Post on 18-Apr-2020
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)
tabo@unex.es
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALS
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
Outline
Rigorous, fast and high-scalability supercomputing solutions for large-scale conductors
Surface integral-equation formulations for nanoscience and nanotechnology applications
Fabrication and characterization
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
Prohibitive computational requirements
Method of Moments.RCS of an Airbus A-380 at 1.2 GHz
Memory > 25 PB CPU time: several decades
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
Fast Multipole Method (FMM)
O(N1.5)FMM
High scalability (parallelization in k-space) High computational cost O(N1.5)
O(N2)
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
MLFMA-FFT: 620 million unknowns
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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.
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
Surface integral-equation (SIE) formulation for plasmonics and metamaterials
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.
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
Surface integral-equation (SIE) formulation for plasmonics and metamaterials
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.
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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 =
Surface integral-equation (SIE) formulation for plasmonics and metamaterials
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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 −=
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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.
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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.
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
E-field for a gold sphere of radius=λ0. XY plane.
Mie series HEMCUVE (numerical)
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.
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
E-field for a gold sphere of radius=λ0. XZ plane.
Mie series
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.
HEMCUVE (numerical)
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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)
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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)
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
Directivity patterns and near fields
Antenna directivity in H-plane
Without ground plane
With ground plane
Electric near field
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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)
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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)
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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.
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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.
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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).
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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
Second Joint Workshop Consolider TERASENSE & ENGINEERING METAMATERIALSUniversidad de
Extremadura
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).