From scattering or impedance matrices to Bloch modes of photonic crystals

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 19, Issue 8, 2002, Pages 1547-1554

  Gralak, Boris ^a   Enoch, Stefan ^a   Tayeb, Gérard ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CRYSTALS; EIGENVALUES AND EIGENFUNCTIONS; LIGHT SCATTERING; MATRIX ALGEBRA; PROBLEM SOLVING; VISION;

PHOTONIC CRYSTALS;

IMAGE ANALYSIS;

EID: 0012263267     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.19.001547     Document Type: Article

References (30)

1. K. Ho, C. Chan, and C. Soukoulis, "Existence of photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
2. J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
3. J. B. Pendry, "Photonic band structures," J. Mod. Opt. 41, 209-229 (1994).
4. A. Moroz, "Density-of-states calculations and multiple-scattering theory for photons," Phys. Rev. B 51, 2068-2081 (1995).
5. A. Moroz and C. Sommers, "Photonic band gaps of three-dimensional face-centered cubic lattices," J. Phys. Condens. Matter 11, 997-1008 (1999).
6. R. C. McPhedran, L. C. Botten, A. A. Asatryan, N. A. Nicorovici, P. A. Robinson, and C. M. de Sterke, "Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders," Phys. Rev. E 60, 7614-7617 (1999).
7. B. Gralak, S. Enoch, and G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012-1020 (2000).
8. L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, "Photonic band structure calculations using scattering matrices," Phys. Rev. E 64, 046603 (2001).
9. A. Modinos, N. Stefanou, and V. Yannopapas, "Applications of the layer-KKR method to photonic crystals," Opt. Express 8, 197-202 (2001).
10. D. M. Whittaker, "Inhibited emission in photonic woodpile lattices," Opt. Lett. 25, 779-781 (2000).
11. R. Petit, "Contribution à l'étude de la diffraction d'une onde plane par un réseau métallique," Rev. Opt. Theor. Instrum. 6, 263-281 (1963).
12. P. Vincent and M. Nevière, "Corrugated dielectric waveguides: a numerical study of the second-order stop bands," Appl. Phys. 20, 345-351 (1979).
13. M. Nevière, R. Reinisch, and D. Maystre, "Surface enhanced second harmonic generation at a silver grating: a numerical study," Phys. Rev. B 32, 3634-3641 (1985).
14. D. Maystre, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 3.
15. E. Popov and M. Nevière, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000).
16. E. Popov and M. Nevière, "Maxwell equations in Fourier space: fast converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media," J. Opt. Soc. Am. A 18, 2886-2894 (2001).
17. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
18. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The finitely conducting lamellar diffraction grating," Opt. Acta 28, 1087-1102 (1981).
19. S.-E. Sandström, G. Tayeb, and R. Petit, "Lossy multistep lamellar gratings in conical diffraction mountings: an exact eigenfunction solution," J. Electromagn. Waves Appl. 7, 631-649 (1993).
20. L. Li, "A modal analysis of lamellar diffraction gratings in conical mountings," J. Mod. Opt. 40, 553-573 (1993).
21. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996).
22. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature (London) 394, 351-353 (1998).
23. J. G. Fleming and S.-Y. Lin, "Three-dimensional photonic crystal with a stop band from 1.35 to 1.95 μm," Opt. Lett. 24, 49-51 (1999).
24. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
25. S.-Y. Lin, J. G. Fleming, R. Lin, M. M. Sigalas, R. Biswas, and K. M. Ho, "Complete three-dimensional photonic band-gap in a simple cubic structure," J. Opt. Soc. Am. B 18, 32-35 (2001).
26. H. Sözüer, J. Haus, and R. Inguva, "Photonic bands: convergence problems with the plane-wave method," Phys. Rev. B 45, 13962-13972 (1992).
27. F. Montiel and M. Nevière, "Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm," J. Opt. Soc. Am. A 11, 3241-3250 (1994).
28. D. Maystre, "Electromagnetic study of photonic band gaps," Pure Appl. Opt. 3, 975-993 (1994).
29. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
30. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).