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ptics ofNanomaterials

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Vladimir I. GavrilenkoNorfolk State University, USA

ptics ofNanomaterials

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Published by

Pan Stanford Publishing Pte. Ltd.

Penthouse Level, Suntec Tower 38 Temasek BoulevardSingapore 038988

Email: editorial@panstanford.comWeb: www.panstanford.com

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.

OPTICS OF NANOMATERIALS

Copyright c© 2011 by Pan Stanford Publishing Pte. Ltd.

All rights reserved. This book, or parts thereof, may not be reproduced in any formor by any means, electronic or mechanical, including photocopying, recording or

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For photocopying of material in this volume, please pay a copying fee through theCopyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA.In this case permission to photocopy is not required from the publisher.

ISBN 978-981-4241-09-0 (Hardcover)ISBN 978-981-4241-23-6 (eBook)

Printed in Singapore

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Dedicated to Ludmila, Natasha, Alexander, Alena, and Joshua

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Contents

List of Figures xi

List of Tables xxxi

Preface xxxiii

1. Fabrication and Classification of Nanomaterials 1

1.1 A Brief Overview of Basic Fabrication Techniques . . . . . . . . . 21.2 Nanomaterials Based on Pure Carbon . . . . . . . . . . . . . . . . 5

1.2.1 Nanostructured Bulk Carbon . . . . . . . . . . . . . . . . . 61.2.2 Carbon Nanoparticles . . . . . . . . . . . . . . . . . . . . . 71.2.3 Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . 71.2.4 Carbon Nanofibers . . . . . . . . . . . . . . . . . . . . . . 91.2.5 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3 Metallic and Metal-Based Nanoparticles . . . . . . . . . . . . . . . 121.3.1 Pure Metals . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3.2 Metal-Based Nanoparticles . . . . . . . . . . . . . . . . . . 14

1.4 Semiconductor Nanoparticles . . . . . . . . . . . . . . . . . . . . . 151.4.1 Semiconductor Quantum Wires . . . . . . . . . . . . . . . 161.4.2 II-VI Nanocrystals . . . . . . . . . . . . . . . . . . . . . . . 181.4.3 Core/Shell Nanocrystals . . . . . . . . . . . . . . . . . . . 191.4.4 Wide-Band-Gap Nanomaterials . . . . . . . . . . . . . . . 201.4.5 Hollow Nanoparticles . . . . . . . . . . . . . . . . . . . . . 23

1.5 Assembled Nanoparticles and Nanostructures . . . . . . . . . . . . 261.6 Nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.7 Nanostructured and Nanocomposite Polymers . . . . . . . . . . . . 281.8 Biological Nanomaterials . . . . . . . . . . . . . . . . . . . . . . . . 29

2. Basics of Nanomaterials Optics 33

2.1 Electrons in a Quantum Well . . . . . . . . . . . . . . . . . . . . . 332.2 Electrons under One-Dimensional Confinement . . . . . . . . . . . 34

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2.2.1 Two-Dimensional Electrons in a Silicon Thin Film . . . . . 352.2.2 Two-Dimensional Electrons in Graphene . . . . . . . . . . 36

2.3 Particle in Spherically Symmetric Potential . . . . . . . . . . . . . 392.4 Description of the Electromagnetic Field in Media . . . . . . . . . 432.5 Semiclassical Theory of Linear Optical Response . . . . . . . . . . 462.6 Semiclassical Theory of Nonlinear Optical Response . . . . . . . . 482.7 Optical Response from First Principles . . . . . . . . . . . . . . . . 502.8 Effect of the Local Field in Classical Optics . . . . . . . . . . . . . 532.9 Optical Local Field Effect from First Principles . . . . . . . . . . . 54

3. Nanoscale Optics 59

3.1 Plasma Excitations in Optics . . . . . . . . . . . . . . . . . . . . . 593.2 Plasmon Resonance in Spherical Nanoparticles . . . . . . . . . . . 623.3 Effective Medium Approximations in Optics of Nanomaterials . . . 673.4 Electromagnetic Field Enhancement in Metallic Nanostructures . . 683.5 Plasmons in Hollow Nanoparticles . . . . . . . . . . . . . . . . . . 753.6 Negative-Index Materials . . . . . . . . . . . . . . . . . . . . . . . 773.7 Near-Field Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4. Optical Absorption and Fluorescence of Nanomaterials 89

4.1 Metallic Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . 894.2 Nanostructures Based on Metallic Alloys . . . . . . . . . . . . . . . 994.3 Metallic Nanowires . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.4 Semiconductor Nanowires . . . . . . . . . . . . . . . . . . . . . . . 1044.5 Semiconductor Nanoparticles . . . . . . . . . . . . . . . . . . . . . 109

4.5.1 Nanoparticles of II–VI Materials . . . . . . . . . . . . . . . 1094.5.2 Group III Nitride Nanomaterials . . . . . . . . . . . . . . . 1134.5.3 Nanocrystalline Group IV Materials . . . . . . . . . . . . . 116

5. Excitons in Quantum Confined Systems 119

5.1 Excitons in Bulk Materials . . . . . . . . . . . . . . . . . . . . . . 1205.2 Two-Dimensional Excitons on Surfaces and Interfaces . . . . . . . 1235.3 One-Dimensional Excitons in Quantum Wires . . . . . . . . . . . . 1245.4 Analysis of Excitons in Quantum Dots within Effective Mass

Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1265.5 Excitons in Quantum Dots beyond Effective Mass Approximation . 1325.6 Experimental Studies of Excitons in Quantum Dots . . . . . . . . 1355.7 Multiexcitons in Quantum Dots . . . . . . . . . . . . . . . . . . . . 139

6. Raman Spectroscopy of Nanomaterials 149

6.1 Basics of the Raman Scattering . . . . . . . . . . . . . . . . . . . . 1506.2 Light Scattering Mechanisms . . . . . . . . . . . . . . . . . . . . . 151

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6.3 Raman Scattering of Quantum Dots . . . . . . . . . . . . . . . . . 1526.4 Exciton Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . 1556.5 Effects of Quantum Confinement on Raman Spectra . . . . . . . . 1606.6 Surface-Enhanced Raman Scattering of Nanostructures . . . . . . 1656.7 Electromagnetic Mechanism of SERS . . . . . . . . . . . . . . . . . 1696.8 Chemical Mechanism of SERS . . . . . . . . . . . . . . . . . . . . . 1726.9 Toward Microscopic Understanding of SERS . . . . . . . . . . . . . 175

7. Coherent Optical Spectroscopy of Quantum Dots 181

7.1 Interaction of Quantized Optical Field with Atomic System . . . . 1837.2 Rabi Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1847.3 Dressed Electronic States . . . . . . . . . . . . . . . . . . . . . . . 1867.4 Quantum Dots in a Coherent Optical Field: Strong and Weak

Coupling Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 1877.5 Quantum Dots in Photonic Crystals . . . . . . . . . . . . . . . . . 1897.6 Optical Absorption of Quantum Dots in a Strong Coherent

Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1927.7 Photoluminescence of Quantum Dots in a Strong Coherent

Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

8. Nonlinear Optics of Nanomaterials and Nanostructures 201

8.1 Nonlinear Optical Response from Nanocrystals . . . . . . . . . . . 2028.2 Second Harmonic Generation from Surfaces and Interfaces . . . . . 2058.3 Electro-Optical Modulation Spectroscopy of Nanostructures . . . . 2158.4 Plasma Resonance Enhancement of Nonlinear Optical Response in

Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2198.5 Nonlinear Optics of Nanostructured Metamaterials . . . . . . . . . 221

9. Optics of Organic Nanomaterials 227

9.1 Organic Molecules and Molecular Aggregates . . . . . . . . . . . . 2289.2 Molecular Nanocrystals . . . . . . . . . . . . . . . . . . . . . . . . 2349.3 Inorganic-Organic Nanocomposites . . . . . . . . . . . . . . . . . . 2389.4 Nanocomposite Conjugated Polymers . . . . . . . . . . . . . . . . 2439.5 Polymer-Based Nanostructures . . . . . . . . . . . . . . . . . . . . 255

10. Optics of Biological Nanomaterials 261

10.1 Optical Labeling of Biological Nanomaterials . . . . . . . . . . . . 26210.2 Fluorescent Nanocrystals for Optical Labeling . . . . . . . . . . . . 26510.3 Single-Molecule Fluorescence as Biolabels . . . . . . . . . . . . . . 26610.4 Raman-Active Labels for Tissue Analysis . . . . . . . . . . . . . . 26910.5 Surface Plasmon Resonance for Biosensing . . . . . . . . . . . . . . 272

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Appendix A Thomas–Fermi Approximation and Basics of theDensity Functional Theory 279

Appendix B Evaluation of Optical Functions within thePerturbation Theory 285

Appendix C Local Field Effect in Optics of Solids from theFirst Principles 291

Appendix D Optical Field Hamiltonian in Second QuantizationRepresentation 293

Appendix E Surface Plasmons and Surface Plasmon Polaritons 295

Bibliography 301

Index 327

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List of Figures

1.1 Single-wall carbon nanotubes of different types: (a) armchair (left),zigzag (middle) and chiral (right) type, which show different electronicbehavior because of their structure. (b) A multi-wall carbon nanotube,where the several nanotubes have different diameters. . . . . . . . . . . 8

1.2 Schematic structure of carbon nanofibers and nanotubes. (a) Graphenelayer, (b) stacked cone (herringbone) nanofiber, and (c) nanotube.(Adapted from [Meleshko et al. (2005)].) . . . . . . . . . . . . . . . . . . 10

1.3 Mechanism of carbon nanofiber formation. (a) Adsorption and decom-position of the reactant hydrocarbon molecule on the surface of the cat-alyst. (b) Dissolution and diffusion of carbon species through or aroundthe metal particle. (c) Precipitation of carbon on the opposite surface ofthe catalyst particle and incorporation into graphene layers. (Adaptedfrom [Meleshko et al. (2005)].) . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Schematic illustration of the fabrication processes of V-shapedGaAs/AlGaAs QWRs: (a) preparation of photoresist pattern, (b) for-mation of V grooves by wet chemical etching, and (c) growth ofGaAs/AlGaAs heterostructures to realize QWRs at the bottom of theV groove. (Adapted from [Wang and Voliotis (2006)].) . . . . . . . . . . 17

1.5 Cross-sectional TEM image of a vertically stacked GaAs/Al0.42Ga0.58

As QWR sample grown at 20 mbars, and 650◦ C on a 3.5 μm pitchedV-grooved substrate by continuous MOVPE. (Adapted from [Gustafssonet al. (1995)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.6 Schematic of a core and core/shell nanocrystal. The core nanocrystal iscoated with a wide-band-gap semiconductor to passivate the core surfacein order to increase radiative recombination processes. Any uncoatedsurface could provide possible trap sites that result in nonradiative re-combination and a reduction in fluorescence quantum yield. (Adaptedfrom [Rosenthal et al. (2007)].) . . . . . . . . . . . . . . . . . . . . . . . 20

xi

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1.7 (a) GaN/AlN nanostructures obtained at a V/III ratio of 20 with silaneincorporation; (b) 2D growth at a V/III ratio of 4.5 without silane; (c)sample grown under the same conditions as in (1.7(b)), but with anactivation step including a temperature ramp up to 970◦C applied afterthe GaN deposition. The activation step enhances 3D growth. (Adaptedfrom [Gupta et al. (2006)].) . . . . . . . . . . . . . . . . . . . . . . . . 21

1.8 (a) Zero percent Mn samples show 2D like behavior; (b) Mn incorpora-tion enhances nucleation which results in 3D growth, and in increasedisland density and reduced lateral dimension; (c) Activation step above880◦C in GaMnN nanostructures leads to ripened islands. (Adaptedfrom [Gupta et al. (2006)].) . . . . . . . . . . . . . . . . . . . . . . . . 22

1.9 (a) Scanning electron micrograph of a GaN nanowire array consisting of1 μm GaN nanowires (the plan view in the inset shows the hexagonalsymmetry of the nanowires); (b) a lower magnification SEM image re-veals the long-range order of the GaN nanowire arrays. (Adapted from[Hersee et al. (2006)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.10 The sulfidation process of Cd nanoparticles. Solid cadmium particles(left) are exposed to elemental sulfur, leading to partially sulfidized struc-tures, with a Cd core remaining inside a polycrystalline CdS shell (cen-ter). Longer reaction times lead to fully hollow CdS structures (right).(Adapted from [Cabot et al. (2008)].) . . . . . . . . . . . . . . . . . . . 24

1.11 TEM micrographs from six aliquots at different stages of the CdS shellgrowth, from the initial Cd particles (panel A) to the final CdS hollowparticles (panel F). The scale bar corresponds to 500 nm. (Adapted from[Cabot et al. (2008)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.12 I. SEM image of ordered silica microspheres asymmetrically coatedwith Ag nanoparticles. II. SEM image of the ordered Ag nanoparticle-doped polymer voids. The insets are high-magnification SEM images.(Adapted from [Sun and Yang (2006)].) . . . . . . . . . . . . . . . . . . 26

1.13 Design (a) and modeling (b) of DNA nanotubes. (Adapted from [Rothe-mund et al. (2004)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1 Spatial distribution of electron density in an infinitely high one-dimensional quantum well. (Adapted from [Gavrilenko and Koch (1995)].) 34

2.2 Spatial distribution of electron density within silicon slabs of differentthicknesses. Right-scale numbers indicate absolute electron level ener-gies (in eV) with respect to the top valence level of the 28-layer slabs.(Adapted from [Gavrilenko and Koch (1995)]). . . . . . . . . . . . . . . 36

2.3 Perspective view of the computer-simulated atomic structure ofmonocrystalline graphite. . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.4 Computer-simulated atomic structure of graphene. . . . . . . . . . . . . 37

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List of Figures xiii

2.5 Dispersion relations of graphene from the one parameter tight-bindingmodel over the central hexagonal Brillouin zone of the 2D reciprocallattice of graphene, with two of the inequivalent (under translationalsymmetry) high-symmetry K points at the corners of the zone labeledK and K ′. (Adapted from [White and Mintmire (2005)].) . . . . . . . . 38

2.6 Cyclotron mass mc of electrons and holes as a function of their concen-tration. Symbols are experimental data, and solid curves the best fit totheory. (Adapted from [Novoselov et al. (2005a)].) . . . . . . . . . . . . 38

2.7 A honeycomb lattice with vacancies. (a) The primitive lattice vectors.(b) Density of states, ρ(ω), multiplied by the cutoff energy D as a func-tion of energy ω (in units of D) for different values of the impurity density(ni). (Adapted from [Peres et al. (2006)].) . . . . . . . . . . . . . . . . . 39

2.8 A typical coordinate dependence of the electron potential energy. Byx0 the equilibrium position of electrons in an atom is indicated. Thedashed line shows the parabolic function. . . . . . . . . . . . . . . . . . 47

2.9 Macroscopic dielectric constant of silicon vs. the number of reciprocallattice vectors. The circles indicate the effect of local field correction andthe dots show the effect of additional nonlocal (exchange-correlation)contributions. (Adapted from [Gavrilenko and Bechstedt (1997)].) . . . 56

3.1 Rose window of the Cathedral of Notre Dame de Paris. (Adapted from[Link and El-Sayed (2003)].) . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2 Detail of a window in the Altenberg Cathedral (near Cologne). The red-colored stained glass consists of small gold colloid particles residing in aglass matrix. (Adapted from [Freund (2002)].) . . . . . . . . . . . . . . 61

3.3 Plasmon oscillation for a sphere, showing the displacement of the conduc-tion electron charge cloud relative to the nuclei. (Adapted from [Kellyet al. (2003)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.4 (a) Real and imaginary part of silver dielectric constants as functionof wavelength. Data are from Lynch and Hunter by [Palik (1985)]; (b)Extinction efficiency for a silver sphere with the radius of 30 nm. (c)The corresponding efficiency for a 60 nm particle, including for quadrupleeffects, and correcting for finite wavelength effects. The exact Mie theoryresult is plotted for comparison. (Adapted from [Kelly et al. (2003)].) . 64

3.5 Absorption spectra of 9, 22, 48, and 99 nm gold nanoparticles in water.All spectra were normalized at their absorption maxima, which are 517,521, 533, and 575 nm, respectively. (Adapted from [Link and El-Sayed(1999)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.6 The enhancement factor of the SHG efficiency GSHG on a silver homo-geneous film as a function of the wavelength (a). Effect of the addi-tional enhancement of the GSHG due to the fluctuation mechanism (b).(Adapted from [Shalaev and Sarychev (1998)].) . . . . . . . . . . . . . 70

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xiv List of Figures

3.7 The dipolar optical absorption as a function of frequency of a singlenanosphere outside the films. The polarization of the incident wave isperpendicular to the surface (m = 0). A small damping of δ = 0.1 eVwas added when calculating the imaginary part of the polarizability ofthe nanosphere. (Adapted from [Nordlander and Le (2006)].) . . . . . . 72

3.8 Extinction spectrum and local field enhancements calculated for a sphereof radius 25 nm over a slab of thickness 4 nm and lateral dimension L×L

for L = 200 nm with a sphere–slab separation of 4 nm. Panels A−Dare the local field enhancements for peaks A−D labeled in the extinctionspectrum, respectively. The maximum electric field enhancements are A(17.8), B (10), C (31.8), and D (32.1). The incident light is polarizedperpendicularly to the slab surface. The metal dielectric functions areDrude with a plasmon frequency of 9 eV and a damping of 0.1 eV. Thegrid size is 1 nm. (Adapted from [Nordlander and Le (2006)].) . . . . . 74

3.9 Schematic illustration of plasmon resonance in solid metal nanoparticle(a), nanorod (b), hollow nanoparticle (c), and aggregate (d). (Adaptedfrom [Schwartzberg and Zhang (2008)].) . . . . . . . . . . . . . . . . . 76

3.10 UV–visible absorption spectra of nine hollow gold nanoparticles withvarying diameters and wall thicknesses. (Adapted from [Schwartzberget al. (2006)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.11 Materials with negative refraction are sometimes called left-handed ma-terials because the Poynting vector has the opposite sign to the wavevector. (Adapted from [Pendry (2004)].) . . . . . . . . . . . . . . . . . . 78

3.12 In a double-negative material as described by Veselago (1968), lightmakes a negative angle with the normal, but the energy flow is oppositeto the wave vector. (Adapted from [Pendry (2004)].) . . . . . . . . . . . 78

3.13 Contour plots of the Ez component of the electric field as computed at12.6 GHz. The radiation propagates from left to right. The wedge anglewas 32.19◦. Right (left) panel corresponds to the Teflon wedge n = 1.4(negative-index material wedge). (Adapted from [Parazzoli et al. (2003)].) 79

3.14 Measured angular profile of the normalized electric field amplitude Ez(r),at a constant frequency f = 12 : 6 GHz for detector distances of 33 and66 cm from the Teflon and 901 HWD negative-index material (NIM)wedges (a). Measured 33 cm data compared to simulated results at 33,66, and 238 cm (100λ) from the Teflon and 901 HWD NIM wedges (b).(Adapted from [Parazzoli et al. (2003)].) . . . . . . . . . . . . . . . . . 80

3.15 A field line within the undistorted (A) coordinate system and after ma-terial related controllable distortions (B). The field line can representthe electric displacement field D, the magnetic field intensity B, and/orthe Poynting vector S. (Adapted from [Pendry et al. (2006)].) . . . . . 82

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3.16 A field line within the undistorted (A) coordinate system and after ma-terial related controllable distortions (B). The field line can representthe electric displacement field D, the magnetic field intensity B, and/orthe Poynting vector S. (Adapted from [Pendry et al. (2006)].) . . . . . 83

3.17 A ray-tracing picture for the point light source located near the cloakedsphere. The optical field is excluded from the cloaked region, but emergesfrom the cloaking sphere undisturbed. (Adapted from [Pendry et al.(2006)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.18 Optical imaging approach to reduce out-of-focus light and diffraction-induced reduction in resolution. Either apertures can be placed in theexcitation and in the detection path (confocal principle). (Adapted from[Lewis et al. (2003)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.19 The approaches to reduce out-of-focus light and diffraction-induced re-duction in resolution prism illumination based on evanescent wave prin-ciple (a) and on near-field optical principle using ultrashort pulse exci-tation (b). (Adapted from [Lewis et al. (2003)].) . . . . . . . . . . . . . 85

3.20 The vector-field imaging apparatus combines an apertureless SNOMwith a polarizer, which allows it to map both the strength and direc-tion of electric-field vectors. (Adapted from [Lee (2007)].) . . . . . . . . 87

4.1 Absorption spectra of 22 nm gold nanodots (dotted line) and goldnanorods having an aspect ratio of 3.3 (solid line). The inset showsthe dependence of the transverse (squares) and longitudinal (circles)plasmon absorption maxima on the aspect ratio (a). The inset showshow the maxima of the transverse (squares) and longitudinal (spheres)surface plasmon modes vary with aspect ratio. Absorption spectrum ofgold–silver alloy nanoparticles with a gold mole fraction of 0.27 (dottedline) and the calculated Mie spectrum. (Eq. (3.5)) (b). (Adapted from[Link and El-Sayed (2003)].) . . . . . . . . . . . . . . . . . . . . . . . . 92

4.2 Absorption (a) and luminescence (b) spectra of colloidal gold nanorodswith aspect ratios of 2.6, 3.3, and 5.4 (480 nm excitation). The insetshows the linear dependence of the luminescence maximum on the aspectratio. (Adapted from [Link and El-Sayed (2003)].) . . . . . . . . . . . . 94

4.3 Experimental reflectance spectrum of bulk silver and nanocrystalline sil-ver films with different particle sizes. (Adapted from [Taneja et al. (2002)].) 95

4.4 Imaginary part of the dielectric constant of silver, ε′′, calculated ac-cording to the Drude model with plasma frequency ωp = 9.1 eV andloss factor Γ = 0.021 eV (curve 1) and including both the Drude andband electron parts for bulk (curve 2) and slabs (curves 3 to 6). Theband electron part was calculated from first principles using the ab ini-tio pseudopotential method for Ag(111) nano slabs containing 7, 10, 13,and 16 monolayers. Trace 7 represents experimental data for bulk Ag[Johnson and Christy (1972)]. (Adapted from [Zhu et al. (2008)].) . . . 97

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xvi List of Figures

4.5 The measured imaginary part of the dielectric function of Ag-coupledstrips with different thickness (see the numbers) in comparison with thebulk dielectric function from Johnson and Christy (1972) (J&C) and[Lynch and Hunter (1985)] (L&H) for different polarizations: TE (a)and TM (b). (Adapted from [Drachev et al. (2008)].) . . . . . . . . . . . 98

4.6 The size-dependent effect on the damping parameter of the dielectricfunction in noble metallic nanoparticles. A = 0.25. (Adapted from[Pinchuk et al. (2004)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.7 Optical absorption spectra for the Cu/Zn colloids (a). The dashed linerepresents the spectrum before annealing, and the solid line representsthe spectrum after annealing. Measured (solid line) optical absorptionspectra for the β-brass colloids in comparison with the simulated spec-trum (dashed line) (b). (Adapted from [Suzuki and Ito (2006)].) . . . . 100

4.8 Normalized photon emission spectra of single Ag–Au alloy clusters onAl2O3/NiAl(110). The Ag content increases from 0 (top) to 100% (bot-tom). (Adapted from [Benten et al. (2005)].) . . . . . . . . . . . . . . . 101

4.9 Selection of relative IR transmittance spectra of various individual wireswith different lengths L and diameters D on different substrates. Theinset shows a scanning electron microscopy image of a gold nanowirewith L = 1.7 μm and D = 100 nm. (Adapted from [Neubrech et al.(2006)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.10 Resonance wavelength vs. wire length L for gold wires with similar D

on KBr: experimental data, detailed calculations, and simple antennamodel. (Adapted from [Neubrech et al. (2006)].) . . . . . . . . . . . . . 104

4.11 Normalized cathodoluminescence spectra of a single GaAs/Al0.45Ga0.55As QWR, obtained at 25 K with an acceleration voltage of12.5 keV. With increasing beam current several one-dimensional QWRsubbands appear in the spectra. The inset shows the full spectrum.(Adapted from [Gustafsson et al. (1995)].) . . . . . . . . . . . . . . . . . 105

4.12 Cross-sectional SEM image of a cleaved (110)-section of nanowires withaverage dimensions of 22 nm (diameter) and 1.2 μm (length), withschematic overview of crystallographic growth direction of the nanowireson the (100) GaP substrate (see inset) (a). The same for nanowireswith average dimensions of 72 nm (diameter) and 1.5 μm (length) (b).(Adapted from [Muskens et al. (2008)].) . . . . . . . . . . . . . . . . . 106

4.13 Transmitted relative intensity at a wavelength of 690 nm, as a func-tion of the azimuthal orientation of the birefringent nanowire layer, forGaP with 22 nm (black squares) and 72 nm (grey diamonds) diameternanowires grown on (100) GaP (see Fig. 4.12a and 4.12b, respectively).Insert shows experimental configuration. (Adapted from [Muskens et al.(2008)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

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4.14 Micro-PL of a single V-shaped QWR at 10 K under 200 nW pump power(a); the μPL spectrum of a 5 nm thick GaAs QWR grown on a V-groovedGaAs substrate preetched with the NH4OH solution (b). (Adapted from[Wang and Voliotis (2006)].) . . . . . . . . . . . . . . . . . . . . . . . . 107

4.15 Room-temperature photoluminescence spectra of GaN nanowire array(solid line), 5 μm planar GaN film (dashed line), and 0.6 μm thick planarGaN film (dotted line). Spectral intensity for the planar GaN films hasbeen magnified by 50. (Adapted from [Hersee et al. (2006)].) . . . . . . 109

4.16 Optical absorption spectra of series of CdSe nanocrystals synthesized inTOPO/HDA/DPA (a) and images of a representative sample of CdSecores under room lights (top) and under UV illumination (bottom) (b).(Adapted from [Rosenthal et al. (2007)].) . . . . . . . . . . . . . . . . . 110

4.17 Absorption (black) and emission (color) spectra of CdSe nanocrystalsobtained from four separate 2 mmol reactions. For each color, the growthtemperature T (◦C), the time duration (min) to reach T from 150◦ C,and the dwell time (min) at T are (a) 220◦, 3, 0; (b) 240◦, 4, 0; (c)240◦, 4, 10; and (d) 240◦, 4, 35, respectively. The inset shows the XRDpattern of the sample (b). The vertical lines represent the diffractionpatterns for bulk ZB CdSe. (Adapted from [Lim et al. (2008)].) . . . . . 111

4.18 Absorption and emission spectra of organic-soluble nanocrystals:CdSe/ZnS, (a), CdSe/ZnSe/ZnS, (b), and CdSe/CdS/ZnS nanocrystals(c). The PL spectra of nanocrystals at 5 K. The percentage of deep trapemission is given in parentheses (d). (Adapted from [Lim et al. (2008)].) 112

4.19 Photoluminescence quantum yield variation with shell thickness forthree different core/shell syntheses starting with core diameters of 23A(circles), 34 A(Xs), and 39 A(squares). (Adapted from [Peng et al.(1997)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.20 Room-temperature photoluminescence spectrum of GaN nanocrytsals onSi substrate synthesized at 650◦C (above spectrum) and the spectrumof GaN nanowires on Si substrate (below) synthesized at 750◦C usingGa2O3 nanoparticles as the self-catalysts. (Adapted from [Bhaviripudiet al. (2006)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4.21 μPL spectra of a few QDs as a function of the angle of the polarizeranalyzing the PL. The spectra are vertically offset for clarity (a), Polarrepresentation of the normalized intensity of the three lines labeled A,B, and C (circles) and their fit by Eq. (4.6)(line) (b), μPL spectra of asingle-quantum dot for two perpendicular polarizations, the spectra withvertically offset for clarity (c). Polar representation of the normalizedintensity of the main line (circles) and its fit by Eq. (4.6)(line), thepolarization degree being P = 90% (d). (Adapted from [Bardoux et al.(2008)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

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4.22 Photoluminescence spectra of nc–Si1−xGex with various Ge contents.(Adapted from [Takeoka et al. (2000)].) . . . . . . . . . . . . . . . . . . 117

5.1 Exciton levels (see footnote below) in relation to the conduction bandedge, for a simple band structure with both conduction and valenceband edges at q = 0. The curvature of the exciton levels is due totheir translational kinetic energy. (Adapted from [Cocoletzi and Mochan(2005)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.2 A singlet exciton created at the band extremum or away from it. (a);the singlet and triplet excitons are characterized by overall spin valuesS = 0 or S = 1, respectively (b). (Adapted from [Dresselhaus et al.(2007)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.3 Exciton energy blue shift Eexc(R, σ) in In0.2Ga0.8N/GaN quantum wireswith interface thickness 5 A (dashed), 10 A (dotted), and 15 A (dotteddashed). (Adapted from [Caetano et al. (2004)].) . . . . . . . . . . . . . 126

5.4 Normalized fluorescence line narrowing spectra for CdSe QDs between12 and 56 A in radius. A 10 Hz Q-switched Nd:YAG dye laser system(∼7 ns pulses) was used as the excitation source. The laser line is shownin the figure by dotted line for reference. All spectra are measured at 10K. (Adapted from [Efros et al. (1996)].) . . . . . . . . . . . . . . . . . . 129

5.5 The size dependence of the resonant Stokes shift. This Stokes shift is thedifference in energy between the pump energy and the peak of the zerophonon line in the luminescence measurement. Symbols label the exper-imental values. The solid line is the theoretical size-dependent splittingbetween the ±1L state and the ±2 exciton ground state. (Adapted from[Efros et al. (1996)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.6 Normalized absorption and full luminescence spectra for CdSe QDs be-tween 12 and 56 A in radius. The absorption and luminescence spectraare shown by solid and dotted lines, respectively. (Adapted from [Efroset al. (1996)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.7 Comparison of the shifts predicted by theory calculated with 5% (dashedline) and 10% (dotted line) to experimental values (symbols) of the non-resonant Stokes shift measured on the samples with a 5% size distribu-tion. (Adapted from [Efros et al. (1996)].) . . . . . . . . . . . . . . . . . 132

5.8 Comparison of calculated (squares joined by lines) and measured (cir-cles) excitonic levels of CdSe nanocrystals as a function of the band-gapenergy. Solid symbols and solid lines denote optically active states, whileopen symbols and dashed lines denote optically inactive states. The en-ergy of the lowest spin-allowed optical transition (EL

±1) was taken as thezero of the energy scale. (Adapted from [Franceschetti et al. (1999)].) . 136

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5.9 Dynamics of the IR-post-pump-induced 1S bleaching changes (electronintraband dynamics) detected at different delay times between visibleand IR pump pulses for ZnS- (a) and pyridine-capped dots (b). Inset topanel (b): Schematics of electron and hole relaxation/transfer processesin pyridine-capped dots. (Adapted from [Klimov et al. (2000)].) . . . . . 137

5.10 Time-resolved spectra of absorption changes in pyridine-capped dots in-duced by the visible interband pump. Inset: Comparison of dynamicsof photo-induced absorption features below the 1S resonance for ZnS-(squares) and pyridine- (circles) capped dots. (Adapted from [Klimovet al. (2000)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

5.11 The 1SU transition shift induced by the biexciton effect in CdSe de-tected by intraband carrier relaxation measurements: after excitationwith a high-energy photons (a) and after complete relaxation of thephotogenerated carriers (b). (Adapted from [Klimov (2007)].) . . . . . 141

5.12 Normalized time-integrated (shaded area) and time-resolved photolu-minescence upconversion (μPL) spectra of CdSe nanocrystals (NCs)(R =2.1 nm; T = 300 K) measured at Δt = 1 ps (red solid line) and200 ps (blue solid circles) following excitation with a 3 eV, 200 fs pumppulse with a per-pulse fluence of 3.4 μJ cm−2(a). Single-exciton (shadedareas) and multiexciton (symbols) emission spectra extracted from the1 ps μPL spectra at different excitation densities (b). (Adapted from[Klimov (2007)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.13 The transient absorption spectra excited at (a) 2.18 (|1Se1Sh〉), (b)3.10 (|1Pe1Ph〉), and (c) 1.11 eV (|1Se1Ph〉) and linear absorbance ofCdS0.6Se0.4 nanocrystals. The spectra shown are in the initial decaystage with time intervals of 0.1 ps. The inset shows the scheme of en-ergy levels of CdS0.6Se0.4 nanocrystals. (Adapted from [Hwang et al.(2001)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.14 Biexciton binding energies calculated in the presence of excitons in var-ious quantum-confined states. The |1Se1Sh; 1Se1Ph〉 biexciton bindingenergy surpass the others in ambient nanoparticle sizes. (Adapted from[Hwang et al. (2001)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.15 The electron and hole DOS for the PbSe and CdSe QDs of varying size.(Adapted from [Prezhdo (2008)].) . . . . . . . . . . . . . . . . . . . . . . 148

6.1 Raman intensity vs. Raman shift predicted for different laser energiesfor the lp = 0, np = 1, np = 2 modes of a 20 A radius CdS sphereembedded in glass. Solid line: modeling the finite potential band offset,dashed line: infinite potential barrier. (Adapted from [Menendez et al.(1997)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

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6.2 Raman intensity as a function of laser energy for the lp = 0, np = 1mode of a 20 A radius CdS sphere embedded in glass. The differentexciton contributions are shown in the figure (N = 1, 2, and 3 excitonicstates). (Adapted from [Menendez et al. (1997)].) . . . . . . . . . . . . . 157

6.3 Intensity of the Raman scattering as a function of the Raman shift (incm−1) measured at T = 5K from CdSe nanocrystals in a glass matrix(open circles). The nanocrystals had different average radius (3.8 nm(a) and 1.8 nm (b)) and different photon excitation energies: 2.182 eV(a) and 2.707 eV (b). Theoretical spectra are shown by lines. Thedifferent exciton contributions to the calculated line shape are shown in(a). Dashed line: N = 1 excitonic state; dotted line: N = 3 excitonicstate; and solid line: N = 2 excitonic state. (Adapted from [Trallero-Giner et al. (1998)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

6.4 The outer shell to bulk volume ratio in nanospheres with diameter D andan external interphase of constant thickness t. The schematic details thedifferent contributions to the Raman spectrum. (Adapted from [Gouadecand Colomban (2007)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6.5 Intensity of the Raman scattering as a function of the Raman shift (incm−1) measured on CdSe (a) and on CdSe−CdS core-shell nanoparticles(b). (Adapted from [Singha and Roy (2005)].) . . . . . . . . . . . . . . 162

6.6 Phonon positions with respect to 1/R for various filter glass samples(indicated in the picture). The experimental values for the correspondingphonons are shown by full symbols. The dotted, full, and dashed linescorrespond to the theoretical values calculated with x = 0.8, 0.5, and0.2, respectively. (Adapted from [Verma et al. (1999)].) . . . . . . . . . 163

6.7 Raman spectra for various-size PbSe QDs at room temperature.(Adapted from [Ikezawa et al. (2001)].) . . . . . . . . . . . . . . . . . . . 164

6.8 Frequencies of the Raman peaks of PbSe QDs as functions of dot size.Solid lines represent the calculation neglecting stress on the surface,while a dashed line represents the calculation with rigid boundary con-dition. The inset represents the displacement in S01 and S21 spheroidalmode. (Adapted from [Ikezawa et al. (2001)].) . . . . . . . . . . . . . . . 165

6.9 Schematics of the regular (a) and surface enhanced (b) Raman scatter-ing. The regular Stockes Raman scattering is determined through thelight interaction with the noninteracting molecules (represented by ballsin (a)). The Raman efficiency in SERS process is determined through thelight interaction with metallic nanoparticles (big balls in (b)), with mole-cules, and by the interaction between molecules and metallic nanoparti-cles. (Adapted from [Kneipp et al. (1999)].) . . . . . . . . . . . . . . . 166

6.10 SERS spectrum for R6G adsorbed on a single Ag nanoparticle. NaCl wasadded at a concentration of 1 mM, and R6G was added at a concentrationof 7 × 10−10 M (Adapted from [Michaels et al. (1998)]). . . . . . . . . . 168

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6.11 The surface-enhanced Raman spectra obtained at different excitationwavelength from the system of Rhodamine 6G molecules coupled withAg nanoparticles. The panels correspond to the enhancement at 488nm (a), 567 nm (b), and 647 nm (c) excitation wavelength, respectively.(Adapted from [Emory et al. (1998)].) . . . . . . . . . . . . . . . . . . . 169

6.12 Frequency dependence of the square of the polarizability derivative(SPD) in the Ag10CO system. The solid and dotted-broken lines are theresults for Γ = 0 and Γ = 0.01 eV, respectively. The broken line showsthe SPD for free CO. The inserted figures are the illustrated geometryof the Ag10CO system and the experimental spectrum for the wave-length dependence of the Raman intensity observed in Ref. [DiLellaet al. (1980)]. (Adapted from [Nakai and Nakatsuji (1995)].) . . . . . . 174

6.13 Model of the dye–nanoparticle interaction geometry and schematics ofthe electron energy structure. (Adapted from [Kelley (2008)]). . . . . . 178

6.14 SERRS enhancement factor for the system having a vibrational fre-quency of 1500 cm−1, (dotted curves) and the same system with a vi-brational frequency of 750 cm−1 (solid curves) at molecular electronicorigin frequencies of 14,000 (top) and 19,000 cm−1 (bottom). (Adaptedfrom [Kelley (2008)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

7.1 Approaches to the generation of quantum light. (a) Excitation of theisolated atomic system. (b) Excitation of atomic system (or QD) withina resonator (cavity). (c) Nonlinear optical generation of two red photonsby one blue photon in nonlinear microstructure shown by box. Thesignals are quantum correlated (or entangled), as indicated by the blacklasso. (d) Conditional state preparation may increase the entanglementbetween signal and idler, if (for example) photons are subtracted fromone of the beams. (Adapted from [Walmsley (2008)].) . . . . . . . . . . 182

7.2 Experimental apparatus for quantum entanglement study. (Adaptedfrom [Raimond et al. (2001)].) . . . . . . . . . . . . . . . . . . . . . . . . 185

7.3 Measured vacuum Rabi oscillations. (Adapted from [Brune et al. (1996)].) 1867.4 Energy diagram of the atom–cavity system in the strong coupling regime

(a). Experimental setup for the observation of the dressed states (b).(Adapted from [Pinkse et al. (2000)].) . . . . . . . . . . . . . . . . . . . 187

7.5 Positioning a photonic crystal cavity mode relative to a single buriedQD. (a) AFM topography of photonic crystal nanocavity aligned to ahill from single QD. Depth is depicted by the bar on the top. (b) Electricfield intensity distribution of photonic cavity mode showing overlap fieldmaximum with the QD. (c) Photoluminescence spectrum of single QD(before cavity fabrication) showing bounded excitons excitations. (d)Photoluminescence spectrum after cavity fabrication showing emissionfrom the cavity at 942.5 nm. (Adapted from [Hennessy et al. (2007)].) . 191

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7.6 Characteristics of the strong coupling regime in the spectral domain. (a)Wavelength of the polaritons for various detunings, Δλ. Calculated spec-tral peak positions describing the strongly coupled system are plotted assolid lines, with measured peak positions extracted from photolumines-cence plotted in red and blue dots. (b) Spectra of the two anticrossingpolariton states near zero detuning. An additional peak was identifiedas the pure photonic state of the cavity. Values of Δλ are shown for eachspectrum. PL, photoluminescence; a.u., arbitrary units. (Adapted from[Hennessy et al. (2007)].) . . . . . . . . . . . . . . . . . . . . . . . . . . 192

7.7 (a) The energy-level diagram of a single neutral QD. The absorption ofthe weak probe beam by scanning either transition V or H is modifiedby the strong pump beam, which is near resonant with transition H. (b)The dressed-state picture of the system shown in (a). (Adapted from[Xu et al. (2007)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

7.8 The sample layer structure is a 100 nm aluminum mask with micron-sized apertures, 5 nm titanium, 10 nm GaAs cap, 40 nm Al0.3Ga0.7As,230 nm GaAs, InAs QDs layer, 80 nm GaAs, 500 nm GaAs Te-doped(∼5 × 107 cm−3) layer, and an electronic contact formed by the GaAssubstrate. (Adapted from [Xu et al. (2007)].) . . . . . . . . . . . . . . . 194

7.9 Autler–Townes splitting by a single QD. A strong pump drives transitionH, and a weak probe scans across transition V . (a) Probe absorptionspectra as a function of the pump intensity when the pump is on reso-nance. I0 equals 1.2 W/cm2. The solid lines are theoretical fits to thedata. The AT splitting (Rabi splitting) as a function of the square rootof the pump intensity in shown in the inset. (b) The probe absorptionspectra as a function of the pump frequency detuning with fixed pumpintensity. The lines are the theoretical fits to the data. (Adapted from[Xu et al. (2007)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

7.10 Measured Mollow absorption spectra when the strong pump and weakprobe beams couple to the same transition. The probe absorption isshown versus pump field intensity when the pump is on resonance.(Adapted from [Xu et al. (2007)].) . . . . . . . . . . . . . . . . . . . . . 196

7.11 Energy schematic and the allowed transitions in the bare (a), XH

dressed (b), and both XV and XH dressed (c) exciton–biexciton com-plex. (Adapted from [Muller et al. (2008)].) . . . . . . . . . . . . . . . 198

7.12 Splitting of exciton and biexciton emission lines with variable Rabifrequency. Panels (a), (b), and (c) show exciton emission spectra atspecific Rabi frequencies for both H and V polarizations. Horizontalaxes denote emission frequency in GHz. (Adapted from [Muller et al.(2008)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

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7.13 Emission spectrum of exciton (a, b) and biexciton (c, d) transitionsunder detuning for a fixed Rabi frequency of 2.4 GHz. Right sides ofeach panel represents the simulated data. (Adapted from [Muller et al.(2008)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

8.1 Left panel: Absorption spectra for the seven CdSe nanocrystal sampleswith the following average radii: (i) 45 A, (ii) 28 A, (iii) 23 A, (iv)17 A, (v) 13.5 A, (vi) 12 A, (vii) 11.5 A. The left arrow depicts theenergy of the inducing laser light, and the right arrow depicts the secondharmonic energy. Right panel: Representative spectra of the Hyper–Rayleigh scattering at various excitation intensities ranging between 0.05and 0.6 W, for the largest nanocrystal sample with radius of 45 showinga well-defined peak at the second harmonic frequency. (Adapted from[Jacobsohn and Banin (2000)].) . . . . . . . . . . . . . . . . . . . . . . 204

8.2 The size dependence of the normalized value of the hyperpolarizabil-ity per unit cell, β, which shows significant systematic enhancementfor small sizes. The primary contributions to the error bars is the un-certainty in the determination of nanocrystal concentrations from themeasured extinction coefficients. (Adapted from [Jacobsohn and Banin(2000)]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

8.3 Conventional experimental configuration for measuring SHG spectra inreflection from surfaces in ultrahigh vacuum. (Adapted from [Downeret al. (2001)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

8.4 Calculated valence charge-density differences between bare and unre-laxed monohydride Si(001)(2×1) surface: ρbare − ρmono. The chargemaps are cut through two vertical [110] planes located at Y = 0 (a) andY = ay (b) in the unit cell. Contours start from ±1 × 10−3 e/a.u.3 andincrease successively by a factor of

√2. Dashed (solid) lines indicate

charge accumulation (depletion) in the electron density. (Adapted from[Gavrilenko et al. (2001)].) . . . . . . . . . . . . . . . . . . . . . . . . . 207

8.5 Comparison of calculated and measured SHG spectra for p-in/p-out con-figuration. (a) Clean Si(001) (2×1), theory (solid curve) and experiment(open circles); Si(001) (2×1): H monohydride, theory (dashed curve) andexperiment (filled circles). Note strong quenching, red-shifting, and lineshape distortion of 3.35 eV (E1) peak in both theory and experiment. (b)Clean Si(001) (2×1), theory (solid curve) and experiment (open circles)as in (a), Si(001):Ge(1 ML), theory (dot-dashed curve) and experiment(diamonds); Si(001):Ge(2 ML), theory (heavy dotted curve: fully re-laxed structure; light dotted curve: reduced buckling structure) and ex-periment (open squares); Si(001):Ge(2 ML) with saturation H-coverage,theory (dashed curve) and experiment (filled squares). (Adapted from[Gavrilenko et al. (2000)].) . . . . . . . . . . . . . . . . . . . . . . . . . . 209

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8.6 Atomic structure of Si(001)(2×2) surface with one local dimer oxygenconfiguration per unit cell (a) and atomic structure of Si(001)(2×1) sur-face with an oxygen atom located on a broken back bond (b). Red- andwhite-colored balls correspond to oxygen and hydrogen atoms, respec-tively. (Adapted from [Gavrilenko (2008)].) . . . . . . . . . . . . . . . . 211

8.7 Fully relaxed atomic configuration of Si(001)–SiO2 interface. Dashedlines indicate unit cells. Red- and white-colored balls correspond tooxygen and hydrogen atoms, respectively. (Adapted from [Gavrilenko(2008)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

8.8 Calculated second harmonic generation efficiency spectra of the Si(001)–SiO2 interface corresponding to the geometry given in Fig. 8.7 (solid line)are shown in comparison to the SHG spectra calculated after removalof the bridge oxygen (dashed line). In the upper (lower) panel, thefully relaxed (unrelaxed) atomic structure of the Si(001)–SiO2 interfaceis used for optical calculations. (Adapted from [Gavrilenko (2008)].) . . 213

8.9 Calculated second harmonic generation efficiency spectra of the Si(001)–SiO2 interface in comparison with experimental data measured on oxi-dized Si(001) surface [Rumpel et al. (2006)] (lower panel) and on Si(001)–SiO2 multiple quantum well structures [Avramenko et al. (2006)] (upperpanel). (Adapted from [Gavrilenko (2008)].) . . . . . . . . . . . . . . . . 214

8.10 Band structure of 2H, 6H, 4H, and 3C SiC polytypes near theconduction-band minimum (located at M point) displayed in the Bril-louin zone for 2H. (Adapted from [Lambrecht et al. (1997)].) . . . . . . 217

8.11 Electroreflectance spectra of nc−Si films with different nanocrystal sizes,<2 nm (a), 2−3 nm (b), and ∼3 nm (c), measured at room temperature.(Adapted from [Toyama et al. (1999)].) . . . . . . . . . . . . . . . . . . 218

8.12 Apparatus for high-harmonic generation by electric field enhancementusing a nanostructure of bow-tie elements. Overall system configurationand zoomed-out view of a single gold bow-tie element interacting withthe incident pulse. Abbreviations: CM, chirped mirror; CW, chamberwindow; FL, focusing lens; M, mirror; PM, photon multiplier; VLSG,varied-line-spacing grating; W, wedge plate; E, electric field; EUV, ex-treme ultraviolet radiation. (Adapted from [Kim et al. (2008b)].) . . . . 220

8.13 Measured spectrum of the generated high harmonics enhanced by plasmaresonance in nanostructure. (Adapted from [Kim et al. (2008b)].) . . . . 221

8.14 Optical transmittance spectra measured on two split-ring resonators ar-rays having two different ring sizes, 220×305 nm2 (a) and 480×630 nm2

(b). The blue bars highlight the corresponding second harmonic sig-nal strengths, normalized to the strongest SHG signal. (Adapted from[Klein et al. (2006)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

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9.1 Exciton splitting in dimers of various geometry. Orientations of themonomer transition dipoles are represented by short arrows. Dipole-forbidden transitions are indicated by dashed lines, and dipole-allowedtransitions by solid lines. The dotted line present for parallel geometriesrepresents nonradiative deactivation to the nonfluorescent, lower-energystate. (Adapted from [Pope and Swenberg (1982)].) . . . . . . . . . . . 229

9.2 Optical absorbance spectra of R6G films at surface coverage correspond-ing to (a) 0.5 monolayers, (b) 1.0 monolayers, (c) 1.3 monolayers, (d) 1.7monolayers, (e) 2.2 monolayers, and (f) 10 monolayers. Note that theabsorbance spectrum labeled f has been scaled by a factor of 2 for easeof comparison with the lower surface coverage spectra. (Adapted from[Kikteva et al. (1999)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

9.3 Predicted equilibrium geometry of H- (a) and J-type (b) dimers of R6Gmolecules. Note the predicted twisted angle of 28◦ and opposite orienta-tion of dipole moments of neighboring molecules in H dimer. Atom typeis indicated on a gray scale as follows: hydrogen (white), carbon (gray),oxygen (dark gray), and nitrogen (black). (Adapted from [Gavrilenkoand Noginov (2006)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

9.4 Calculated optical absorption spectra of H- (a) and J-type (b) dimersof R6G molecules (bold lines) in comparison with that of single R6Gmolecule (dotted line). Weakly allowed transitions to the antisymmetri-cal states in H dimer (due to the twisting) result in a small red-shiftedpeak indicated by the arrow. (Adapted from [Gavrilenko and Noginov(2006)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

9.5 Chemical formulas for para-hexaphenylene (top), symmetrically func-tionalized para-quaterphenylenes (middle), and nonsymmetrically func-tionalized para-quaterphenylenes (bottom). (Adapted from [Schiek et al.(2008)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

9.6 Fluorescence microscopy image obtained at the excitation wavelengthof 365 nm of mutually parallel, blue-light-emitting methoxy-cyano-p-quaterphenylene (MOCNP4) fibers on muscovite mica. Image area was135 × 100 μm2. (Adapted from [Schiek et al. (2008)].) . . . . . . . . . . 235

9.7 Nonlinear optical emission spectra of MOCLP4, MONHP4, and p6Pnanofibers following 100 fs infrared laser excitation at 790 nm (4.5 mW).(Adapted from [Schiek et al. (2008)].) . . . . . . . . . . . . . . . . . . . 236

9.8 The extinction (solid line) and the scattering (dashed line) spectra ofpoly-DCHD nanocrystals in suspensions in dependence on the statis-tically estimated mean long axis value. (Adapted from [Volkov et al.(2004)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

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xxvi List of Figures

9.9 Optical absorption spectra of Ag nanoparticles on various substrates:(A) fused silica (λmax = 611 nm). (B) Borosilicate optical glass (λmax =616 nm). (C) Mica (λmax = 622 nm). (D) SF-10 (λmax = 635 nm) ina N2 environment. The spectra have been vertically spaced for clarity.(Adapted from [Malinsky et al. (2001)].) . . . . . . . . . . . . . . . . . . 240

9.10 Spectral position of plasma resonance wavelength as a function of particlearea in contact with substrate. The calculations were performed for aAg core of radius 10 nm and a partial mica shell of radius 30 nm. Theembedding was changed by truncating the mica shell along the verticalaxis at different levels, as depicted. (Adapted from [Malinsky et al.(2001)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

9.11 Morphology of gold particle arrays on ITO substrates after 355 nm laserirradiation with different numbers of pulses: (a) 40 pulses and (b) 500pulses. (Adapted from [Sun et al. (2005)].) . . . . . . . . . . . . . . . . 241

9.12 Optical absorption spectra of gold particle arrays on quartz versuslaser irradiation with the indicated number of laser pulses. Inset: thecorresponding morphology of individual dots at each irradiation dose.(Adapted from [Sun et al. (2005)].) . . . . . . . . . . . . . . . . . . . . . 242

9.13 Cross-sectional scanning electronmicroscopy (SEM) image (a) and sketchof the ASOS device (b), which combines the concepts of a solid-statenanocrystal-sensitized solar cell and a nanocrystal/polymer-blend solarcell. ITO: indium tin oxide. (Adapted from [Gunes et al. (2006)].) . . . 244

9.14 Electronic configuration contributing to the ground state S0 and thelowest singlet excited states S1 and S2 of octatetraene (a); thedimerization of the geometric structure due to the uneven distributionof the π electrons over the bonds (b). (Adapted from [Bredas et al.(1999)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

9.15 Experimental absorption and photoluminescence spectra measured at77 K of PPV oligomers containing two to five rings. (Adapted from[Bredas et al. (1999)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

9.16 (a) Structure of the Th6 cofacial dimer. (b) Sketch of the one-electronlevels for the Th6 isolated chain (left) and a cofacial dimer in the caseof strong interaction (right). (Adapted from [Bredas et al. (1999)].) . . 249

9.17 (a) Structure of the Th6 cofacial dimer. (b) Sketch of the one-electronlevels for the Th6 isolated chain (left) and a cofacial dimer in the caseof strong interaction (right). (Adapted from [Bredas et al. (1999)].) . . 250

9.18 (a) Chemical structure of PTV. (b) Optical absorption spectradependence on heating and sonification treatment of PTV polymersat the concentration of 1 mM. (Adapted from [Gavrilenko et al.(2008b)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

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List of Figures xxvii

9.19 3D view of the PTV unit cell and equilibrium geometries of straight andtilted chain configurations. Optimized unit cell dimensions are shownby numbers. (Adapted from [Gavrilenko et al. (2008b)].) . . . . . . . . . 253

9.20 Total energy of the system vs. PTV unit cell length d2. Dashed andsolid lines correspond to straight and tilted chain geometries shown inparts b and c of Fig. 9.19, respectively. (Adapted from [Gavrilenko et al.(2008b)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

9.21 Calculated optical absorption spectra for the PTV configurations (a)shown in parts (b) and (c) of Fig. 9.19. Comparison of experimentalspectrum coresponding to low-heating and sonification treatment of thePTV polymer, solid (black) line, and the calculated optical absorptionspectra including contributions of the two (tilted and untilted) predictedphases shown in (a), dashed (blue) line (b). (Adapted from [Gavrilenkoet al. (2008b)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

9.22 Several equilibrium morphologies of block copolymers frequently usedfor nanofabrication. Diblock copolymers: body-centered cubic-packedspheres structure (1), haxagonally ordered cylinders (2), lamellae (3); tri-block copolymers: lamellae (4), hexagonal coaxial cylinders (5), spheresbetween lamellae (6); for amphiphilic copolymer in solution: sphericalmicells (7), and cylindrical micells (8). Typical periodicity of the micel-lar dimensions are in the range 10–100 nm. (Adapted from [Lazzari andLopez-Quintela (2003)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

9.23 Reflectivity of a self-assembled layered styrene isoprene diblock copoly-mer. The structure has CdSe nanocrystallites, which enhance the dielec-tric contrast between the layers. (Adapted from [Fink et al. (1999)].) . . 257

9.24 Fluorescence emission spectra from CdSe/CdS QD encoded on plasti-cized PVC, in response to different sodium activities in acetate buffersat pH 4.8. (Adapted from [Xu and Bakker (2007)].) . . . . . . . . . . . 258

9.25 Optical absorption (A) and photoluminescence (PL) spectra (B) of L-cysteine-capped CdTe QDs grown at 180◦C (growth time is given ininserts). (Adapted from [Cao et al. (2007)].) . . . . . . . . . . . . . . . . 259

10.1 Currently used bioconjugation methods. (a) Use of a bifunctional ligand(e.g., mercaptoacetic acid) for linking QDs to biomolecules. (b) TOPO(tri-n-octylphosphine oxide)-capped QDs bound to a modified acrylicacid polymer by hydrophobic forces. (c) QD solubilization and biocon-jugation using a mercaptosilane compound [Bruchez et al. (1998)]. (d)Positively charged biomolecules are linked to negatively charged QDs byelectrostatic attraction [Murray et al. (2000)]. (e) Incorporation of QDsin microbeads and nanobeads. (Adapted from [Chan et al. (2002)].) . . 264

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xxviii List of Figures

10.2 Size- and material-dependent fluorescence spectra of semiconductornanocrystals having silica shell. The blue series represents different sizesof CdSe nanocrystals with average diameters of 2.1, 2.4, 3.1, 3.6, and4.6 nm (from right to left). The green series is of InP nanocrystals withdiameters of 3.0, 3.5, and 4.6 nm. The red series is of InAs nanocrystalswith diameters of 2.8, 3.6, 4.6, and 6.0 nm. (Adapted from [Bruchezet al. (1998)]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

10.3 Energy transfer study by single-molecule fluoresce measurements ofsurface-tethered molecules. (a) The single molecule (the Holliday junc-tions) was tethered via biotin-neutravidin conjugation on the bovineserum albumin coated surface. The fluorescence was excited by theevanescent wave created via total internal reflection. (b) The time-resolved fluorescence of the Cy3 and Cy5 dyes attached to the Hollidayjunction. Adapted from [Joo et al. (2008)] . . . . . . . . . . . . . . . . 267

10.4 Single-particle tracking of a motor protein. (a) The hand-over-handmechanism predicts a sequence of large (37 + 2x nm) and small (37 −2x nm) steps. (b) The stepwise motility (52 and 23 nm) of the myosin Vlabeled with bifunctional rhodamine. (Adapted from [Yildiz and Selvin(2005)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

10.5 COIN encapsulation and functionalization method for SERS diagnosticsof biomolecules. (a) Encapsulation procedure. Bovine serum albumin(BSA) was coated to the COIN surface and cross-linked by glutaralde-hyde. (b) Functionalization procedure. Carboxylic acid groups on thesurface of the BSA encapsulation layer were activated by EDC and re-acted with amines groups in the antibody. (Adapted from [Sun et al.(2007)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

10.6 Multiplex SERS analysis of protein bounded with COIN. (a) A duplexdirect binding analysis detecting PSA and CK18 analytes. The PSA andCK18 proteins were immobilized together in the same well. (b) Ramansignal intensities from the measurements using different concentrationratios of CK18 and PSA immobilized proteins. (c) Raman spectra ofduplex direct binding measurements in a well coated with both PSA andCK18 (upper line). The blue (lower) and red (center) lines represent sin-gle spectra from BFU-AbPSA and R6G-AbCK18 measured in separatewells coated with only PSA or only CK18, respectively. (Adapted from[Sun et al. (2007)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

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10.7 Multiplex SERS analysis of protein bounded with COIN. (a)Light microscopy images of human tissue samples showing stroma (S),epithelium (E), and lumen (L). (b) Same image as in the part (a),with each individual square representing where a Raman spectrum wasobtained. The red squares indicate the detection of AOH, whereas theblue squares represent the detection of BFU. (c) Raman spectrum whenboth COINs are present, and the resulting deconvoluted spectra of thetwo probes, each with a unique Raman-active molecule, acridine orange(AOH) or basic fuchsin (BFU), and the background (autofluorescence,bottom line). (Adapted from [Sun et al. (2007)].) . . . . . . . . . . . . 272

10.8 Typical setup for a surface plasmon resonance (SPR) biosensor.Changes in the refractive index in the area near the surface layer ofa sensor chip result in variations of spectral characteristics of the SPR.The SPR is observed as a peak in the angular dependence of reflectedlight from the surface at an angle that is dependent on the amountof material at the surface. The SPR angle shifts (from I to II in thelower left-hand diagram) when biomolecules create bonds with thesurface atoms and change the optical constants of the surface layer.This time-dependent change in resonant angle can be monitored in realtime as shown in the plot of resonance signal versus time. (Adaptedfrom [Cooper (2002)].) . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

10.9 Schematics of a biosensor based on surface plasmon resonance fromAu nanoparticles functionalized with biotinylated BSA, which werebounded to streptavidin. (Adapted from [Raschke et al. (2003)].) . . . 274

10.10 Experimental setup facilitating dark-field microscopy of single goldnanoparticles immersed in liquids (a). True color photograph ofa sample of functionalized gold nanoparticles (b). (Adapted from[Raschke et al. (2003)].) . . . . . . . . . . . . . . . . . . . . . . . . . . 275

10.11 Measured dependence of the refractive index sensitivity on spectralpeak position in air for Au nanodisks deposited on glass substrate (redcircles), and having additional 20 nm SiO2 pillars (blue squares), and80 nm SiO2 pillars (green diamonds) compared with both the Au nano-ellipses (longitudinal resonance) fabricated directly on glass substrate(red crosses) and on additional 40 nm SiO2 pillars (ruby-red cross).(Adapted from [Dmitriev et al. (2008)].) . . . . . . . . . . . . . . . . . 276

10.12 Association and dissociation kinetics observed by the SPR absorbancechange measurements during interaction of colloidal gold nanoparticlescoated with a specific anti-TnI monoclonal antibody with three dosesof the ligand. (Adapted from [Englebienne et al. (2003)].) . . . . . . . 277

E.1 Schematic of charge and field distribution for a surface plasmondescribed by Eq. (E.9). Adapted from [Hofmann (2008)] . . . . . . . . 296

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E.2 Bold solid lines represent the dispersion of light in the retarded (upperline) and the nonretarded surface plasmon polariton regions (lower line).By the thin line the dispersion of light striking the interface at differentangles is shown. The thin horizontal lines indicate the values of bulk ωp

and surface plasmon frequencies ωs = ωp/√

2. (Adapted from [Hofmann(2008)]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

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List of Tables

3.1 Comparison of resolution limits presently achievable in different opticalimaging approachesa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.1 Electron energy structure parameters of InN and GaN . . . . . . . . . 1255.2 Crystal-field splitting parameter ΔCF and exchange parameter ΔX

of InP and CdSe nanocrystals calculated using the configuration-interaction approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

6.1 Selection rules for dipole allowed (deformation potential, DP) and dipole-forbidden (Frohlich, FR) Raman scattering in zinc-blend crystals . . . . 152

6.2 Values of the material parameters used in the numerical simulations byMenendez et al. (1997) . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

6.3 Values of the CdSe material parameters used in the numerical simula-tions shown in Fig. 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

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Preface

The main distinctive feature of nanomaterials is that they have structures on thenanometer scale. This class of materials includes a variety of novel inorganic (carbonnanotubes, fullerenes, ceramic and metallic nanoparticles, semiconductor quantumdots), organic (polymers, molecular aggregates, molecule–metallic nanoparticle as-semblies), and biological nanomaterials. Their optical properties are fascinatingand useful for a variety of applications. Nanotechnologies are poised to revolution-ize medicine, manufacturing, energy production, and other fundamental featuresof everyday life in the 21st century. The unique optical properties of nanoscalematerials are size dependent; they do not naturally occur in larger bulk materi-als. This book systematically presents evidence in analysis of specific features innanomaterials optics compared with bulk.

The chemical, physical, and optical properties of simple atoms and moleculesare fairly well understood, predictable, and no longer considered overly complex.This book demonstrates that this contrasts markedly with the current state ofknowledge about the optics of nanomaterials. It is challenging to understand op-tical properties of different complex materials (aggregated molecular and polymersystems, crystalline and noncrystalline solids) at the microscopic scale. Remark-able progress has been made in developing optics of nanomaterials within classicalelectrodynamics.

On the other hand, a detailed picture of optical excitations at the quantumlevel is required for future work in this field. The primary aim of the present bookis to provide the community with the current status of knowledge and to high-light the problems while making a bridge between the classical and microscopicoptics of nanomaterials. The problem is that the optics of materials, which isbased on microscopic (quantum) theory is still far from complete despite substan-tial progress in the field. Through comparative analysis of the size-dependent opticalresponse from nanomaterials, it is shown that although strides have been made incomputational chemistry and physics, bridging across length scales from nano tomacro remains a major challenge. Molecular, polymer, and biological systems havebeen shown in this book as potentially useful models for assembly; the progressin the current understanding of optical properties of molecular and biological

xxxiii

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xxxiv Preface

nanomaterials that are described is an important driving force for a variety ofapplications.

In the monograph, nanomaterials are generally categorized into three maingroups: fundamental building blocks, dispersions or composites of building blocks inrandomly ordered matrices, and spatially resolved, ordered nanostructures. Today,nanomaterials that offer some unique optical properties may find application as purematerials or may be integrated into larger structures. The book presents examplesof both pure and composite materials that include organic-inorganic nanocompos-ites and quantum dots embedded into different matrices for various applications inmodern nanotechnology.

A major failing of nanoscience is the lack of a detailed understanding of thephysics and chemistry behind the interaction between objects (surfaces, particles,individual molecules) at the nanoscale. Questions need to be answered regardinghow nanoparticles can be stabilized, and in what media, how nanoparticles interactand influence each other, and what proportions in a hybrid system make a criticaldifference. How can these characteristics be predicted?

With chapters addressing related fundamental questions of physics, chemistry,and quantum theory, this book helps the reader to achieve a better orientation inmodern nano-optics. The need for more and better modeling is becoming impera-tive. The more of the basic science that can be achieved via machine experiments,the faster the throughput of new molecular combinations for the production of newmaterials and nanostructures. The examples in the book addressing computationaldetails, as well as the appendixes, will help in better understanding the basics ofmodeling and simulations in optics of nanomaterials.

This book is written for a broad readership: materials scientists, researchers,engineers, as well as graduate students who want to deepen their knowledge aboutboth basics and applications of the nanomaterials optics. The monograph presentsan introduction to the current knowledge in the field. Chapter 1 contains a briefdescription of mostly used fabrication techniques in nanotechnologies. Chapter 2focuses on a theoretical description of electron energy structure and optical func-tions of nanomaterials. This chapter and the appendixes are designed to providean introductory overview, which seems reasonable considering the interdisciplinarynature of the field. Fundamental properties and applications of the surface plas-mon resonance and related phenomena in nanoparticles are addressed in Chapter3. Spectroscopies of optical absorption and emission are most widely used tech-niques for characterization of nanostructured materials. References to these kind ofdata can be found throughout this book. In Chapter 4, selected results of relevantexperimental and theoretical studies are reviewed as typical examples. An impor-tant optical phenomenon, the excitons in quantum-confined systems, is addressedin Chapter 5. Chapter 6 is focused on the Raman spectroscopy of nanomaterials.Cavity quantum electrodynamics (CQED) and nonlinear optics of nanomaterials,relatively new areas of nano-optics, are reviewed in Chapters 7 and 8, respectively.

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Preface xxxv

Optics of organic and biological nanomaterials and recent developments in thesefields are described in Chapters 9 and 10.

It is a pleasure to acknowledge my gratitude to many colleagues and collabora-tors for numerous helpful discussions and feedback. These include O. Aktsipetrov,F. Bechstedt, M. Cardona, V. Drachev, M. Downer, K. Kolasinski, M. Noginov, SirJohn B. Pendry, A. Pradhan, G. Schatz, W. G. Schmidt, V. Shalaev. I am verygrateful to my wife, Ludmila, and children, Natasha, Alexander, and Alena, fortheir support and help in the preparation of the manuscript.

Norfolk, Virginia

Vladimir I. Gavrilenko

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