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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 4 — Apr. 1, 2012
  • pp: 531–540

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

Andrew D. Baczewski, Nicholas C. Miller, and Balasubramaniam Shanker  »View Author Affiliations


JOSA A, Vol. 29, Issue 4, pp. 531-540 (2012)
http://dx.doi.org/10.1364/JOSAA.29.000531


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Abstract

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 O(N2) operations, N 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 O(N) 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.

© 2012 Optical Society of America

ToC Category:
Scattering

History
Original Manuscript: September 19, 2011
Manuscript Accepted: December 4, 2011
Published: March 22, 2012

Citation
Andrew D. Baczewski, Nicholas C. Miller, and Balasubramaniam Shanker, "Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions," J. Opt. Soc. Am. A 29, 531-540 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-4-531


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References

  1. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef]
  2. S.-Y. Lin, E. Chow, V. Hietala, P. Villeneuve, and J. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998). [CrossRef]
  3. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004). [CrossRef]
  4. A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968). [CrossRef]
  5. W. Barnes, A. Dereuk, and T. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef]
  6. T. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]
  7. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). [CrossRef]
  8. V. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007). [CrossRef]
  9. S. Xiao, V. Drachev, A. Kildishev, X. Ni, U. Chettiar, H.-K. Yuan, and V. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010). [CrossRef]
  10. J. Song and W. Chew, “Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering,” Microw. Opt. Technol. Lett. 10, 14–19 (1995). [CrossRef]
  11. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225–1251 (1996). [CrossRef]
  12. L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325–348 (1987). [CrossRef]
  13. V. Rokhlin and S. Wandzura, “The fast multipole method for periodic structures,” in Antennas and Propagation Society International Symposium (IEEE, 1994), pp. 424–426.
  14. Y. Otani and N. Nishimura, “A periodic FMM for Maxwell’s equations in 3D and its applications to problems related to photonic crystals,” J. Comput. Phys. 227, 4630–4652(2008). [CrossRef]
  15. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “Rigorous modeling of electromagnetic wave interactions with large dense systems of discrete scatterers,” in Ultra-Wideband, Short Pulse Electromagnetics 9 (Springer, 2010), pp. 65–77.
  16. T. Eibert and J. Volakis, “Adaptive integral method for hybrid FE/BI modelling of 3-D doubly periodic structures,” IEE Proc. H Microw. Antennas Propag. 146, 17–22 (1999). [CrossRef]
  17. S. Li, D. Orden Van, and V. Lomakin, “Fast periodic interpolation method for periodic unit cell problems,” IEEE Trans. Antennas Propag. 58, 4005–4014 (2010). [CrossRef]
  18. S. Li, B. Livshitz, and V. Lomakin, “Fast evaluation of Helmholtz potential on graphics processing units (GPUs),” J. Comput. Phys. 229, 8463–8483 (2010). [CrossRef]
  19. B. Shanker and H. Huang, “Accelerated Cartesian expansions—a fast method for computing of potential of the form r−ν for all real ν,” J. Comput. Phys. 226, 732–753 (2007). [CrossRef]
  20. M. Vikram and B. Shanker, “Fast evaluation of time domain fields in sub-wavelength source/observer distributions using accelerated Cartesian expansions (ACE),” J. Comput. Phys. 227, 1007–1023 (2007). [CrossRef]
  21. M. Vikram, A. Baczewski, B. Shanker, and L. Kempel, “Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein–Gordon potentials,” J. Comput. Phys. 229, 9119–9134 (2010). [CrossRef]
  22. A. Baczewski and B. Shanker, “An O(N) method for rapidly computing periodic potentials using accelerated Cartesian expansions,” submitted for publication to Journal of Computational Physics. Preprint available at http://arxiv.org/abs/1107.3069v1 .
  23. L. Greengard, J. Huang, V. Rokhlin, and S. Wandzura, “Accelerating fast multipole methods for the Helmholtz equation at low frequencies,” IEEE Comput. Sci. Eng. 5, 32–38 (1998). [CrossRef]
  24. L. Jiang and W. Chew, “A mixed-form fast multipole algorithm,” IEEE Trans. Antennas Propag. 53, 4145–4156 (2005). [CrossRef]
  25. M. Vikram, H. Huang, B. Shanker, and T. Van, “A novel wideband FMM for fast integral equation solution of multiscale problems in electromagnetics,” IEEE Trans. Antennas Propag. 57, 2094–2104 (2009). [CrossRef]
  26. A. Peterson, S. Ray, and R. Mittra, Computational Methods for Electromagnetics (Wiley-IEEE, 1998).
  27. D. Schaubert, D. Wilton, and A. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Trans. Antennas Propag. 32, 77–85 (1984). [CrossRef]
  28. R. Harrington, Time-Harmonic Electromagnetic Fields (Wiley-IEEE, 2001).
  29. Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, 2003).
  30. D. Wilton, S. Rao, A. Glisson, D. Schaubert, O. Al-Bundak, and C. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antennas Propag. 32, 276–281 (1984). [CrossRef]
  31. G. Kobidze, B. Shanker, and D. Nyquist, “Efficient integral-equation-based method for accurate analysis of scattering from periodically arranged nanostructures,” Phys. Rev. E 72, 056702 (2005). [CrossRef]
  32. T. Eibert, J. Volakis, D. Wilton, and D. Jackson, “Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation,” IEEE Trans. Antennas Propag. 47, 843–850 (1999). [CrossRef]
  33. M. Inoue, K. Ohtaka, and S. Yanagawa, “Light scattering from macroscopic spherical bodies. II. Reflectivity of light and electromagnetic localized state in a periodic monolayer of dielectric spheres.” Phys. Rev. B 25, 689–699 (1982). [CrossRef]
  34. M. Srinivasarao, “Nano-optics in the biological world: Beetles, butterflies, birds, and moths,” Chem. Rev. 99, 1935–1962 (1999). [CrossRef]
  35. P. Vukusic and J. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003). [CrossRef]
  36. A. Parker and H. Townley, “Biomimetics of photonic nanostructures,” Nat. Nanotechnol. 2, 347–353 (2007). [CrossRef]
  37. J. Huang, X. Wang, and Z. Wang, “Controlled replication of butterfly wings for achieving tunable photonic properties,” Nano Lett. 6, 2325–2331 (2006). [CrossRef]
  38. F. Gervais, Handbook of Optical Constants of Solids (Academic, 1991), Vol. 2, pp. 761–775.
  39. S. Xiao, U. Chettiar, A. Kildishev, V. Drachev, and V. Shalaev, “Yellow-light negative-index metamaterials,” Opt. Lett. 34, 3478–3480 (2009). [CrossRef]
  40. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
  41. N. Nair and B. Shanker, “Generalized method of moments: a framework for analyzing scattering from homogeneous dielectric bodies,” J. Opt. Soc. Am. A 28, 328–340 (2011). [CrossRef]

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