Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions

Baczewski, Andrew David; Miller, Nicholas C.; Shanker, Balasubramaniam

doi:10.1364/JOSAA.29.000531

Title: Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions

Journal Article · Thu Mar 22 00:00:00 EDT 2012 · Journal of the Optical Society of America. A, Optics, Image Science, and Vision

DOI:https://doi.org/10.1364/JOSAA.29.000531· OSTI ID:1252696

Baczewski, Andrew David ^[1]; Miller, Nicholas C. ^[1]; Shanker, Balasubramaniam ^[1]

Michigan State Univ., East Lansing, MI (United States)

Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν²) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1252696

Report Number(s):: SAND-2016-1053J; JOAOD6; 619145

Journal Information:: Journal of the Optical Society of America. A, Optics, Image Science, and Vision, Vol. 29, Issue 4; ISSN 1084-7529

Publisher:: Optical Society of America (OSA)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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References (33)

Experimental Demonstration of Guiding and Bending of Electromagnetic Waves in a Photonic Crystal Lin, S. Science, Vol. 282, Issue 5387 https://doi.org/10.1126/science.282.5387.274	journal	October 1998
Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity Yoshie, T.; Scherer, A.; Hendrickson, J. Nature, Vol. 432, Issue 7014 https://doi.org/10.1038/nature03119	journal	November 2004
Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection Otto, Andreas Zeitschrift für Physik A Hadrons and nuclei, Vol. 216, Issue 4 https://doi.org/10.1007/BF01391532	journal	August 1968
Surface plasmon subwavelength optics Barnes, William L.; Dereux, Alain; Ebbesen, Thomas W. Nature, Vol. 424, Issue 6950, p. 824-830 https://doi.org/10.1038/nature01937	journal	August 2003
Extraordinary optical transmission through sub-wavelength hole arrays Ebbesen, T. W.; Lezec, H. J.; Ghaemi, H. F. Nature, Vol. 391, Issue 6668, p. 667-669 https://doi.org/10.1038/35570	journal	February 1998
Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions Ozbay, E. Science, Vol. 311, Issue 5758 https://doi.org/10.1126/science.1114849	journal	January 2006
Optical negative-index metamaterials Shalaev, Vladimir M. Nature Photonics, Vol. 1, Issue 1 https://doi.org/10.1038/nphoton.2006.49	journal	January 2007
Loss-free and active optical negative-index metamaterials Xiao, Shumin; Drachev, Vladimir P.; Kildishev, Alexander V. Nature, Vol. 466, Issue 7307 https://doi.org/10.1038/nature09278	journal	August 2010
Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering Song, J. M.; Chew, W. C. Microwave and Optical Technology Letters, Vol. 10, Issue 1 https://doi.org/10.1002/mop.4650100107	journal	September 1995
AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems Bleszynski, E.; Bleszynski, M.; Jaroszewicz, T. Radio Science, Vol. 31, Issue 5 https://doi.org/10.1029/96RS02504	journal	September 1996
A fast algorithm for particle simulations Greengard, L.; Rokhlin, V. Journal of Computational Physics, Vol. 73, Issue 2 https://doi.org/10.1016/0021-9991(87)90140-9	journal	December 1987
A periodic FMM for Maxwell’s equations in 3D and its applications to problems related to photonic crystals Otani, Yoshihiro; Nishimura, Naoshi Journal of Computational Physics, Vol. 227, Issue 9 https://doi.org/10.1016/j.jcp.2008.01.029	journal	April 2008
Adaptive integral method for hybrid FE/BI modelling of 3-D doubly periodic structures Eibert, T. F.; Volakis, J. L. IEE Proceedings - Microwaves, Antennas and Propagation, Vol. 146, Issue 1 https://doi.org/10.1049/ip-map:19990388	journal	January 1999
Fast Periodic Interpolation Method for Periodic Unit Cell Problems Li, Shaojing; Van Orden, Derek A.; Lomakin, Vitaliy IEEE Transactions on Antennas and Propagation, Vol. 58, Issue 12 https://doi.org/10.1109/TAP.2010.2078480	journal	December 2010
Fast evaluation of Helmholtz potential on graphics processing units (GPUs) Li, Shaojing; Livshitz, Boris; Lomakin, Vitaliy Journal of Computational Physics, Vol. 229, Issue 22 https://doi.org/10.1016/j.jcp.2010.07.029	journal	November 2010
Accelerated Cartesian expansions – A fast method for computing of potentials of the form R−ν for all real ν Shanker, B.; Huang, H. Journal of Computational Physics, Vol. 226, Issue 1 https://doi.org/10.1016/j.jcp.2007.04.033	journal	September 2007
Fast evaluation of time domain fields in sub-wavelength source/observer distributions using accelerated Cartesian expansions (ACE) Vikram, M.; Shanker, B. Journal of Computational Physics, Vol. 227, Issue 2 https://doi.org/10.1016/j.jcp.2007.08.017	journal	December 2007
Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein–Gordon potentials Vikram, M.; Baczewski, A.; Shanker, B. Journal of Computational Physics, Vol. 229, Issue 24 https://doi.org/10.1016/j.jcp.2010.08.025	journal	December 2010
Accelerating fast multipole methods for the Helmholtz equation at low frequencies Greengard, L.; Rokhlin, V. IEEE Computational Science and Engineering, Vol. 5, Issue 3 https://doi.org/10.1109/99.714591	journal	January 1998
A mixed-form fast multipole algorithm IEEE Transactions on Antennas and Propagation, Vol. 53, Issue 12 https://doi.org/10.1109/TAP.2005.859915	journal	December 2005
A Novel Wideband FMM for Fast Integral Equation Solution of Multiscale Problems in Electromagnetics Vikram, Melapudi; Huang, He; Shanker, Balasubramaniam IEEE Transactions on Antennas and Propagation, Vol. 57, Issue 7 https://doi.org/10.1109/TAP.2009.2019926	journal	July 2009
A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies Schaubert, D.; Wilton, D.; Glisson, A. IEEE Transactions on Antennas and Propagation, Vol. 32, Issue 1 https://doi.org/10.1109/TAP.1984.1143193	journal	January 1984
Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains Wilton, D.; Rao, S.; Glisson, A. IEEE Transactions on Antennas and Propagation, Vol. 32, Issue 3 https://doi.org/10.1109/TAP.1984.1143304	journal	March 1984
Efficient integral-equation-based method for accurate analysis of scattering from periodically arranged nanostructures Kobidze, G.; Shanker, B.; Nyquist, D. P. Physical Review E, Vol. 72, Issue 5 https://doi.org/10.1103/PhysRevE.72.056702	journal	November 2005
Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation Eibert, T. F.; Volakis, J. L.; Wilton, D. R. IEEE Transactions on Antennas and Propagation, Vol. 47, Issue 5 https://doi.org/10.1109/8.774139	journal	May 1999
Light scattering from macroscopic spherical bodies. II. Reflectivity of light and electromagnetic localized state in a periodic monolayer of dielectric spheres Inoue, M.; Ohtaka, K.; Yanagawa, S. Physical Review B, Vol. 25, Issue 2 https://doi.org/10.1103/PhysRevB.25.689	journal	January 1982
Nano-Optics in the Biological World: Beetles, Butterflies, Birds, and Moths Srinivasarao, Mohan Chemical Reviews, Vol. 99, Issue 7 https://doi.org/10.1021/cr970080y	journal	July 1999
Photonic structures in biology Vukusic, Pete; Sambles, J. Roy Nature, Vol. 424, Issue 6950 https://doi.org/10.1038/nature01941	journal	August 2003
Biomimetics of photonic nanostructures Parker, Andrew R.; Townley, Helen E. Nature Nanotechnology, Vol. 2, Issue 6 https://doi.org/10.1038/nnano.2007.152	journal	June 2007
Controlled Replication of Butterfly Wings for Achieving Tunable Photonic Properties Huang, Jingyun; Wang, Xudong; Wang, Zhong Lin Nano Letters, Vol. 6, Issue 10 https://doi.org/10.1021/nl061851t	journal	October 2006
Yellow-light negative-index metamaterials Xiao, Shumin; Chettiar, Uday K.; Kildishev, Alexander V. Optics Letters, Vol. 34, Issue 22 https://doi.org/10.1364/OL.34.003478	journal	January 2009
Optical Constants of the Noble Metals Johnson, P. B.; Christy, R. W. Physical Review B, Vol. 6, Issue 12, p. 4370-4379 https://doi.org/10.1103/PhysRevB.6.4370	journal	December 1972
Generalized method of moments: a framework for analyzing scattering from homogeneous dielectric bodies Nair, Naveen V.; Shanker, Balasubramaniam Journal of the Optical Society of America A, Vol. 28, Issue 3 https://doi.org/10.1364/JOSAA.28.000328	journal	January 2011

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