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Rayleigh Multipole Methods for Photonic Crystal Calculations

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Progress In Electromagnetics Research, Vol. 41, 21-60, 2003
doi:10.2528/PIER02010802

Abstract

Multipole methods have evolved to be an important class of theoretical and computational techniques in the study of photonic crystals and related problems. In this chapter, we present a systematic and unified development of the theory, and apply it to a range of scattering problems including finite sets of cylinders, two-dimensional stacks of grating and the calculation of band diagrams from the scattering matrices of grating layers. We also demonstrate its utility in studies of finite systems that involve the computation of the local density of states.

Citation

 (See works that cites this article)
, "Rayleigh Multipole Methods for Photonic Crystal Calculations," Progress In Electromagnetics Research, Vol. 41, 21-60, 2003.
doi:10.2528/PIER02010802
http://www.jpier.org/PIER/pier.php?paper=0201082

References


    1. Pendry, J. B. and A. MacKinnon, Phys. Rev. Lett., Vol. 69, 2772, 1992.
    doi:10.1103/PhysRevLett.69.2772

    2. Sigalas, M. M., et al., Phys. Rev. B, Vol. 52, 11744, 1995.
    doi:10.1103/PhysRevB.52.11744

    3. Ho, K. M., C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett., Vol. 65, 3152, 1990.
    doi:10.1103/PhysRevLett.65.3152

    4. Rayleigh, J. W. S., Philos. Mag., Vol. 34, 481, 1892.

    5. von Ignatowsky, W., Ann. Physik, Vol. 44, 1914.

    6. Twersky, V., Arch. Rational Mech. Anal., Vol. 8, 323, 1961.

    7. McPhedran, R. C., et al., Aust. J. Phys., Vol. 52, 791, 1999.

    8. Botten, L. C., et al., "Electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations Part 1: Method," J. Opt. Soc. Am. A, Vol. 17, 2165, 2000.

    9. Botten, L. C., et al., "Electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations Part 2: Properties and implementation," J. Opt. Soc. Am. A, Vol. 17, 2177, 2000.

    10. Modinos, A., V. Karathanos, and N. Stefanou, "Optical properties of layers and crystals of spherical particles," Appl. Surface Science, Vol. 13, 65, 1993.

    11. Stefanou, N., V. Yannopapas, and A. Modinos, , Comput. Phys. Comm., Vol. 113, 49, 1998.
    doi:10.1016/S0010-4655(98)00060-5

    12. Kohn, W. and N. Rostoker, Phys. Rev., Vol. 94, 1111, 1954.
    doi:10.1103/PhysRev.94.1111

    13. Nicorovici, N. A., R. C. McPhedran, and L. C. Botten, Phys. Rev. Lett., Vol. 75, 1507, 1995.
    doi:10.1103/PhysRevLett.75.1507

    14. Nicorovici, N. A., R. C. McPhedran, and L. C. Botten, Phys. Rev. E, Vol. 52, 1135, 1995.
    doi:10.1103/PhysRevE.52.1135

    15. McPhedran, R. C., D. H. Dawes, L. C. Botten, and N. A. Nicorovici, J. Electromagn. Waves Applications, Vol. 10, 1083, 1996.

    16. Botten, L. C., R. C. McPhedran, N. A. Nicorovici, and A. B. Movchan, J. Electromagn. Waves Applications, Vol. 12, 847, 1998.

    17. Poulton, C. G., et al., "Noncommuting limits in electromagnetic scattering: asymptotic analysis for an array of highly conducting inclusions," SIAM J. Appl. Math., Vol. 61, 1706, 2001.
    doi:10.1137/S0036139999352262

    18. Lo, K. M., et al., IEEE J. Lightwave Technol., Vol. 12, 396, 1994.
    doi:10.1109/50.285321

    19. Felbacq, D., et al., J. Opt. Soc. Am. A, Vol. 11, 2526, 1994.

    20. Chin, S. K., N. A. Nicorovici, and R. C. McPhedran, Phys. Rev. E, Vol. 49, 4590, 1994.
    doi:10.1103/PhysRevE.49.4590

    21. Ewald, P. P., Ann. Phys., Vol. 64, 253, 1921.

    22. McPhedran, R. C., N. A. Nicorovici, L. C. Botten, and K. A. Grubits, J. Math. Phys., Vol. 41, 7808, 2000.
    doi:10.1063/1.1310361

    23. Asatryan, A. A., P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martijn de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals,'' Phys. Rev. E, Vol. 60, 6118, 1999; Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E, Vol. 62, 5711, 2000.
    doi:10.1103/PhysRevE.62.5711

    24. Cao, H., et al., Phys. Rev. Lett., Vol. 82, 2278, 2000.
    doi:10.1103/PhysRevLett.82.2278

    25. McPhedran, R. C., N. A. Nicorovici, L. C. Botten, and K.- D. Bao, "Green's function, lattice sum and Rayleigh's identity for a dynamic scattering problem," IMA Volumes in Mathematics and its Applications, Vol. 96, 155-186, 1997.

    26. Born, M. and E. Wolf, Principles of Optics, University Press, Cambridge, 1998.

    27. Wijngaard, W., J. Opt. Soc. Am., Vol. 63, 944, 1973.

    28. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.

    29. Oberhettinger, F., Fourier Expansions, 33, Academic, New York, 1973.

    30. Sözuer, H. S. and J. P. Dowling, J. Mod. Opt., Vol. 41, 231-239, 1994.

    31. Line, S. H. and J. G. Fleming, IEEE J. Lightwave Technol., Vol. 17, 1944, 1999.
    doi:10.1109/50.802977

    32. Botten, L. C., et al., Optica Acta, Vol. 28, 413, 1981.

    33. McRae, E. G., Surface Science, Vol. 11, 479, 1968.
    doi:10.1016/0039-6028(68)90058-7

    34. Gralak, B., S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A, Vol. 17, 1012, 2000.

    35. Parker, A. R., et al., Nature, Vol. 409, 36, 2000.
    doi:10.1038/35051168

    36. Guida, G., Opt. Comm., Vol. 156, 294, 1998.
    doi:10.1016/S0030-4018(98)00462-3

    37. Sigalas, M. M., et al., Phys. Rev. B, Vol. 53, 8340, 1996.
    doi:10.1103/PhysRevB.53.8340

    38. Sprik, R., B. A. van Tiggelen, and A. Lagendijk, Europhys. Lett., Vol. 35, 265, 1996.
    doi:10.1209/epl/i1996-00564-y

    39. John, S. and J. Wang, Phys. Rev. B, Vol. 43, 12772, 1991.
    doi:10.1103/PhysRevB.43.12772

    40. Busch, K. and S. John, Phys. Rev. E, Vol. 58, 3896, 1998.
    doi:10.1103/PhysRevE.58.3896

    41. Moroz, A., Europhys. Lett., Vol. 46, 419, 1999.
    doi:10.1209/epl/i1999-00278-2

    42. Asatryan, A. A., et al., "Two-dimensional Green function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E, Vol. 63, 046612, 2001.
    doi:10.1103/PhysRevE.63.046612

    43. Balian, R. and C. Bloch, Ann. Phys., Vol. 64, 271, 1971.
    doi:10.1016/0003-4916(71)90286-7

    44. Martin, O. J. F. and N. B. Piller, Phys. Rev. E, Vol. 58, 3909, 1998.
    doi:10.1103/PhysRevE.58.3909

    45., http://www.netlib.org/liblist.html.

    46. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University, New Jersey, 1995.

    47. Zhang, W. Y., et al., Phys. Rev. Lett., Vol. 84, 2853, 2000.
    doi:10.1103/PhysRevLett.84.2853

    48. Knight, J. C., T. A. Birks, P. St J. Russell, and D. M. Atkin, Opt. Lett., Vol. 21, 1547, 1996.

    49. Botten, L. C., N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, "Photonic band structure calculations using scattering matrices," Phys. Rev. E, Vol. 64, 046603, 2001.
    doi:10.1103/PhysRevE.64.046603

    50. Asatryan, A. A., K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green's function and local density of states in photonic crystals, consisting of a finite number of cylinders of infinite length," Phys. Rev. E, Vol. 63, 046612, 2001.
    doi:10.1103/PhysRevE.63.046612