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Rayleigh Multipole Methods for Photonic Crystal Calculations

By L. C. Botten, R. C. McPhedran, N. A. Nicorovici, A. A. Asatryan, C. M. de Sterke, P. A. Robinson, K. Busch, G. H. Smith, and T. N. Langtry

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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)
L. C. Botten, R. C. McPhedran, N. A. Nicorovici, A. A. Asatryan, C. M. de Sterke, P. A. Robinson, K. Busch, G. H. Smith, and T. N. Langtry, "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


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