω)

ǫ0 αr(r, ω) = −µ0 βT

r(r, ω)

, (42)

where the superscript T stands for the transpose. Hence, a reciprocal linear material

cannot be characterized by more than 21 complex-valued scalars.

It may be reasonable to ignore dissipation in a certain frequency range. Then, the

conditions of nondissipation [17]

ǫr(r, ω) = ǫ†

r(r, ω)

µr(r, ω) = µ†

r(r, ω)

ǫ0 αr(r, ω) = µ0 β†

r(r, ω)

(43)

9

may be presumed, the superscript † indicating transposition as well as complex conjuga-

tion.

Other symmetries may enter because of textured morphology, e.g., crystallinity [10,

20]. Let σr

represent any one of the four constitutive matrixes in Eqs. (39) and (40).

With u and v denoting two unit vectors, the following simplifications are then possible:

σr

=

σr I , isotropy

σ⊥ (I − uu) + σ‖ uu , uniaxiality

σ⊥ (I − uu) + σ‖ uu + iσg u× I , gyrotropy

σa I + σb

2(uv + vu) , biaxiality

. (44)

Complete isotropy demands no more than three complex-valued constitutive scalars in

Eqs. (39) and (40) [15].

In more compact notation, time-harmonic electromagnetic fields in a linear bian-

siotropic medium obey the differential equation

[

L(∇) + iωK(r, ω)]

• F(r, ω) = 0 . (45)

The linear differential operator L(∇) and the constitutive 6×6 matrix K(r, ω) have the

representations

L(∇) =

0 ∇× I

−∇× I 0

(46)

and

K(r, ω) =

ǫ(r, ω) ξ(r, ω)

ζ(r, ω) µ(r, ω)

, (47)

whereas the electromagnetic field (phasor)

F(r, ω) =

E(r, ω)

H(r, ω)

(48)

is a 6–vector.

10

4.3 Nonlinear bianisotropic materials

A general description of bianisotropic nonlinearity (and, therefore, also anisotropic non-

linearity) proceeds as follows: The nonlinear constitutive relations are expressed in matrix

notation as [19]

C(r, ω) = K0

• F(r, ω) + Q(r, ω) , (49)

where

K0

=

ǫ0 I 0

0 µ0 I

(50)

is the constitutive 6×6 matrix of free space, and the 6–vector

C(r, ω) =

D(r, ω)

B(r, ω)

. (51)

The 6–vector Q(r, ω) is the sum of linear and nonlinear parts, i.e.,

Q(r, ω) = Qℓin(r, ω) + Qnℓ(r, ω) . (52)

The linear part

Qℓin(r, ω) =[

Kℓin(r, ω) −K0

]

• F(r, ω), (53)

involves Kℓin(r, ω) as the constitutive 6×6 matrix to characterize the linear response of

the nonlinear medium, as delineated by Eq. (47). The exclusively nonlinear response of

the medium, under the simultaneous stimulation by an ensemble of M > 1 fields F(r, ωm),

(m = 1, 2, . . . , M), is characterized by the 6–vector Qnℓ(r, ω). At the frequency ω = ωnℓ,

the jth element of Qnℓ(r, ωNL) is given by

Qnℓj (r, ωnℓ) =

6∑

j1=1

6∑

j2=1

· · ·

6∑

jm=1

· · ·

6∑

jM=1

{

χnℓjj1j2···jm···jM

(ωnℓ;W)

M∏

n=1

[ Fjn(r, ωn) ]

}

, (54)

for j ∈ [1, 6], where W = {ω1, ω2, . . . , ωM } and not all members of W have to be distinct.

The angular frequency ωnℓ is the sum

ωnℓ =M

∑

m=1

amωm , am = ±1 ; (55)

11

if an = −1 then Fjn(r, ω) in (54) should be replaced by its complex conjugate. The

nonlinear susceptibility tensor

χnℓjj1j2···jm···jM

(ωnℓ;W) (56)

delineates the nonlinear constitutive properties. A vast range of nonlinear electromagnetic

phenomenons may be described in terms of (54) [20, 21].

5 Complex-mediums electromagnetics

With this introduction to constitutive relations, let me go on to the question: “What is

a complex medium?”

I would not have been able to give a coherent answer to this question in 1990. A

decade later, the subdiscipline of complex-mediums electromagnetics (CME) had taken

shape. At least two series of conferences on CME are held regularly, and many scientific

and technical meetings have special sessions devoted to CME. Among other complex

mediums, carbon nanotubes, metamaterials, materials in which light bends “differently”,

and materials in which light “rotates” are commonly written about in science magazines

as well as in monthly organs of learned societies.

Today, a short answer to the question is that a positive definition of complex mediums

still remains elusive. The consensus among CME researchers is that a complex medium

is not a simple medium; and that the response properties of any complex medium must

be different from linear, isotropic dielectric. A longer answer proceeds as follows:

Giant strides were made during much of the 20th century in understanding and

commercially exploiting the electromagnetic properties of our atmosphere and virtually

matter-free space. Yet materials research for the most part remained confined to sim-

ple (preferably, isotropic dielectric) response properties. The situation began to change

during the 1980s. Scientific and technological progress came to be dominated by the

12

conceptualization, characterization, fabrication, and application of many different classes

of materials, described by complex constitutive relations. Although some of these mate-

rials are found in nature, laboratory processing is often needed for efficient use. Others

are entirely synthetic, created by chemical and physical processes. Certain materials are

multiphase composites designed for certain desirable response properties otherwise un-

available. Multifunctional materials as well as functional gradient materials are needed

for special purposes. Nanoengineering is often used to make material samples with the

same chemical composition but different response characteristics. Thus, novel fabrication

techniques and a multifarious understanding of the relationship between the macroscopic

properties and the microstructural morphology of materials led to rapid progress in re-

search on the interaction of the electromagnetic field and matter.

A simple medium—most easily exemplified by a linear, homogeneous, isotropic dielec-

tric material—affects the progress of electromagnetic signals in two ways:

(i) a delay is created with respect to propagation in vacuum, and

(ii) absorption of electromagnetic energy takes place.

Both effects evince dependencies on frequency, but not on spatial direction. Calculations

can be made and measurements can be interpreted on the per unit amplitude/intensity

basis. An isotropic dielectric medium is thus equivalent to an isotropic contraction of

space with absorption overlaid.

In complex mediums, the progress of electromagnetic signals is additionally affected

in one or more of several ways:

(i) anisotropy: the direction-dependent contraction of space and absorption;

(ii) chirality: the twisting of space;

13

(iii) nonhomogeneity: the dispersal of energy into different directions by either interfaces

between uniform mediums or continuous gradients in material dispersal; and

(iv) nonlinearity: the emission of absorbed energy at (generally) some other frequency.

All of these effects can be described with the help of complex constitutive relations, such

as the ones discussed in Sections 4.2 and 4.3. But the variety of complexity of materials

is such that CME research has several characteristics different from research on simple

mediums.

First, CME formulations are best couched in terms of the fundamental entity in

modern electromagnetics: the electromagnetic field. It happens to have two parts, named

the macroscopic electric field E and the macroscopic magnetic field B, and identified

separately for historical reasons as well as convenience. The two parts cannot be separated

from the other, except after making some approximation or the other. A Lorentz-covariant

description is therefore the only proper description of electromagnetic response properties

to begin analysis with.

Second, causality must be incorporated in CME research. Every material responds

after a delay. The instantaneous part of its response properties cannot be different from

that of free space; otherwise, the material would possess foreknowledge, a prospect best

left for science-fiction authors to exploit. The development of femtosecond-pulse optics

and the generation of attosecond pulses suggest that it is better not to cast time aside by

the artifice of the Fourier transform. Even for time-harmonic fields, causality takes the

form of dissipation and dispersion, which are the two sides of the same coin.

Third, although matter is nonhomogeneous at microscopic length scales, piecewise

homogeneity is commonplace at macroscopic length scales. Statistical techniques provide

a bridge between the two length scales. Complicated macroscopic response properties

should not be assumed casually. For instance, if a homogeneous piece of a medium

with a certain set of response properties cannot be found, the existence of continuously

14

nonhomogeneous analogs of that set at macroscopic length scales is a dubious proposition.

The development of homogenization techniques for complex mediums is a major challenge

today.

Fourth, nonlinearity is an essential attribute of wave-material interaction. Nonlinear-

ity introduces dependency on amplitude, and is responsible for the occurrence of mul-

tiwavelength processes. It also accounts for the electromagnetic exposure histories of

materials—we all know from experience that not only does matter modify electromag-

netic waves, but waves also modify matter.

The complexity of actual materials cannot yet be handled in its entirety. Complexity

is like Gulliver, while CME researchers are like the Lilliputians. Although an individual

CME researcher takes only one or two meaningful steps towards the taming of complexity,

different steps are taken by different CME researchers. CME commands the attentions of

scientists from a wide spectrum of disciplines: from physics and optics to electrical and

electronic engineering, from chemistry to materials science, from applied mathematics

to biophysics. Thus, CME is presently a multidisciplinary research area spanning basic

theoretical and experimental research at universities to the industrial production of a

diverse array of electrical, microwave, infrared and optical materials and devices. A recent

impetus for multidisciplinarity is the unrelenting progress of nanotechnology, which is now

beginning to engender mesoscopic approaches in CME.

6 Scope of my research from 2001 to 2005

In 1984, I began working on electromagnetic fields in isotropic chiral materials [22], and

quickly realized the paucity of my basic knowledge on electromagnetic fields in complex

mediums. Several strands of CME research developed over the next two decades. The

five relevant CME strands included in this thesis are as follows:

15

A. Initiated in 1992, my research on sculptured thin films (STFs) matured during the

period 2001-2005, to a point that I ended up as the lead author of the first book

on these nanoengineered materials [23]. My publications on STFs are presented in

Section 7.

B. I had been heavily involved from 1989 onwards in estimating the effective electro-

magnetic properties of particulate composite materials [24]. This strand matured

between 2001 and 2005 in two different ways: first, the strong-property-fluctuation

theory was developed; second, a control model to predict the optical response prop-

erties of STFs emerged. The control model is discussed in Section 7, whereas the

remainder of my homogenization research is contained in Section 8.

C. The fabrication of negatively refracting materials in 2001 [25] had a major effect

on my research in that I began to examine the issue of plane waves with negative

phase velocity (NPV) in complex materials, as well as to explore the concept of

nihility underlying the so-called perfect lens. That research also led to examining

NPV propagation in gravitationally affected vacuum. Section 9 is a presentation of

my NPV publications.

D. Related topics in nanotechnology that I examined included broadband ultraviolet

lithography of high-aspect-ratio features, the electromagnetic response properties

of carbon nanotubes, and photonic bandgap structures for microwaves and optics.

These are summarized in Section 10.

E. During the last five years, while working on topics included in the foregoing strands,

I occasionally had the good fortune of examining some fundamental issues in CME.

Papers published on these issues constitute the fifth strand, presented in Section

11.

In the following sections, my research in these strands is classified and summarized.

Each section carries a list of books, book chapter, and journal papers that I have either

16

authored or co-authored from 2001 to 2005. The titles of the publications are good guides

to their contents, and should be regarded as integral parts of this Extended Abstract. I

have excluded my conference publications, so that this thesis is not unreasonably large

in size.

7 Sculptured thin films (STFs)

In its decadal survey entitled Physics in a New Era conducted during the 1990s, the

U.S. National Research Council (NRC) explored research trends and requirements in

the materials sciences. A dominant theme that emerged is of nanoscience and nano-

technology. The nanoscale is Janusian: matter at the 10- to 100-nm length scale exhibits

continuum characteristics, but molecules and their clusters of small size can still display

their individuality. For that reason, the U.S. National Science Foundation began to focus

on material morphologies and architectures with at least one dimension smaller than

100 nm in its research initiatives.

Among the nanoengineered materials identified by the NRC are STFs. These nanos-

tructured materials with anisotropic and unidirectionally varying properties can be de-

signed and fabricated in a controlled manner using vapor deposition techniques. STFs are

assemblies of parallel nanowires (or submicronwires), and ahe ability to virtually instan-

taneously change the growth direction of the nanowire shape, through simple variations

in the direction of the incident vapor flux, leads to a wide spectrum of morphological

forms. These forms can be

(i) two-dimensional, ranging from the simple slanted columns and chevrons to the more

complex C- and S-shaped morphologies; or

(ii) three-dimensional, including simple helixes and superhelixes.

17

The nanowire diameter can range from ∼ 10 to 300 nm, while the mass density may lie

between its theoretical maximum value and less than 20% thereof. The crystallinity must

be at a scale smaller than the nanowire diameter. The chemical composition is essen-

tially unlimited, ranging from insulators to semiconductors to metals. For many optical

applications, STFs can be thought of at macroscopic length scales as unidirectionally

nonhomogeneous dielectric materials.

Although precursors of STFs can be traced to as early as 1959, the STF concept was

enunciated by me and my colleague, Prof. R. Messier, from 1992 to 1995. During the

period 2001-2005, overviews of STF research were published as an invited paper [A1], two

book chapters [A2, A3], and quite recently a book [A4].

A control model for the structure-property relations of chiral STFs was created for

optical applications [A5]–[A8], as also empirical models for use by device designers [A9,

A10]. A structure-property control model was also created for the elastodynamic and

elastostatic properties of STFs [A11].

STFs were identified as nanoscale laboratories to test various optical and other con-

cepts [A12]. Along with experimentalist colleagues, STFs were deposited on topographic

substrates in order to blend the microscale and the nanoscale [A13, A14]. Most STFs

are deposited by variants of physical vapor deposition [A4]; however, polymeric STFs

were deposited in a one-step process combining physical and chemical vapor deposition

processes [A15], which is beginning to show its importance for tissue engineering for cell

adhesion and proliferation.

A1 A. Lakhtakia, Sculptured thin films: accomplishments and emerging uses, Mater Sci Engg C 19 (2002),

427-434.

A2 A. Lakhtakia and R. Messier, The past, the present, and the future of sculptured thin films, Introduction

to complex mediums for optics and electromagnetics (W.S. Weiglhofer and A. Lakhtakia, eds), SPIE

Press, Bellingham, WA, USA, 2003, pp. 447-478.

A3 A. Lakhtakia and R. Messier, Sculptured thin films, Nanometer structures: Theory, modeling, and

18

simulation (A. Lakhtakia, ed), SPIE Press, Bellingham, WA, USA, 2004, pp. 5-44.

A4 A. Lakhtakia and R. Messier, Sculptured thin films: Nanoengineered morphology and optics, SPIE

Press, Bellingham, WA, USA, 2005.

A5 J.A. Sherwin and A. Lakhtakia, Nominal model for structure-property relations of chiral dielectric

sculptured thin films, Math. Comput. Model. 34 (2001), 1499-1514; corrections: 35 (2002), 1355-

1363.

A6 J.A. Sherwin, A. Lakhtakia, and I.J. Hodgkinson, On calibration of a nominal structure-property re-

lationship model for chiral sculptured thin films by axial transmittance measurements, Opt Commun

209 (2002), 369-375.

A7 J.A. Sherwin and A. Lakhtakia, Nominal model for the optical response of a chiral sculptured thin film

infiltrated with an isotropic chiral fluid, Opt Commun 214 (2002), 231-245.

A8 J.A. Sherwin and A. Lakhtakia, Nominal model for the optical response of a chiral sculptured thin film

infiltrated by an isotropic chiral fluid—oblique incidence, Opt Commun 222 (2003), 305-329.

A9 F. Chiadini and A. Lakhtakia, Gaussian model for refractive indexes of columnar thin films and Bragg

multilayers, Opt Commun 231 (2004), 257-261.

A10 F. Chiadini and A. Lakhtakia, Extension of Hodgkinson s model for optical characterization of columnar

thin films, Microw Opt Technol Lett 42 (2004), 72-73.

A11 A. Lakhtakia, Microscopic model for elastostatic and elastodynamic excitation of chiral sculptured thin

films, J Compos Mater 36 (2002), 1277-1298.

A12 A. Lakhtakia and J.B. Geddes III, Nanotechnology for optics is a phase-length-time sandwich, Opt

Engg 43 (2004), 2410-2417.

A13 M.W. Horn, M.D. Pickett, R. Messier, and A. Lakhtakia, Blending of nanoscale and microscale in

uniform large-area sculptured thin-film architectures, Nanotechnology 15 (2004), 303-310.

A14 M.W. Horn, M.D. Pickett, R. Messier, and A. Lakhtakia, Selective growth of sculptured nanowires on

microlithographic substrates, J Vac Sci Technol B 22 (2004), 3426-3430.

A15 S. Pursel, M.W. Horn, M.C. Demirel, and A. Lakhtakia, Growth of sculptured polymer submicronwire

assemblies by vapor deposition, Polymer 46 (2005), 9544-9548.

19

7.1 Plane-wave response characteristics of chiral STFs

Chiral STFs, which are assemblies of helical nanowires, exhibit the circular Bragg phe-

nomenon (CBP): when sufficiently thick, a chiral STF mostly reflects a normally incident

circularly polarized wave of the same handedness as its own structure, but not otherwise,

in a frequency regime called the Bragg regime. The exhibition of CBPs makes chiral

STFs very useful as polarization filters, theoretical studies were undertaken for simple

interpretations of the response characteristics of chiral STFs to normally incident plane

waves [A16]–[A19], with the reasonable assumptions that the materials are purely di-

electric in their electromagnetic response characteristics. Two remarkable features—to

negate and to maximize the Bragg regime—were identified for device-designers [A20].

The frequency-dependence of the constitutive matrixes was highlighted by comparing

pre- and post-resonant manifestations of the CBP [A21].

Although initial studies of the response characteristics of chiral STFs to obliquely in-

cident plane waves had been undertaken in the late 1990s, a major accomplishment there-

after was the numerical implementation [A22, A23] of a matrix series solution method

formulated in 1995. Resonant regimes in chiral STFs [A24] as well as Goos-Hanchen

shifts of Gaussian beams [A25] were investigated. The concept of magneto-optical STFs

was advanced by showing that magnetostatic fields can be used to manipulate the CBP

[A26, A27].

A16 M.W. McCall and A. Lakhtakia, Development and assessment of coupled wave theory of axial prop-

agation in thin-film helicoidal bi-anisotropic media. Part 2: dichroisms, ellipticity transformation and

optical rotation, J Modern Opt 48 (2001), 143-158.

A17 A. Lakhtakia and M.W. McCall, Simple expressions for Bragg reflection from axially excited chiral

sculptured thin films, J Modern Opt 49 (2002), 1525-1535.

A18 M.W. McCall and A. Lakhtakia, Explicit expressions for spectral remittances of axially excited chiral

sculptured thin films, J Modern Opt 51 (2004), 111-127.

A19 M.W. McCall and A. Lakhtakia, Analysis of plane-wave light normally incident to an axially excited

20

structurally chiral half-space, J Modern Opt 52 (2005), 541-550.

A20 A. Lakhtakia, Pseudo-isotropic and maximum-bandwidth points for axially excited chiral sculptured

thin films, Microw Opt Technol Lett 34 (2002), 367-371.

A21 A. Lakhtakia and J.T. Moyer, Post- versus pre-resonance characteristics of axially excited chiral sculp-

tured thin films, Optik 113 (2002), 97-99.

A22 J.A. Polo, Jr. and A. Lakhtakia, Numerical implementation of exact analytical solution for oblique

propagation in a cholesteric liquid crystal, Microw Opt Technol Lett 35 (2002), 397-400; correction:

44 (2005), 205.

A23 J.A. Polo, Jr. and A. Lakhtakia, Comparison of two methods for oblique propagation in helicoidal

bianisotropic mediums, Opt Commun 230 (2004), 369-386.

A24 A. Lakhtakia and I.J. Hodgkinson, Resonances in the Bragg regimes of axially excited, chiral sculptured

thin films, Microw Opt Technol Lett 32 (2002), 43-46.

A25 A. Lakhtakia, Truncation of angular spread of Bragg zones by total reflection, and Goos-Hanchen shifts

exhibited by chiral sculptured thin films, AEU Int J Electron Commun 56 (2002), 169-176; corrections:

57 (2003), 79.

A26 M.D. Pickett and A. Lakhtakia, On gyrotropic chiral sculptured thin films for magneto-optics, Optik

113 (2002), 367-371.

A27 M.D. Pickett, A. Lakhtakia and J.A. Polo, Jr., Spectral responses of gyrotropic chiral sculptured thin

films to obliquely incident plane waves, Optik 115 (2004), 393-398.

7.2 Optical applications of chiral STFs

The circular Bragg phenomenon exhibited by chiral STFs makes these films useful both as

polarization filters [A28, A29] and as bandpass filters. Five ways to alter the morphology

in order to enhance the bandwidth of the Bragg regime were formulated and theoretically

analyzed [A30]–[A34]. A piezoelectric method to control the bandwidth was set up [A35,

A36]. Coupling of chiral STFs with surface diffraction gratings was studied in order

to potentially obtain nonspecular versions of the CBP [A37, A38]. A major effort was

devoted to spectral hole filters realizable by inserting a central phase defect in a chiral STF

21

[A39]–[A44]. The use of a spectral hole filter for optical sensing of fluid concentration was

experimentally established [A45]. Yet another major effort was to establish the physical

feasibility of using a chiral STF as an optical emitter, for biosensing and genomic sensing

[A46]–[A49] as well as for high-purity light sources [A50]. Theoretical investigation also

established the possibility of using chiral STFs as optical interconnects for integrated

electronics [A51].

Variations of the basic morphology of chiral STFs were explored for various appli-

cations. Three variations concerned modifications for reflectors of elliptically polarized

plane waves [A52], rugate filters [A53], and linear-polarization filters [A54]. Slanting of

the nanohelical morphology was formulated for nonspecular versions of the CBP [A55,

A56].

The plane-wave response characteristics of chiral STFs were used to determine their

responses to radiation for dipole sources [A57, A58], for potential application towards

near-field scanning optical microscopy.

A28 M.W. McCall and A. Lakhtakia, Integrated optical polarization filtration via chiral sculptured-thin-film

technology, J Modern Opt 48 (2001), 2179-2184.

A29 A. Lakhtakia and M.W. McCall, Circular polarization filters, Encyclopedia of optical engineering, Vol.

1 (R. Driggers, ed), Marcel Dekker, New York, NY, USA, 2003, pp. 230-236.

A30 A. Lakhtakia, Axial excitation of tightly interlaced chiral sculptured thin films: “averaged” circular

Bragg phenomenon, Optik 112 (2001), 119-124.

A31 A. Lakhtakia, Stepwise chirping of chiral sculptured thin films for Bragg bandwidth enhancement,

Microw Opt Technol Lett 28 (2001), 323-326.

A32 F. Chiadini and A. Lakhtakia, Design of wideband circular-polarization filters made of chiral sculptured

thin films, Microw Opt Technol Lett 42 (2004), 135-138.

A33 A. Lakhtakia, Enhancement of optical activity of chiral sculptured thin films by suitable infiltration of

void regions, Optik 112 (2001), 145-148; correction: 112 (2001), 544.

A34 A. Lakhtakia and M.W. Horn, Bragg-regime engineering by columnar thinning of chiral sculptured thin

films, Optik 114 (2003), 556-560.

22

A35 F. Wang, A. Lakhtakia, and R. Messier, Towards piezoelectrically tunable chiral sculptured thin film

lasers, Sens Actuat A: Phys 102 (2002), 31-35.

A36 F. Wang, A. Lakhtakia, and R. Messier, On piezoelectric control of sculptured thin films, J Modern

Opt 49 (2003), 239-249.

A37 M.W. McCall and A. Lakhtakia, Coupling of a surface grating to a structurally chiral volume grating,

Electromagnetics 23 (2003), 1-26.

A38 J.P. McIlroy, M.W. McCall, A. Lakhtakia, and I.J. Hodgkinson, Strong coupling of a surface-relief

dielectric grating to a structurally chiral volume grating, Optik 116 (2005), 311-324.

A39 I.J. Hodgkinson, Q.h. Wu, L. De Silva, M. Arnold, M.W. McCall, and A. Lakhtakia, Supermodes of

chiral photonic filters with combined twist and layer defects, Phys Rev Lett 91 (2003), 223903.

A40 I.J. Hodgkinson, Q.h. Wu, M. Arnold, M.W. McCall, and A. Lakhtakia, Chiral mirror and optical

resonator designs for circularly polarized light: suppression of cross-polarized reflectances and trans-

mittances, Opt Commun 210 (2002), 202-211.

A41 F. Wang and A. Lakhtakia, Optical crossover phenomenon due to a central 90◦-twist defect in a chiral

sculptured thin film or chiral liquid crystal, Proc R Soc Lond A 461 (2005), 2985-3004.

A42 F. Wang and A. Lakhtakia, Defect modes in multisection helical photonic crystals, Opt Exp 13 (2005),

7319-7335.

A43 F. Wang and A. Lakhtakia, Specular and nonspecular, thickness-dependent, spectral holes in a slanted

chiral sculptured thin film with a central twist defect, Opt Commun 215 (2003), 79-92.

A44 F. Wang and A. Lakhtakia, Third method for generation of spectral holes in chiral sculptured thin

films, Opt Commun 250 (2005), 105-110.

A45 A. Lakhtakia, M.W. McCall, J.A. Sherwin, Q.H. Wu, and I.J. Hodgkinson, Sculptured-thin-film spectral

holes for optical sensing of fluids, Opt Commun 194 (2001), 33-46.

A46 A. Lakhtakia, On bioluminescent emission from chiral sculptured thin films, Opt Commun 188 (2001),

313-320.

A47 A. Lakhtakia, Local inclination angle: a key structural factor in emission from chiral sculptured thin

films, Opt Commun 202 (2002), 103-112; correction: 203 (2002), 447.

A48 A. Lakhtakia, On radiation from canonical source configurations in structurally chiral materials, Microw

Opt Technol Lett 37 (2003), 37-40.

23

A49 E.E. Steltz and A. Lakhtakia, Theory of second-harmonic-generated radiation from chiral sculptured

thin films for bio-sensing, Opt Commun 216 (2003), 139-150.

A50 A. Lakhtakia and J. Xu, An essential difference between dielectric mirrors and chiral mirrors, Microw

Opt Technol Lett 47 (2005), 63-64.

A51 E. Ertekin and A. Lakhtakia, Optical interconnects realizable with thin-film helicoidal bianisotropic

mediums, Proc R Soc Lond A 457 (2001), 817-836.

A52 I. Hodgkinson, Q.h. Wu, L. De Silva, M. Arnold, A. Lakhtakia, and M. McCall, Structurally perturbed

chiral Bragg reflectors for elliptically polarized light, Opt Lett 30 (2005), 2629-2631.

A53 J.A. Polo, Jr. and A. Lakhtakia, Sculptured nematic thin films with periodically modulated tilt angle

as rugate filters, Opt Commun 251 (2005), 10-22.

A54 J.A. Polo, Jr. and A. Lakhtakia, Tilt-modulated chiral sculptured thin films: an alternative to quarter-

wave stacks, Opt Commun 242 (2004), 13-21.

A55 F. Wang, A. Lakhtakia and R. Messier, Coupling of Rayleigh-Wood anomalies and the circular Bragg

phenomenon in slanted chiral sculptured thin films, Eur Phys J Appl Phys 20 (2002), 91-103; correc-

tions: 24 (2003), 91.

A56 F. Wang and A. Lakhtakia, Lateral shifts of optical beams on reflection by slanted chiral sculptured

thin films, Opt Commun 235 (2004), 107-132.

A57 A. Lakhtakia and M.W. McCall, Response of chiral sculptured thin films to dipolar sources, AEU Int

J Electron Commun 57 (2003), 23-32.

A58 F. Wang and A. Lakhtakia, Response of slanted chiral sculptured thin films to dipolar sources, Opt

Commun 235 (2004), 133-151.

7.3 Pulse propagation in chiral STFs

“What is time-domain counterpart of the CBP?” The answer was not known when this

question was first posed in 1999, because chiral STFs are dispersive, unidirectionally

nonhomogeneous, and anisotropic. Time-domain solutions of the macroscopic Maxwell

postulates had been calculated only for much simpler materials, and analytical solutions

are virtually impossible.

24

With the help of a supercomputer, and with the assumption of the incident signal

being a pulse that modulates the amplitude of a normally incident carrier plane wave,

the time-domain signature of the CBP was identified as the backward bleeding of the

pulse under appropriate conditions [A59]–[A62]. Calculations were made for many-cycle

pulses, few-cycle pulses, as well as rectangular pulses. The possibility of multiple CBPs

was established [A63], and the crucial role of the phase of the carrier plane wave was

elucidated [A64].

Calculations were also made for carrier pulse beams (of finite extent) [A65], but the

available capabilities of the Pittsburgh Supercomputing Center were exhausted at that

stage. More realistic calculations await the easy availability of more powerful supercom-

puters.

A59 J.B. Geddes III and A. Lakhtakia, Reflection and transmission of optical narrow-extent pulses by axially

excited chiral sculptured thin films, Eur Phys J Appl Phys 13 (2001), 3-14; corrections: 16 (2001),

247.

A60 J.B. Geddes III and A. Lakhtakia, Time–domain simulation of the circular Bragg phenomenon exhibited

by axially excited chiral sculptured thin films, Eur Phys J Appl Phys 14 (2001), 97-105; corrections:

16 (2001), 247.

A61 J.B. Geddes III and A. Lakhtakia, Pulse-coded information transmission across an axially excited chiral

sculptured thin film in the Bragg regime, Microw Opt Technol Lett 28 (2001), 59-62.

A62 J.B. Geddes III and A. Lakhtakia, Videopulse bleeding in axially excited chiral sculptured thin films in

the Bragg regime, Eur Phys J Appl Phys 17 (2002), 21-24.

A63 J. Wang, A. Lakhtakia, and J.B. Geddes III, Multiple Bragg regimes exhibited by a chiral sculptured

thin film half-space on axial excitation, Optik 113 (2002), 213-221.

A64 J.B. Geddes III and A. Lakhtakia, Effects of carrier phase on reflection of optical narrow-extent pulses

from axially excited chiral sculptured thin films, Opt Commun 225 (2003), 141-150.

A65 J.B. Geddes III and A. Lakhtakia, Numerical investigation of reflection, refraction, and diffraction of

pulsed optical beams by chiral sculptured thin films, Opt Commun 252 (2005), 307-320.

25

8 Homogenization of composite materials

A particulate composite material is formed by dispersing electrically small bodies or

particles called inclusions in a homogeneous material that makes up the host material

phase. Below a certain frequency, the inclusions are small enough that the composite

material can be effectively considered as a homogenous material. The prediction of the

effective electromagnetic properties of a composite material from those of its component

material phases is the major objective of various homogenization formalisms.

Early efforts yielded simple mixture formulas that generally work well when the vol-

umetric proportion of the one material phase is small and the contrast between the

electromagnetic properties of the two material phases is not large. Later, many refined

homogenization formalisms emerged that often yield improved predictions. Yet the sim-

ple mixture formulas continue to be used, in part because of their simplicity. A selection

of milestone papers on homogenization over more than 180 years was published in 1996

[24].

8.1 Linear materials

Improvement of simple homogenization formalisms remains attractive. An attempt to

combine the attributes of the Maxwell Garnett and the Bruggeman formalisms was re-

ported [B1], and the attributes of the Bruggeman formalism for complex mediums were

clarified [B2, B3]. The Bragg-Pippard formalism was extended to bianisotropic composite

materials [B4]; and the currently hot topic of negative refraction inspired the extension of

the Bruggeman formalism to dielectric-magnetic composite materials with inclusion size

taken explicitly into account [B5]. The Bruggeman formalism was also exploited to devise

a control model for the prediction of structure-property relations of STFs [A5]–[A8].

Inclusion size as well as the distributional statistics were incorporated in the strong-

26

property-fluctuation theory (SPFT) for bianisotropic materials [B6, B7]. SPFT is an

iterative approach beginning with the Bruggeman formalism as the initial guess. It was

implemented for ellipsoidal particles, and its convergence was numerically explored [B8].

A major success was the establishment of the possibility of the group velocity being

larger in a homogenized composite medium than in its component material phases [B9,

B10]. Another was to explore conditions for the propagation of Voigt waves—plane

waves with nonuniform amplitude variations—in a homogenized composite medium in

the absence of Voigt-wave propagation in the component material phases [B11, B12]. Yet

another was to show that certain homogenized composite mediums can support plane-

wave propagation with opposing phase velocity and time-averaged Poynting vector, even

though the component material phases do not [B13]. This last paper was extensively

commented in the popular science press during the second half of 2005.

B1 B. Michel, A. Lakhtakia, W.S. Weiglhofer, and T.G. Mackay, Incremental and differential Maxwell

Garnett formalisms for bianisotropic composites, Compos Sci Technol 61 (2001), 13-18.

B2 B.M. Ross and A. Lakhtakia, Bruggeman approach for isotropic chiral mixtures revisited, Microw Opt

Technol Lett 44 (2005), 524-527.

B3 T.G. Mackay and A. Lakhtakia, A limitation of the Bruggeman formalism for homogenization, Opt

Commun 234 (2004), 35-42.

B4 J.A. Sherwin and A. Lakhtakia, Bragg-Pippard formalism for bianisotropic particulate composites,

Microw Opt Technol Lett 33 (2002), 40-44.

B5 A. Lakhtakia and T.G. Mackay, Size-dependent Bruggeman approach for dielectric-magnetic composite

materials, AEU Int J Electron Commun 59 (2005), 348-351.

B6 T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Ellipsoidal topology, orientation diversity and corre-

lation length in bianisotropic composite mediums, AEU Int J Electron Commun 55 (2001), 243-251.

B7 T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Homogenisation of similarly oriented, metallic,

ellipsoidal inclusions using the bilocally approximated strong-property-fluctuation theory, Opt Commun

197 (2001), 89-95.

27

B8 T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Third-order implementation and convergence of the

strong-property-fluctuation theory in electromagnetic homogenization, Phys Rev E 64 (2001), 066616.

B9 T.G. Mackay and A. Lakhtakia, Enhanced group velocity in metamaterials, J Phys A: Math Gen 37

(2004), L19-L24.

B10 T.G. Mackay and A. Lakhtakia, Anisotropic enhancement of group velocity in a homogenized dielectric

composite medium, J Opt A: Pure Appl Opt 7 (2005), 669-674.

B11 T.G. Mackay and A. Lakhtakia, Voigt wave propagation in biaxial composite materials, J Opt A: Pure

Appl Phys 5 (2003), 91-95.

B12 T.G. Mackay and A. Lakhtakia, Correlation length facilitates Voigt wave propagation, Waves Random

Media 14 (2004), L1-L11.

B13 T.G. Mackay and A. Lakhtakia, Negative phase velocity in isotropic dielectric-magnetic media via

homogenization, Microw Opt Technol Lett 47 (2005), 313-315.

8.2 Nonlinear materials

Homogenization formalisms for nonlinear material properties are in their infancy, in part

due to the considerable difficult nature of the macroscopic Maxwell postulates despite

their simplicity at first glance. A perturbative approach was grafted on to the Bruggeman

formalism for composite mediums with intensity-dependent permittivity matrix [B14].

Also, the SPFT was extended to isotropic, cubically nonlinear composite mediums [B15]–

[B17].

B14 M.N. Lakhtakia and A. Lakhtakia, Anisotropic composite materials with intensity-dependent permit-

tivity tensor: The Bruggeman approach, Electromagnetics 21 (2001), 129-137.

B15 A. Lakhtakia, Application of strong permittivity fluctuation theory for isotropic, cubically nonlinear,

composite mediums, Opt Commun 192 (2001), 145-151.

B16 T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Homogenisation of isotropic, cubically nonlinear,

composite mediums by the strong-property-fluctuation theory: Third-order considerations, Opt Com-

mun 204 (2002), 219-228.

28

B17 T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, The strong-property-fluctuation theory for cubically

nonlinear, isotropic chiral composite mediums, Electromagnetics 23 (2003), 455-479.

9 Negative-phase-velocity propagation

The fabrication of isotropic dielectric-magnetic materials wherein the phase velocity of

a plane wave is oppositely directed to its time-averaged Poynting vector took the elec-

tromagnetic research community by a storm about five years ago [25]. A host of exotic

electromagnetic phenomenons follow as a consequence of a negative phase velocity (NPV),

most notably negative refraction. The realization of artificial metamaterials which are

effectively homogeneous and which support NPV propagation has been the focus of con-

siderable attention during this decade. NPV metamaterials for performance in the mi-

crowave regime have been realized, and progress towards the same goal in the optical

regime continues to be made.

Early progress was reviewed with two co-authors in 2002 and 2003 [C1, C2], and a

simple explanation was offered to elucidate the chief characteristic of NPV propagation

[C3]. The concept of nihility was created [C4] to explain the vaunted capabilities of

the so-called perfect lens [C5, C6], which is a planar lens that is supposed to produce

distortion-free images.

C1 A. Lakhtakia, M.W. McCall, and W.S. Weiglhofer, Brief overview of recent developments on negative

phase-velocity mediums (alias left-handed materials), AEU Int J Electron Commun 56 (2002), 407-410.

C2 A. Lakhtakia, M.W. McCall, and W.S. Weiglhofer, Negative phase-velocity mediums, Introduction to

complex mediums for optics and electromagnetics (W.S. Weiglhofer and A. Lakhtakia, eds), SPIE,

Bellingham, WA, USA, 2003, pp. 347-363.

C3 M.W. McCall, A. Lakhtakia, and W.S. Weiglhofer, The negative index of refraction demystified, Eur J

Phys 23 (2002), 353-359.

C4 A. Lakhtakia, An electromagnetic trinity from “negative permittivity” and “negative permeability”, Int

29

J Infrared Millim Waves 22 (2001), 1731- 1734; correctly reprinted: 23 (2002), 813-818.

C5 A. Lakhtakia, On perfect lenses and nihility, Int J Infrared Millim Waves 23 (2002), 339-343.

C6 A. Lakhtakia and J.A. Sherwin, Orthorhombic materials and perfect lenses, Int J Infrared Millim Waves

24 (2003), 19-23.

9.1 NPV propagation in materials

NPV characteristics in isotropic dielectric-magnetic mediums were explored in several

different contexts. A time-domain study was carried out to validate the NPV concept

[C7]. Simple condition to identify NPV materials were obtained [C2, C3, C8], and the

boundary between NPV propagation and the commonplace positive-phase-velocity (PPV)

propagation was established as that of an infinite phase velocity [C9]. The possibility of

a simple method to make NPV materials was demonstrated [B13].

The plane-wave response characteristics of planar multilayered materials containing

NPV layers were analyzed for both distributed Bragg reflectors [C10] and Cantor filters

[C11]. The restricted equivalence of certain multilayers comprising thin PPV layers to a

NPV material was established [C12]. Goos-Hanchen shifts of linearly polarized beams on

total reflection by NPV slabs were shown to be either negative or positive [C13, C14], in

contrast to the prevailing understanding that such shifts are necessarily negative.

The concept of NPV propagation in more complex mediums was generalized as the

angle between the phase velocity and the time-averaged Poynting vector being obtuse

[C15]. The effects of NPV propagation in bianisotropic mediums [C15, C16], isotropic

chiral mediums [C17], and dielectric-magnetic analogs of chiral STFs were studied [C18,

C19]. Amphoteric propagation in crystals such as calcite was shown not to be the same

as NPV propagation [C20].

A comprehensive study of diffraction gratings made of isotropic dielectric-magnetic

NPV mediums was undertaken using three different theoretical methods, valid under dif-

30

ferent conditions and differing in their algorithmic complexities [C21]–[C23]. Qualitative

comparison was made with an experimental result [C24], and extension to anisotropic

NPV gratings was begun [C25].

C7 J. Wang and A. Lakhtakia, On reflection from a half-space with negative real permittivity and perme-

ability, Microw Opt Technol Lett 33 (2002), 465-467.

C8 R.A. Depine and A. Lakhtakia, A new condition to identify isotropic dielectric-magnetic materials

displaying negative phase velocity, Microw Opt Technol Lett 41 (2004), 315-316.

C9 A. Lakhtakia and T.G. Mackay, Infinite phase velocity as the boundary between negative and positive

phase velocities, Microw Opt Technol Lett 41 (2004), 165-166.

C10 J. Gerardin and A. Lakhtakia, Negative index of refraction and distributed Bragg reflectors, Microw

Opt Technol Lett 34 (2002), 409-411.

C11 J. Gerardin and A. Lakhtakia, Spectral response of Cantor multilayers made of materials with negative

refractive index, Phys Lett A 301 (2002), 377-381.

C12 A. Lakhtakia and C.M. Krowne, Restricted equivalence of paired epsilon-negative and mu-negative

layers to a negative phase-velocity material (alias left-handed material), Optik 114 (2003), 305-307.

C13 A. Lakhtakia, On planewave remittances and Goos-Hanchen shifts of planar slabs with negative real

permittivity and permeability, Electromagnetics 23 (2003), 71-75.

C14 A. Lakhtakia, Positive and negative Goos-Hanchen shifts and negative phase-velocity mediums (alias

left-handed materials), AEU Int J Electron Commun 58 (2004), 229-231.

C15 T.G. Mackay and A. Lakhtakia, Plane waves with negative phase velocity in Faraday chiral mediums,

Phys Rev E 69 (2004), 026602.

C16 T.G. Mackay and A. Lakhtakia, Negative phase velocity in a material with simultaneous mirror-

conjugated and racemic chirality characteristics, New J Phys 7 (2005), 165.

C17 A. Lakhtakia, Reversed circular dichroism of isotropic chiral mediums with negative real permeability

and permittivity, Microw Opt Technol Lett 33 (2002), 96-97.

C18 A. Lakhtakia, Reversal of circular Bragg phenomenon in ferrocholesteric materials with negative real

permittivities and permeabilities, Adv Mater 14 (2002), 447-449.

C19 A. Lakhtakia, Handedness reversal of circular Bragg phenomenon due to negative real permittivity and

permeability, Opt Exp 11 (2003), 716-722.

31

C20 A. Lakhtakia and M.W. McCall, Counterposed phase velocity and energy-transport velocity vectors in

a dielectric-magnetic uniaxial medium, Optik 115 (2004), 28-30.

C21 R.A. Depine and A. Lakhtakia, Diffraction gratings of isotropic negative-phase velocity materials, Optik

116 (2005), 31-43.

C22 R.A. Depine and A. Lakhtakia, Perturbative approach for diffraction due to a periodically corrugated

boundary between vacuum and a negative phase-velocity material, Opt Commun 233 (2004), 277-282.

C23 R.A. Depine and A. Lakhtakia, Plane-wave diffraction at the periodically corrugated boundary of

vacuum and a negative-phase-velocity material, Phys Rev E 69 (2004), 057602.

C24 R.A. Depine, A. Lakhtakia, and D. R. Smith, Enhanced diffraction by a rectangular grating made of a

negative phase-velocity (or negative index) material, Phys Lett A 337 (2005), 155-160.

C25 R.A. Depine and A. Lakhtakia, Diffraction by a grating made of a uniaxial dielectric-magnetic medium

exhibiting negative refraction, New J Phys 7 (2005), 158.

9.2 NPV propagation in outer space

A natural question that arose from investigating NPV propagation was if its character-

istics are Lorentz-covariant. In other words, would a non-co-moving inertial observer

imagine a homogeneous medium to be capable of supporting NPV propagation, whereas

a co-moving inertial observer rule out that possibility? Marriage of the macroscopic

Maxwell postulates with the special theory of relativity provided an answer in the affirma-

tive for the simplest materials [C26]. This has profound implications for communications

in outer space.

Even more interesting consequences emerged, albeit theoretically still, when condi-

tions for NPV propagation in gravitationally affected vacuum were investigated. Gravi-

tationally affected vacuum can be thought of as a nondispersive, nondissipative, nonho-

mogeneous, spatially local, bianisotropic medium—after a manipulation of the equations

of the general theory of relativity. It turned out NPV propagation can be supported

by gravitationally affected vacuum [C27]–[C29], provided certain conditions hold. Those

32

conditions were shown to be satisfied by the de Sitter spacetime [C30], a combination of

the de Sitter spacetime and the Schwarzschild spacetimes [C31], and in the ergosphere

of a rotating black hole [C32]. NPV propagation in a rotating black hole can be dis-

tinguished from the superradiance phenomenon [C33]. The philosophical implications of

these findings were commented upon in the popular science press during mid-2005.

C26 T.G. Mackay and A. Lakhtakia, Negative phase velocity in a uniformly moving, homogeneous, isotropic,

dielectric-magnetic medium, J Phys A: Math Gen 37 (2004), 5697-5711.

C27 A. Lakhtakia and T.G. Mackay, Towards gravitationally assisted negative refraction by vacuum, J Phys

A: Math Gen 37 (2004), L505-L510; correction: 37 (2004), 12093; comment: 38 (2005), 2543-2544;

reply: 38 (2005), 2545-2546.

C28 A. Lakhtakia, T.G. Mackay, and S. Setiawan, Global and local perspectives of gravitationally assisted

negative-phase-velocity propagation of electromagnetic waves in vacuum, Phys Lett A 336 (2005),

89-96.

C29 T.G. Mackay, A. Lakhtakia, and S. Setiawan, Gravitation and electromagnetic wave propagation with

negative phase velocity, New J Phys 7 (2005), 75.

C30 T.G. Mackay, S. Setiawan, and A. Lakhtakia, Negative phase velocity of electromagnetic waves and

the cosmological constant, Eur Phys J C Direct (2005), doi:10.1140/epjcd/s2005-01-001-9.

C31 T.G. Mackay, A. Lakhtakia, and Sandi Setiawan, Electromagnetic waves with negative phase velocity

in Schwarzschild-de Sitter spacetime, Europhys Lett 71 (2005), 925-931.

C32 T.G. Mackay, A. Lakhtakia and Sandi Setiawan, Electromagnetic negative-phase-velocity propagation

in the ergosphere of a rotating black hole, New J Phys 7 (2005), 171.

C33 S. Setiawan, T.G. Mackay, and A. Lakhtakia, A comparison of superradiance and negative phase

velocity phenomenons in the ergosphere of a rotating black hole, Phys Lett A 341 (2005), 15-21.

10 Related topics in nanotechnology

Sculptured thin films are nanoengineered materials, and my extensive work on these

materials right from the conceptual stage to designing and testing optical and other

33

devices led to interests in related topics in nanotechnology.

The electromagnetic properties of carbon nanotubes were formulated in a semiclassi-

cal approach by using a quantum-mechanical model for the conductivity of a single-wall

carbon nanotube, which was then modeled as a two-sided impedance sheet. Both in-

finitely long and semi-infinite nanotubes were analyzed [D1], and insulator-to-conductor

transitions in the frequency spectrum were predicted [D2].

A spectral model of near-field phase-shifting contact lithography was formulated [D3],

and then used to validate experimental results that demonstrated the formation of high-

aspect-ratio features in masked photoresists on broadband ultraviolet illumination [D4,

D5].

One-dimensional photonic bandgap structures with Kronig-Penney morphology in-

serted in microwave waveguides were analyzed in terms of dispersion equations for Bloch

waves and gap maps that would lead to design principles [D6]–[D8]. Comparison was

made with experimental results [D8, D9], and a novel two-dimensional photonic bandgap

structure was also incorporated in waveguides [D9]. Optical propagation in magneto-

optical photonic bandgap structures made of different types of garnets was also examined

with the transfer matrix approach [D10, D11].

D1 G.Ya. Slepyan, N.A. Krapivin, S.A. Maksimenko, A. Lakhtakia and O.M. Yevtushenko, Scattering of

electromagnetic waves by a semi-infinite carbon nanotube, AEU Int J Electron Commun 55 (2001),

273-280.

D2 G.Ya. Slepyan, S.A. Maksimenko, A. Lakhtakia, and O.M. Yevtushenko, Electromagnetic response of

carbon nanotubes and nanotube ropes, Syn Metals 124 (2001), 121-123.

D3 F. Wang, M.W. Horn, and A. Lakhtakia, Rigorous electromagnetic modeling of near-field phase-shifting

contact lithography, Microelectron Engg 71 (2004), 34-53.

D4 F. Wang, K.E. Weaver, A. Lakhtakia, and M.W. Horn, On contact lithography of high-aspect-ratio

features with incoherent broadband ultraviolet illumination, Microelectron Engg 77 (2005), 55-57.

34

D5 F. Wang, K.E. Weaver, A. Lakhtakia, and M.W. Horn, Electromagnetic modeling of near-field phase-

shifting contact lithography with broadband ultraviolet illumination, Optik 116 (2005), 1-9.

D6 A. Gomez, A. Lakhtakia, M.A. Solano, and A. Vegas, Parallel-plate waveguides with Kronig-Penney

morphology as photonic band-gap filters, Microw Opt Technol Lett 36 (2003), 4-8; correctly reprinted:

38 (2003), 511-514.

D7 A. Gomez, M.A. Solano, A. Lakhtakia, and A. Vegas, Circular waveguides with Kronig-Penney mor-

phology as electromagnetic band-gap filters, Microw Opt Technol Lett 37 (2003), 316-321.

D8 M.A. Solano, A. Gomez, A. Lakhtakia, and A. Vegas, Rigorous analysis of guided wave propagation of

dielectric electromagnetic band-gaps in a rectangular waveguide, Int J Electron 92 (2005), 117-130.

D9 A. Gomez, A. Vegas, M.A. Solano, and A. Lakhtakia, On one- and two-dimensional electromagnetic

band gap structures in rectangular waveguides at microwave frequencies, Electromagnetics 25 (2005),

437-460.

D10 I.L. Lyubchanskii, N.N. Dadoenkova, M.I. Lyubchankskii, E.A. Shapovalov, A. Lakhtakia, and Th.

Rasing, Spectra of bigyrotropic magnetic photonic crystals, Phys Stat Sol (a) 201 (2004), 3338-3344.

D11 I.L. Lyubchanskii, N.N. Dadoenkova, M.I. Lyubchankskii, E.A. Shapovalov, A. Lakhtakia, and Th.

Rasing, One-dimensional bigyrotropic magnetic photonic crystals, Appl Phys Lett 85 (2004), 5932-

5934.

11 Fundamental issues in CME

Quite naturally, several fundamental issues in electromagnetics came to the fore, while

working on electromagnetic fields in complex mediums. Symmetries of linear constitutive

relations due to reciprocity [E1] and uniqueness [E2] were discussed, and a new conjuga-

tion symmetry of the time-harmonic macroscopic Maxwell postulates for linear mediums

was identified [E3]. Beltrami fields, which are proportional to their circulation, were

shown to constitute a common class of solutions for linear bianisotropic mediums [E4,

E5]. Fractional electromagnetics in isotropic chiral mediums was shown to be a simple

consequence of the structure of electromagnetic theory [E6]. Finally, conditions for Voigt

wave propagation in anisotropic dielectric materials were established [E7].

35

E1 A. Lakhtakia and R.A. Depine, On Onsager relations and linear electromagnetic materials, AEU Int J

Electron Commun 59 (2005), 101-104.

E2 A. Lakhtakia, On the genesis of Post constraint in modern electromagnetism, Optik 115 (2004),

151-158.

E3 A. Lakhtakia, Conjugation symmetry in linear electromagnetism in extension of materials with negative

real permittivity and permeability scalars, Microw Opt Technol Lett 40 (2004), 160-161.

E4 A. Lakhtakia, Beltrami field phasors are eigenvectors of 6×6 linear constitutive dyadics, Microw Opt

Technol Lett 30 (2001), 127-128.

E5 A. Lakhtakia, Conditions for circularly polarized plane wave propagation in a linear bianisotropic

medium, Electromagnetics 22 (2002), 123-127.

E6 A. Lakhtakia, A representation theorem involving fractional derivatives for linear homogeneous chiral

mediums, Microw Opt Technol Lett 28 (2001), 385-386.

E7 J. Gerardin and A. Lakhtakia, Conditions for Voigt wave propagation in linear, homogeneous, dielectric

mediums, Optik 112 (2001), 493-495.

12 Concluding remarks

As the 133 books, book chapters, and journal publications presented in Sections 7–11

indicate, I examined electromagnetic fields in a variety of complex mediums, from 2001

to 2005. Most of my research was theoretical, but some experimental research was also

undertaken.

The topics examined are at the forefront of CME as well as, to a large extent, of

nanotechnology—inasmuchas they cover

(i) the propagation of electromagnetic waves and pulses in sculptured thin films

(ii) homogenization of particulate composite materials ranging from isotropic to bian-

isotropic, and linear to nonlinear; and

36

(iii) negative-phase-velocity propagation in complex materials as well as in gravitation-

ally affected vacuum.

Less comprehensively, attention was paid to carbon nanotubes, broadband, ultraviolet

lithography, and photonic bandgap structures; and some fundamental issues in CME

were also examined.

Clearly, the wealth of CME is such that fruitful investigations shall be undertaken by

researchers for several decades. I hope to remain in the ranks of those researchers.

13 References

1. A. Lakhtakia (ed), Essays on the formal aspects of electromagnetic theory , World

Scientific, Singapore, 1993.

2. J.Z. Buchwald, From Maxwell to microphysics: Aspects of electromagnetic theory

in the last quarter of the nineteenth century , University of Chicago Press, Chicago,

IL, USA, 1985.

3. E.J. Post, Separating field and constitutive equations in electromagnetic theory,

Introduction to complex mediums for optics and electromagnetics (W.S. Weiglhofer

and A. Lakhtakia, eds), SPIE, Bellingham, WA, USA, 2003, pp. 3-26.

4. O.N. Singh and A. Lakhtakia (eds), Electromagnetic fields in unconventional ma-

terials and structures, Wiley, New York, NY, USA, 2000.

5. W.S. Weiglhofer and A. Lakhtakia (eds), Introduction to complex mediums for optics

and electromagnetics, SPIE, Bellingham, WA, USA, 2003.

6. W.S. Weiglhofer, Constitutive characterization of simple and complex mediums,

Introduction to complex mediums for optics and electromagnetics (W.S. Weiglhofer

and A. Lakhtakia, eds), SPIE, Bellingham, WA, USA, 2003, pp. 27-61.

37

7. J.Z. Buchwald, The creation of scientific effects: Heinrich Hertz and electric waves ,

University of Chicago Press, Chicago, IL, USA, 1994.

8. T.K. Simpson, Maxwell on the electromagnetic field: A guided study , Rutgers Uni-

versity Press, New Brunswick, NJ, USA, 1997.

9. J.D. Jackson, Classical electrodynamics, 3rd ed , Wiley, New York, NY, USA, 1999.

10. D.R. Lovett, Tensor properties of crystals, Adam Hilger, Bristol, United Kingdom,

1989.

11. C. Kittel, Introduction to solid state physics, 4th ed , Wiley Eastern, New Delhi,

India, 1971.

12. T.G. Mackay and A. Lakhtakia, Anisotropy and bianisotropy, Wiley encyclopedia

of rf & microwave engineering, Vol. 1 (K. Chang, ed), Wiley, New York, NY, USA,

2005, pp. 137-146.

13. T.H. O’Dell, The electrodynamics of magneto-electric media, North-Holland, Ams-

terdam, The Netherlands, 1970.

14. A. Lakhtakia (ed), Selected papers on natural optical activity , SPIE, Bellingham,

WA, USA, 1990.

15. A. Lakhtakia, On the genesis of Post constraint in modern electromagnetism, Optik

115 (2004), 151-158.

16. C.M. Krowne, Electromagnetic theorems for complex anisotropic media, IEEE

Trans Antennas Propagat 32 (1984), 1224-1230.

17. H.C. Chen, Theory of electromagnetic waves: A coordinate-free approach, McGraw-

Hill, New York, NY, USA, 1983.

18. J.F. Nye, Physical properties of crystals, Clarendon Press, Oxford, United Kingdom,

1985.

38

19. A. Lakhtakia and W.S. Weiglhofer, Maxwell Garnett formalism for weakly nonlin-

ear, bianisotropic, dilute, particulate composite media, Int J Electron 87 (2000),

1401-1408.

20. T. Kobayashi, Introduction to nonlinear optical materials, Nonlin Opt 1 (1991),

91-117.

21. R.W. Boyd, Nonlinear optics, Academic Press, London, United Kingdom, 1992.

22. A. Lakhtakia, Beltrami fields in chiral media, World Scientific, Singapore, 1994.

23. A. Lakhtakia and R. Messier, Sculptured thin films: Nanoengineered morphology

and optics , SPIE Press, Bellingham, WA, USA, 2005.

24. A. Lakhtakia (ed), Selected papers on linear optical composite materials, SPIE Op-

tical Engineering Press, Bellingham, WA, USA, 1996.

25. A. Lakhtakia, M.W. McCall, and W.S. Weiglhofer, Negative phase-velocity medi-

ums, Introduction to complex mediums for optics and electromagnetics (W.S. Wei-

glhofer and A. Lakhtakia, eds), SPIE, Bellingham, WA, USA, 2003, pp. 347-363.

39

LIST OF PUBLICATIONS

1. A. Lakhtakia, Sculptured thin films: accomplishments and emerging uses, Mater

Sci Engg C 19 (2002), 427-434.

2. A. Lakhtakia and R. Messier, The past, the present, and the future of sculptured

thin films, Introduction to complex mediums for optics and electromagnetics (W.S.

Weiglhofer and A. Lakhtakia, eds), SPIE Press, Bellingham, WA, USA, 2003, pp.

447-478.

3. A. Lakhtakia and R. Messier, Sculptured thin films, Nanometer structures: Theory,

modeling, and simulation (A. Lakhtakia, ed), SPIE Press, Bellingham, WA, USA,

2004, pp. 5-44.

4. A. Lakhtakia and R. Messier, Sculptured thin films: Nanoengineered morphology

and optics , SPIE Press, Bellingham, WA, USA, 2005.

5. J.A. Sherwin and A. Lakhtakia, Nominal model for structure-property relations of

chiral dielectric sculptured thin films, Math. Comput. Model. 34 (2001), 1499-1514;

corrections: 35 (2002), 1355-1363.

6. J.A. Sherwin, A. Lakhtakia, and I.J. Hodgkinson, On calibration of a nominal

structure-property relationship model for chiral sculptured thin films by axial trans-

mittance measurements, Opt Commun 209 (2002), 369-375.

7. J.A. Sherwin and A. Lakhtakia, Nominal model for the optical response of a chiral

sculptured thin film infiltrated with an isotropic chiral fluid, Opt Commun 214

(2002), 231-245.

8. J.A. Sherwin and A. Lakhtakia, Nominal model for the optical response of a chiral

sculptured thin film infiltrated by an isotropic chiral fluid—oblique incidence, Opt

Commun 222 (2003), 305-329.

41

9. F. Chiadini and A. Lakhtakia, Gaussian model for refractive indexes of columnar

thin films and Bragg multilayers, Opt Commun 231 (2004), 257-261.

10. F. Chiadini and A. Lakhtakia, Extension of Hodgkinson s model for optical char-

acterization of columnar thin films, Microw Opt Technol Lett 42 (2004), 72-73.

11. A. Lakhtakia, Microscopic model for elastostatic and elastodynamic excitation of

chiral sculptured thin films, J Compos Mater 36 (2002), 1277-1298.

12. A. Lakhtakia and J.B. Geddes III, Nanotechnology for optics is a phase-length-time

sandwich, Opt Engg 43 (2004), 2410-2417.

13. M.W. Horn, M.D. Pickett, R. Messier, and A. Lakhtakia, Blending of nanoscale and

microscale in uniform large-area sculptured thin-film architectures, Nanotechnology

15 (2004), 303-310.

14. M.W. Horn, M.D. Pickett, R. Messier, and A. Lakhtakia, Selective growth of sculp-

tured nanowires on microlithographic substrates, J Vac Sci Technol B 22 (2004),

3426-3430.

15. S. Pursel, M.W. Horn, M.C. Demirel, and A. Lakhtakia, Growth of sculptured

polymer submicronwire assemblies by vapor deposition, Polymer 46 (2005), 9544-

9548.

16. M.W. McCall and A. Lakhtakia, Development and assessment of coupled wave

theory of axial propagation in thin-film helicoidal bi-anisotropic media. Part 2:

dichroisms, ellipticity transformation and optical rotation, J Modern Opt 48 (2001),

143-158.

17. A. Lakhtakia and M.W. McCall, Simple expressions for Bragg reflection from axially

excited chiral sculptured thin films, J Modern Opt 49 (2002), 1525-1535.

42

18. M.W. McCall and A. Lakhtakia, Explicit expressions for spectral remittances of

axially excited chiral sculptured thin films, J Modern Opt 51 (2004), 111-127.

19. M.W. McCall and A. Lakhtakia, Analysis of plane-wave light normally incident to

an axially excited structurally chiral half-space, J Modern Opt 52 (2005), 541-550.

20. A. Lakhtakia, Pseudo-isotropic and maximum-bandwidth points for axially excited

chiral sculptured thin films, Microw Opt Technol Lett 34 (2002), 367-371.

21. A. Lakhtakia and J.T. Moyer, Post- versus pre-resonance characteristics of axially

excited chiral sculptured thin films, Optik 113 (2002), 97-99.

22. J.A. Polo, Jr. and A. Lakhtakia, Numerical implementation of exact analytical

solution for oblique propagation in a cholesteric liquid crystal, Microw Opt Technol

Lett 35 (2002), 397-400; correction: 44 (2005), 205.

23. J.A. Polo, Jr. and A. Lakhtakia, Comparison of two methods for oblique propaga-

tion in helicoidal bianisotropic mediums, Opt Commun 230 (2004), 369-386.

24. A. Lakhtakia and I.J. Hodgkinson, Resonances in the Bragg regimes of axially

excited, chiral sculptured thin films, Microw Opt Technol Lett 32 (2002), 43-46.

25. A. Lakhtakia, Truncation of angular spread of Bragg zones by total reflection, and

Goos-Hanchen shifts exhibited by chiral sculptured thin films, AEU Int J Electron

Commun 56 (2002), 169-176; corrections: 57 (2003), 79.

26. M.D. Pickett and A. Lakhtakia, On gyrotropic chiral sculptured thin films for

magneto-optics, Optik 113 (2002), 367-371.

27. M.D. Pickett, A. Lakhtakia and J.A. Polo, Jr., Spectral responses of gyrotropic

chiral sculptured thin films to obliquely incident plane waves, Optik 115 (2004),

393-398.

43

28. M.W. McCall and A. Lakhtakia, Integrated optical polarization filtration via chiral

sculptured-thin-film technology, J Modern Opt 48 (2001), 2179-2184.

29. A. Lakhtakia and M.W. McCall, Circular polarization filters, Encyclopedia of optical

engineering, Vol. 1 (R. Driggers, ed), Marcel Dekker, New York, NY, USA, 2003,

pp. 230-236.

30. A. Lakhtakia, Axial excitation of tightly interlaced chiral sculptured thin films:

“averaged” circular Bragg phenomenon, Optik 112 (2001), 119-124.

31. A. Lakhtakia, Stepwise chirping of chiral sculptured thin films for Bragg bandwidth

enhancement, Microw Opt Technol Lett 28 (2001), 323-326.

32. F. Chiadini and A. Lakhtakia, Design of wideband circular-polarization filters made

of chiral sculptured thin films, Microw Opt Technol Lett 42 (2004), 135-138.

33. A. Lakhtakia, Enhancement of optical activity of chiral sculptured thin films by

suitable infiltration of void regions, Optik 112 (2001), 145-148; correction: 112

(2001), 544.

34. A. Lakhtakia and M.W. Horn, Bragg-regime engineering by columnar thinning of

chiral sculptured thin films, Optik 114 (2003), 556-560.

35. F. Wang, A. Lakhtakia, and R. Messier, Towards piezoelectrically tunable chiral

sculptured thin film lasers, Sens Actuat A: Phys 102 (2002), 31-35.

36. F. Wang, A. Lakhtakia, and R. Messier, On piezoelectric control of the optical

response of sculptured thin films, J Modern Opt 49 (2003), 239-249.

37. M.W. McCall and A. Lakhtakia, Coupling of a surface grating to a structurally

chiral volume grating, Electromagnetics 23 (2003), 1-26.

44

38. J.P. McIlroy, M.W. McCall, A. Lakhtakia, and I.J. Hodgkinson, Strong coupling of

a surface-relief dielectric grating to a structurally chiral volume grating, Optik 116

(2005), 311-324.

39. I.J. Hodgkinson, Q.h. Wu, L. De Silva, M. Arnold, M.W. McCall, and A. Lakhtakia,

Supermodes of chiral photonic filters with combined twist and layer defects, Phys

Rev Lett 91 (2003), 223903.

40. I.J. Hodgkinson, Q.h. Wu, M. Arnold, M.W. McCall, and A. Lakhtakia, Chiral

mirror and optical resonator designs for circularly polarized light: suppression of

cross-polarized reflectances and transmittances, Opt Commun 210 (2002), 202-211.

41. F. Wang and A. Lakhtakia, Optical crossover phenomenon due to a central 90◦-

twist defect in a chiral sculptured thin film or chiral liquid crystal, Proc R Soc Lond

A 461 (2005), 2985-3004.

42. F. Wang and A. Lakhtakia, Defect modes in multisection helical photonic crystals,

Opt Exp 13 (2005), 7319-7335.

43. F. Wang and A. Lakhtakia, Specular and nonspecular, thickness-dependent, spec-

tral holes in a slanted chiral sculptured thin film with a central twist defect, Opt

Commun 215 (2003), 79-92.

44. F. Wang and A. Lakhtakia, Third method for generation of spectral holes in chiral

sculptured thin films, Opt Commun 250 (2005), 105-110.

45. A. Lakhtakia, M.W. McCall, J.A. Sherwin, Q.H. Wu, and I.J. Hodgkinson, Sculptured-

thin-film spectral holes for optical sensing of fluids, Opt Commun 194 (2001), 33-46.

46. A. Lakhtakia, On bioluminescent emission from chiral sculptured thin films, Opt

Commun 188 (2001), 313-320.

45

47. A. Lakhtakia, Local inclination angle: a key structural factor in emission from chiral

sculptured thin films, Opt Commun 202 (2002), 103-112; correction: 203 (2002),

447.

48. A. Lakhtakia, On radiation from canonical source configurations in structurally

chiral materials, Microw Opt Technol Lett 37 (2003), 37-40.

49. E.E. Steltz and A. Lakhtakia, Theory of second-harmonic-generated radiation from

chiral sculptured thin films for bio-sensing, Opt Commun 216 (2003), 139-150.

50. A. Lakhtakia and J. Xu, An essential difference between dielectric mirrors and chiral

mirrors, Microw Opt Technol Lett 47 (2005), 63-64.

51. E. Ertekin and A. Lakhtakia, Optical interconnects realizable with thin-film heli-

coidal bianisotropic mediums, Proc R Soc Lond A 457 (2001), 817-836.

52. I. Hodgkinson, Q.h. Wu, L. De Silva, M. Arnold, A. Lakhtakia, and M. McCall,

Structurally perturbed chiral Bragg reflectors for elliptically polarized light, Opt

Lett 30 (2005), 2629-2631.

53. J.A. Polo, Jr. and A. Lakhtakia, Sculptured nematic thin films with periodically

modulated tilt angle as rugate filters, Opt Commun 251 (2005), 10-22.

54. J.A. Polo, Jr. and A. Lakhtakia, Tilt-modulated chiral sculptured thin films: an

alternative to quarter-wave stacks, Opt Commun 242 (2004), 13-21.

55. F. Wang, A. Lakhtakia and R. Messier, Coupling of Rayleigh-Wood anomalies and

the circular Bragg phenomenon in slanted chiral sculptured thin films, Eur Phys J

Appl Phys 20 (2002), 91-103; corrections: 24 (2003), 91.

56. F. Wang and A. Lakhtakia, Lateral shifts of optical beams on reflection by slanted

chiral sculptured thin films, Opt Commun 235 (2004), 107-132.

46

57. A. Lakhtakia and M.W. McCall, Response of chiral sculptured thin films to dipolar

sources, AEU Int J Electron Commun 57 (2003), 23-32.

58. F. Wang and A. Lakhtakia, Response of slanted chiral sculptured thin films to

dipolar sources, Opt Commun 235 (2004), 133-151.

59. J.B. Geddes III and A. Lakhtakia, Reflection and transmission of optical narrow-

extent pulses by axially excited chiral sculptured thin films, Eur Phys J Appl Phys

13 (2001), 3-14; corrections: 16 (2001), 247.

60. J.B. Geddes III and A. Lakhtakia, Time–domain simulation of the circular Bragg

phenomenon exhibited by axially excited chiral sculptured thin films, Eur Phys J

Appl Phys 14 (2001), 97-105; corrections: 16 (2001), 247.

61. J.B. Geddes III and A. Lakhtakia, Pulse-coded information transmission across an

axially excited chiral sculptured thin film in the Bragg regime, Microw Opt Technol

Lett 28 (2001), 59-62.

62. J.B. Geddes III and A. Lakhtakia, Videopulse bleeding in axially excited chiral

sculptured thin films in the Bragg regime, Eur Phys J Appl Phys 17 (2002), 21-24.

63. J. Wang, A. Lakhtakia, and J.B. Geddes III, Multiple Bragg regimes exhibited by a

chiral sculptured thin film half-space on axial excitation, Optik 113 (2002), 213-221.

64. J.B. Geddes III and A. Lakhtakia, Effects of carrier phase on reflection of optical

narrow-extent pulses from axially excited chiral sculptured thin films, Opt Commun

225 (2003), 141-150.

65. J.B. Geddes III and A. Lakhtakia, Numerical investigation of reflection, refraction,

and diffraction of pulsed optical beams by chiral sculptured thin films, Opt Commun

252 (2005), 307-320.

47

66. B. Michel, A. Lakhtakia, W.S. Weiglhofer, and T.G. Mackay, Incremental and differ-

ential Maxwell Garnett formalisms for bianisotropic composites, Compos Sci Tech-

nol 61 (2001), 13-18.

67. B.M. Ross and A. Lakhtakia, Bruggeman approach for isotropic chiral mixtures

revisited, Microw Opt Technol Lett 44 (2005), 524-527.

68. T.G. Mackay and A. Lakhtakia, A limitation of the Bruggeman formalism for ho-

mogenization, Opt Commun 234 (2004), 35-42.

69. J.A. Sherwin and A. Lakhtakia, Bragg-Pippard formalism for bianisotropic partic-

ulate composites, Microw Opt Technol Lett 33 (2002), 40-44.

70. A. Lakhtakia and T.G. Mackay, Size-dependent Bruggeman approach for dielectric-

magnetic composite materials, AEU Int J Electron Commun 59 (2005), 348-351.

71. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Ellipsoidal topology, orientation

diversity and correlation length in bianisotropic composite mediums, AEU Int J

Electron Commun 55 (2001), 243-251.

72. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Homogenisation of similarly

oriented, metallic, ellipsoidal inclusions using the bilocally approximated strong-

property-fluctuation theory, Opt Commun 197 (2001), 89-95.

73. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Third-order implementation and

convergence of the strong-property-fluctuation theory in electromagnetic homoge-

nization, Phys Rev E 64 (2001), 066616.

74. T.G. Mackay and A. Lakhtakia, Enhanced group velocity in metamaterials, J Phys

A: Math Gen 37 (2004), L19-L24.

75. T.G. Mackay and A. Lakhtakia, Anisotropic enhancement of group velocity in a

48

homogenized dielectric composite medium, J Opt A: Pure Appl Opt 7 (2005), 669-

674.

76. T.G. Mackay and A. Lakhtakia, Voigt wave propagation in biaxial composite ma-

terials, J Opt A: Pure Appl Phys 5 (2003), 91-95.

77. T.G. Mackay and A. Lakhtakia, Correlation length facilitates Voigt wave propaga-

tion, Waves Random Media 14 (2004), L1-L11.

78. T.G. Mackay and A. Lakhtakia, Negative phase velocity in isotropic dielectric-

magnetic media via homogenization, Microw Opt Technol Lett 47 (2005), 313-315.

79. M.N. Lakhtakia and A. Lakhtakia, Anisotropic composite materials with intensity-

dependent permittivity tensor: The Bruggeman approach, Electromagnetics 21

(2001), 129-137.

80. A. Lakhtakia, Application of strong permittivity fluctuation theory for isotropic,

cubically nonlinear, composite mediums, Opt Commun 192 (2001), 145-151.

81. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, Homogenisation of isotropic,

cubically nonlinear, composite mediums by the strong-property-fluctuation theory:

Third-order considerations, Opt Commun 204 (2002), 219-228.

82. T.G. Mackay, A. Lakhtakia, and W.S. Weiglhofer, The strong-property-fluctuation

theory for cubically nonlinear, isotropic chiral composite mediums, Electromagnetics

23 (2003), 455-479.

83. A. Lakhtakia, M.W. McCall, and W.S. Weiglhofer, Brief overview of recent devel-

opments on negative phase-velocity mediums (alias left-handed materials), AEU Int

J Electron Commun 56 (2002), 407-410.

84. A. Lakhtakia, M.W. McCall, and W.S. Weiglhofer, Negative phase-velocity medi-

ums, Introduction to complex mediums for optics and electromagnetics (W.S. Wei-

49

glhofer and A. Lakhtakia, eds), SPIE, Bellingham, WA, USA, 2003, pp. 347-363.

85. M.W. McCall, A. Lakhtakia, and W.S. Weiglhofer, The negative index of refraction

demystified, Eur J Phys 23 (2002), 353-359.

86. A. Lakhtakia, An electromagnetic trinity from “negative permittivity” and “nega-

tive permeability”, Int J Infrared Millim Waves 22 (2001), 1731- 1734; correctly

reprinted: 23 (2002), 813-818.

87. A. Lakhtakia, On perfect lenses and nihility, Int J Infrared Millim Waves 23 (2002),

339-343.

88. A. Lakhtakia and J.A. Sherwin, Orthorhombic materials and perfect lenses, Int J

Infrared Millim Waves 24 (2003), 19-23.

89. J. Wang and A. Lakhtakia, On reflection from a half-space with negative real per-

mittivity and permeability, Microw Opt Technol Lett 33 (2002), 465-467.

90. R.A. Depine and A. Lakhtakia, A new condition to identify isotropic dielectric-

magnetic materials displaying negative phase velocity, Microw Opt Technol Lett 41

(2004), 315-316.

91. A. Lakhtakia and T.G. Mackay, Infinite phase velocity as the boundary between

negative and positive phase velocities, Microw Opt Technol Lett 41 (2004), 165-166.

92. J. Gerardin and A. Lakhtakia, Negative index of refraction and distributed Bragg

reflectors, Microw Opt Technol Lett 34 (2002), 409-411.

93. J. Gerardin and A. Lakhtakia, Spectral response of Cantor multilayers made of

materials with negative refractive index, Phys Lett A 301 (2002), 377-381.

94. A. Lakhtakia and C.M. Krowne, Restricted equivalence of paired epsilon-negative

and mu-negative layers to a negative phase-velocity material (alias left-handed ma-

terial), Optik 114 (2003), 305-307.

50

95. A. Lakhtakia, On planewave remittances and Goos-Hanchen shifts of planar slabs

with negative real permittivity and permeability, Electromagnetics 23 (2003), 71-75.

96. A. Lakhtakia, Positive and negative Goos-Hanchen shifts and negative phase-velocity

mediums (alias left-handed materials), AEU Int J Electron Commun 58 (2004),

229-231.

97. T.G. Mackay and A. Lakhtakia, Plane waves with negative phase velocity in Faraday

chiral mediums, Phys Rev E 69 (2004), 026602.

98. T.G. Mackay and A. Lakhtakia, Negative phase velocity in a material with simulta-

neous mirror-conjugated and racemic chirality characteristics, New J Phys 7 (2005),

165.

99. A. Lakhtakia, Reversed circular dichroism of isotropic chiral mediums with negative

real permeability and permittivity, Microw Opt Technol Lett 33 (2002), 96-97.

100. A. Lakhtakia, Reversal of circular Bragg phenomenon in ferrocholesteric materials

with negative real permittivities and permeabilities, Adv Mater 14 (2002), 447-449.

101. A. Lakhtakia, Handedness reversal of circular Bragg phenomenon due to negative

real permittivity and permeability, Opt Exp 11 (2003), 716-722.

102. A. Lakhtakia and M.W. McCall, Counterposed phase velocity and energy-transport

velocity vectors in a dielectric-magnetic uniaxial medium, Optik 115 (2004), 28-30.

103. R.A. Depine and A. Lakhtakia, Diffraction gratings of isotropic negative-phase ve-

locity materials, Optik 116 (2005), 31-43.

104. R.A. Depine and A. Lakhtakia, Perturbative approach for diffraction due to a pe-

riodically corrugated boundary between vacuum and a negative phase-velocity ma-

terial, Opt Commun 233 (2004), 277-282.

51

105. R.A. Depine and A. Lakhtakia, Plane-wave diffraction at the periodically corrugated

boundary of vacuum and a negative-phase-velocity material, Phys Rev E 69 (2004),

057602.

106. R.A. Depine, A. Lakhtakia, and D. R. Smith, Enhanced diffraction by a rectangular

grating made of a negative phase-velocity (or negative index) material, Phys Lett

A 337 (2005), 155-160.

107. R.A. Depine and A. Lakhtakia, Diffraction by a grating made of a uniaxial dielectric-

magnetic medium exhibiting negative refraction, New J Phys 7 (2005), 158.

108. T.G. Mackay and A. Lakhtakia, Negative phase velocity in a uniformly moving, ho-

mogeneous, isotropic, dielectric-magnetic medium, J Phys A: Math Gen 37 (2004),

5697-5711.

109. A. Lakhtakia and T.G. Mackay, Towards gravitationally assisted negative refraction

by vacuum, J Phys A: Math Gen 37 (2004), L505-L510; correction: 37 (2004),

12093; comment: 38 (2005), 2543-2544; reply: 38 (2005), 2545-2546.

110. A. Lakhtakia, T.G. Mackay, and S. Setiawan, Global and local perspectives of grav-

itationally assisted negative-phase-velocity propagation of electromagnetic waves in

vacuum, Phys Lett A 336 (2005), 89-96.

111. T.G. Mackay, A. Lakhtakia, and S. Setiawan, Gravitation and electromagnetic wave

propagation with negative phase velocity, New J Phys 7 (2005), 75.

112. T.G. Mackay, S. Setiawan, and A. Lakhtakia, Negative phase velocity of elec-

tromagnetic waves and the cosmological constant, Eur Phys J C Direct (2005),

doi:10.1140/epjcd/s2005-01-001-9.

113. T.G. Mackay, A. Lakhtakia, and Sandi Setiawan, Electromagnetic waves with neg-

ative phase velocity in Schwarzschild-de Sitter spacetime, Europhys Lett 71 (2005),

925-931.

52

114. T.G. Mackay, A. Lakhtakia and Sandi Setiawan, Electromagnetic negative-phase-

velocity propagation in the ergosphere of a rotating black hole, New J Phys 7 (2005),

171.

115. S. Setiawan, T.G. Mackay, and A. Lakhtakia, A comparison of superradiance and

negative phase velocity phenomenons in the ergosphere of a rotating black hole,

Phys Lett A 341 (2005), 15-21.

116. G.Ya. Slepyan, N.A. Krapivin, S.A. Maksimenko, A. Lakhtakia and O.M. Yev-

tushenko, Scattering of electromagnetic waves by a semi-infinite carbon nanotube,

AEU Int J Electron Commun 55 (2001), 273-280.

117. G.Ya. Slepyan, S.A. Maksimenko, A. Lakhtakia, and O.M. Yevtushenko, Elec-

tromagnetic response of carbon nanotubes and nanotube ropes, Syn Metals 124

(2001), 121-123.

118. F. Wang, M.W. Horn, and A. Lakhtakia, Rigorous electromagnetic modeling of

near-field phase-shifting contact lithography, Microelectron Engg 71 (2004), 34-53.

119. F. Wang, K.E. Weaver, A. Lakhtakia, and M.W. Horn, On contact lithography

of high-aspect-ratio features with incoherent broadband ultraviolet illumination,

Microelectron Engg 77 (2005), 55-57.

120. F. Wang, K.E. Weaver, A. Lakhtakia, and M.W. Horn, Electromagnetic modeling

of near-field phase-shifting contact lithography with broadband ultraviolet illumi-

nation, Optik 116 (2005), 1-9.

121. A. Gomez, A. Lakhtakia, M.A. Solano, and A. Vegas, Parallel-plate waveguides

with Kronig-Penney morphology as photonic band-gap filters, Microw Opt Technol

Lett 36 (2003), 4-8; correctly reprinted: 38 (2003), 511-514.

122. A. Gomez, M.A. Solano, A. Lakhtakia, and A. Vegas, Circular waveguides with

53

Kronig-Penney morphology as electromagnetic band-gap filters, Microw Opt Tech-

nol Lett 37 (2003), 316-321.

123. M.A. Solano, A. Gomez, A. Lakhtakia, and A. Vegas, Rigorous analysis of guided

wave propagation of dielectric electromagnetic band-gaps in a rectangular waveg-

uide, Int J Electron 92 (2005), 117-130.

124. A. Gomez, A. Vegas, M.A. Solano, and A. Lakhtakia, On one- and two-dimensional

electromagnetic band gap structures in rectangular waveguides at microwave fre-

quencies, Electromagnetics 25 (2005), 437-460.

125. I.L. Lyubchanskii, N.N. Dadoenkova, M.I. Lyubchankskii, E.A. Shapovalov, A.

Lakhtakia, and Th. Rasing, Spectra of bigyrotropic magnetic photonic crystals,

Phys Stat Sol (a) 201 (2004), 3338-3344.

126. I.L. Lyubchanskii, N.N. Dadoenkova, M.I. Lyubchankskii, E.A. Shapovalov, A.

Lakhtakia, and Th. Rasing, One-dimensional bigyrotropic magnetic photonic crys-

tals, Appl Phys Lett 85 (2004), 5932-5934.

127. A. Lakhtakia and R.A. Depine, On Onsager relations and linear electromagnetic

materials, AEU Int J Electron Commun 59 (2005), 101-104.

128. A. Lakhtakia, On the genesis of Post constraint in modern electromagnetism, Optik

115 (2004), 151-158.

129. A. Lakhtakia, Conjugation symmetry in linear electromagnetism in extension of ma-

terials with negative real permittivity and permeability scalars, Microw Opt Technol

Lett 40 (2004), 160-161.

130. A. Lakhtakia, Beltrami field phasors are eigenvectors of 6×6 linear constitutive

dyadics, Microw Opt Technol Lett 30 (2001), 127-128.

54

131. A. Lakhtakia, Conditions for circularly polarized plane wave propagation in a linear

bianisotropic medium, Electromagnetics 22 (2002), 123-127.

132. A. Lakhtakia, A representation theorem involving fractional derivatives for linear

homogeneous chiral mediums, Microw Opt Technol Lett 28 (2001), 385-386.

133. J. Gerardin and A. Lakhtakia, Conditions for Voigt wave propagation in linear,

homogeneous, dielectric mediums, Optik 112 (2001), 493-495.

55

PERSONAL PROFILE

Akhlesh Lakhtakia was born in Lucknow, UP, India on July 1,

1957. He received his B.Tech. degree in Electronics Engineer-

ing from Banaras Hindu University (1979), and his M.S. and

Ph.D. degrees in Electrical Engineering from the University of

Utah, Salt Lake City, USA (1981 & 1983). Joining the Penn-

sylvania State University in USA as a post-doctoral scholar in

1983, he is now Distinguished Professor of Engineering Science

and Mechanics. In 2004, he was appointed to a three-year term

as Visiting Professor of Physics at Imperial College, London.

He has published more than 530 journal articles; contributed chapters to 14 research

books and encyclopedias; edited, co-edited, authored or co-authored eleven books and

six conference proceedings; and reviewed for 85 journals. He was the Editor-in-Chief

of the international journal Speculations in Science and Technology from 1993 to 1995,

and is on the editorial boards for four electromagnetics and optics journals. He headed

the IEEE EMC Technical Committee on Nonsinusoidal Fields from 1992 to 1994, served

as the 1995 Scottish Amicable Visiting Lecturer at the University of Glasgow, and held

short-term visiting professorships at the University of Buenos Aires, Argentina (1990 &

1992) and the University of Otago, Dunedin, New Zealand (2004).

He is a Fellow of the Optical Society of America, SPIE–International Society for

Optical Engineering, and the Institute of Physics (UK). He was awarded the PSES Out-

standing Research Award in 1996, and the PSES Outstanding Advising Award in 2005.

He was also awarded the Faculty Scholar Medal in Engineering in 2005. His current re-

search interests lie in the electromagnetics of complex mediums, nanotechnology, and the

socioethical and educational implications of nanotechnology.

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