supercomputing electromagnetics for the design of terahertz...

Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de

Extremadura

Supercomputing electromagnetics for the design of terahertz nano-antennas and metamaterial

applications.

José Manuel Taboada, Luis Landesa, Javier Rivero (Universidad de Extremadura)

Fernando Obelleiro, Diego M. Solís, Marta G. Araújo, Óscar Rubiños (Universidad de Vigo)

[email protected]

Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALS

mailto:[email protected]�

mailto:[email protected]�


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Outline

Rigorous, fast and high-scalability supercomputing solutions for large-scale conductors

Surface integral-equation formulations for nanoscience and nanotechnology applications

Fabrication and characterization


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Surface integral equation (SIE) methods: Method of moments

Great success in solving electromagnetic wave scattering and radiation problems involving large complex bodies

Only the discretizations of the surface of the object are needed Radiation condition at infinite is analytically included in the free-space Green’s function

Real life problems imply the solution of systems with millions of unknowns

Solving with iterative methods

O(N2) in memory O(N2) in CPU time

Required number of unknowns N

N grows proportional to the square of the frequency

⋅ =Z I V


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Prohibitive computational requirements

Method of Moments.RCS of an Airbus A-380 at 1.2 GHz

Memory > 25 PB CPU time: several decades


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Fast Multipole Method (FMM)

O(N1.5)FMM

High scalability (parallelization in k-space) High computational cost O(N1.5)

O(N2)


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Multilevel Fast Multipole Algorithm(MLFMA)

J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Transactions on Antennas and Propagation 45, pp. 1488-1493 (1997).

MLFMA

Lowest computational cost O(N logN) Difficult to obtain high scalability


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MLFMA-FFT: highly scalable O(N logN)

Finis Terrae (CESGA)142 cc-NUMA Integrity rx7640 nodes16 processor cores and 128 GB each.INFINIBAND at 20Gbps

LUSITANIA (CénitS)2 Superdome Integrity nodes128 processor cores and 1,024GB each.

MLFMA-FFT

High scalability (parallelization k-space) Lowest computational cost O(N logN)

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems”, IEEE Antennas and Propagation Magazine, vol. 51, no. 6, pp. 20-28, Dec. 2009


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MLFMA-FFT: 620 million unknowns


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MLFMA-FFT: 1 billion unknowns. Current World Record in CEM

1 042 977 546 unknowns

NASA Almond at 3 THzICTS HPC resource petition1024 parallel processors / 5TB

International Awards

J. M. Taboada, M. Araújo, J. M. Bértolo, L. Landesa, F. Obelleiro, J. L. Rodríguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics (Invited Paper)”, Progr. in Electromagnetics Research (PIER), 105, pp. 15-30, 2010

J. M. Taboada, M. G. Araújo, F. Obelleiro, J. L. Rodríguez, L. Landesa, “MLFMA-FFT parallel algorithm for the solution of extremely large problems in electromagnetics”, to appear in Proceedings of the IEEE, 2012.


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Surface integral-equation (SIE) formulation for plasmonics and metamaterials

Next objective: to extend the scope of application of SIE techniques to newmaterials in the context of nanoscience and nanotechnology

THz, IR and optical frequencies

Wide range of leading-edge applications

Nano-optical communications (miniaturization) Quantum-information processing: nanochips Efficient detection of molecules for biological diagnostics:

nano-optical microscopy and spectroscopy RAMAN scattering High-efficiency solar cells Plasmonic/metamaterial invisibility cloaking


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RF rules do not apply in plasmonics…

The penetration of fields cannot be neglected It is crucial to take into account the precise plasmonic

electromagnetic response of metals Negative permittivity real part that originates from a complex

conductivity, which in turn is given by the retarded coherentcollective electron oscillations due to the non-negligible massof the electrons.


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Plasmonic metallic nanoparticles at optical frequencies enable the controlof light surpassing the diffraction limit

Strong field enhancement and shorten wavelength due to localized strongplasmon resonances (LSPR) of metallic nanoparticles

S. Kawata, Y. Inouye, and P. Verma, “Plasmonics for near-field nano-imaging and superlensing,” Nature photonics, Vol. 3, July 2009.


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1 1 1( , )R ε µ

2 2 2( , )R ε µ

1n

2n

S

1J

2J

1M

2M

T-EFIE2

T-MFIE2

N-EFIE2

N-MFIE2

Tangential/normal combined formulations (JMCFIE)2 2

1 1

1 T-EFIE N-MFIEl l l ll ll

a bη= =

+∑ ∑2 2

1 1N-EFIE T-MFIEl l l l l

l lc dη

= =

− +∑ ∑

JCFIE1 + JCFIE2 =

MCFIE1 + MCFIE2 =


Maxwell equations work well for plasmonics…

Fortunately, the optical response of plasmonic materials iswell described by classical electrodynamics

T-EFIE1

T-MFIE1

N-EFIE1

N-MFIE1


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Derivation of wave parameters

Physical constraints for the wave parameters: Guarantee causality, representing

energy flowing away from the source: Wave (energy) attenuation as it

propagates away in a lossy medium Some authors propose the use of

This prevents the ambiguity in a number of cases…

Re( ) 0η ≥

Im( ) 0κ ≤

κ ω µ= µ

η =

…but is not enough to handle the complete casuistic for all kind of media

The problem arises when the complex arguments or µ lie just on the branch cut (the negative real axis under the C++ standard).This happens for LHM and plasmonic media without magnetic orwithout electric losses


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Derivation of wave parameters

The wave parameters in the case of LHM and plasmonic media withoutmagnetic and/or electric losses can be properly derived by considering thelossless case as the limit of the lossy case when the losses tend to zero

Numerically, this can be easily done for all cases (without specialconsiderations) by adding an infinitesimally small quantity of losses

'' 0or/and

'' 0

lim ' '' ' ''j jµ

κ ω µ µ→

→

= − −

'' 0or/and

'' 0

' ''lim

' ''jjµ

µ µη

→

→

−=

−

' 'j jκ ω µ δ δ= − −

''

jj

µ δη

δ−

=−

710δ −=


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Gold sphere illuminated by an -polarized plane wave impinging in thedirection at λ0 =548.6 nm

Comparative study for plasmonic media.

Gold5.843 2.111

1r

r

jµ= − −=

x z

Sphere of radius λ0

Mesh size = λ0/20Bistatic RCS calculation for MoM-based formulation vs. Mie

J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, "Method-of-moments formulation for the analysis of plasmonic nano-optical antennas," J. Opt. Soc. Am. A, vol. 28, pp. 1341-1348, 2011.


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Absorption (Qa), scattering (Qs) and extinction (Qe) efficiencies vs. k0r

Plasmonic sphere of varying radiiλ0=548.6 nmMesh size = λ0/15JMCFIE-MLFMA vs. Mie series

Gold5.843 2.111

1r

r

jµ= − −=

M. G. Araújo, D. M. Solís, J. Rivero, J. M. Taboada, F. Obelleiro, “Solution of large-scale plasmonic problems with the Multilevel Fast Multipole Algorithm,” to appear in Optics Letters, 2012.


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E-field for a gold sphere of radius=λ0. XY plane.

Mie series HEMCUVE (numerical)



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E-field for a gold sphere of radius=λ0. XZ plane.

Mie series


HEMCUVE (numerical)


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Plasmonic nano-optical Yagi-Uda antenna.Directing the emission of light

Yagi-Uda made of gold nanorodsAntenna optimized for λ0 = 817 nmDielectric constant: εr = −25.81−1.62 jInfinitesimal source placed at 4 nm from thelower extreme of the feed elementPMCHWT with 6,060 unknowns (includingboth J and M unknowns)

A. G. Curto, et al., “Unidirectional Emission of a Quantum Dot Coupled to a Nanoantenna Radiative Emission,” Science 329, 930(2010)


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Metallo-Dielectric nano-optical antenna

TiO2 dielectric microsphere (radius 250 nm)Two silver nanospheres (radius 30 nm) separated by 8 nmDielectric background of refractive index n0=1.3 Infinitesimal Hertzian emitter, λ0 = 525 nm

A. Devilez, B. Stout, N. Bonod, “Compact Metallo-dielectric Optical Antenna For Ultra Directional and Enhanced Radiative Emission,” ACS Nano 4, 3390-3396 (2010)


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Plasmonic nano-optical log-periodic antenna

Circular-tooth structure consisting oftwo coplanar arms of silver

Radii equally spaced if plotted on alogarithmic scale, with a period of

Antenna fed by a near-field coupledinfinitesimal dipole (quantum-dot)placed at the gap, oriented in thelongitudinal direction

1 1

n n

n n

R rR r

τ+ +

= =

An antenna described completely by angles would make an ideal broadbandradiator. In practice, nonetheless, the antenna must have finite dimensions

The log-periodic antenna is a modification of an angular antenna that reducesthe “end effect”

lnτ


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Directivity patterns and near fields

Antenna directivity in H-plane

Without ground plane

With ground plane

Electric near field


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Advantages of SIE-MoM approach in plasmonics

Avoid the discretization of volumes Do not suffer from numerical dispersion or instability due to rapid field

variations The field singularities and hot-spots given by the localized strong plasmon

resonances (LSPR) in the vicinity of sharp wedges and small gaps are accurately modeled by the analytical Green’s function

The latest breakthroughs in fast algorithms and supercomputing can be applied to speed-up the solution of large plasmonic problems


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Fabrication techniques

Top-down techniques:Standard electron-beam lithography (EBL)Focused-ion-beam milling (FIB)Nano-imprint lithography (NIL)

Down-top techniques:Chemically grown nanostructures


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Electron-beam lithography (EBL)

Standard electron-beam lithography (EBL) followed by metal evaporation and a liftoff procedure.

Fabrication accuracies below 50 nm can beobtained.

Paolo Biagioni et al, “Nanoantennas for visible and infrared radiation,” Reports on Progress in Physics, 75 024402 (2012)


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Electron-beam lithography (EBL)

Due to the multicrystallinity of the deposited metal layer, the final structural resolution is usually not as good

Curto AG, Volpe G, Taminiau TH, Kreuzer MP, Quidant R, van Hulst NF. Unidirectional emission of a quantum dot coupled to a nanoantenna. Science, 329, 930–933 (2010).

Maksymov IS, Staude I, Miroshnichenko AE, DeckerM, Tan HH, Neshev DN, Jagadish C, Kivshar YuS.Arrayed nanoantennas for efficient broadband unidirectionalemission enhancement. Conference on Lasers andElectro-Optics (CLEO)/USA


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Focused-ion-beam milling (FIB)

Localized sputtering of material using accelerated Gaions extracted from a liquid metal ion source

Ion collisions give rise to local surface erosion Broad applicability to almost any type of material and

the very good resolution When applied to chemically grown single-crystalline

metal flakes, highly reproducible resolutions and gaps below 10 nm can be obtained

Paolo Biagioni et al, “Nanoantennas for visible and infrared radiation,” Reports on Progress in Physics, 75 024402 (2012)


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Focused-ion-beam milling (FIB)

Left: FIB from single-crystalline chemically grown Au film

Right: FIB form multi-crystalline conventional Au film

J.-S. Huang, V. Callegari, P. Geisler, C. Br¨uning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures forplasmonic nanocircuitry,” Nature Comm. 1:150, 2010.


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Other techniques

Nano-imprint lithography (NIL): based on the direct mechanical deformation of the resist material.

The resolution is beyond the limitations set by light diffraction or beam scattering in previous techniques

Pressing a stamp with the design at a controlled temperature and pressure creates a thickness contrast in the polymer which can be latterly removed

Botton-up techniques: chemically grown nanostructures

A. Boltasseva, “Plasmonic componentsfabrication via nanoimprint,” J. Opt. A: Pure Appl. Opt.,11:114001, 2009.


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Far-field measurement techniques

Measurement of nanoantenna arrays by linear-optical reflectance and transmittance spectroscopy

Back-focal-plane imaging within a confocal microscope: the objective’s back focal plane or Fourier-plane, which contains the directions of emission towards the substrate, is imaged on an electron-multiplying CCD camera.

Curto AG, Volpe G, Taminiau TH, Kreuzer MP, Quidant R, van Hulst NF. Unidirectional emissionof a quantum dot coupled to a nanoantenna. Science, 329, 930–933 (2010).


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Near-field measurement techniques

Nanoantennas in receiving mode can be investigated experimentally using cross-polarization apertureless near-field optical microscopy

Dorfmüller J, Dregely D, Esslinger M, Khunsin W, Vogelgesang R, Kern K, Giessen H. Near-fielddynamics of optical Yagi-Uda nanoantennas. Nano Lett 2011, 11, 2819–2824


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Conclusion

Combining rigorous CEM simulation techniques with the principles of antenna design from radio and microwave technology will enable control of light for leading-edge nanoscience applications

Complement simulation with fabrication and measurements


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This work was supported by Spanish Government and ERDF:

Acknowledgments

Projects: TEC2008-06714-C02-02 CONSOLIDER-INGENIO2010 CSD2008-00068 ICTS-2009-40 Junta de Extremadura (project GR10126).

supercomputing electromagnetics for the design of terahertz...

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