Progress In Electromagnetics Research
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Homogenization of Three-Dimensional Finite Photonic Crystals

By S. Guenneau and F. Zolla

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S. Guenneau and F. Zolla, "Homogenization of Three-Dimensional Finite Photonic Crystals," Progress In Electromagnetics Research, Vol. 27, 91-127, 2000.

1. Bensoussan, A., J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.

2. Bouchitte, G. and R. Petit, "Homogenization techniques as applied in the electromagnetic theory of gratings," Electromagnetics, Vol. 5, 17-36, 1985.

3. Mc Phedran, R. C., L. C. Botten, M. S. Craig, M. Neviere, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Optica Acta, Vol. 29, 289-312, 1982.

4. Petit, R. and G. Bouchitte, "Replacement of a very fine grating by a stratified layer: homogenization techniques and the multiplescale method," SPIE Proceedings Application and Theory of Periodic Structures, Diffraction Gratings, and Moire Phenomena 431, Vol. 815, ed. J. Lerner, 1987.

5. Mc Phedran, R. C., C. G. Poulton, N. A. Nicorovivi, and A. B. Movchan, "Low frequency corrections to the static effective dielectric constant of a two-dimensional composite material," Proc. Royal Soc. Lon. A, Vol. 452, 2231-2245, 1996.

6. Felbacq, D. and G. Bouchitte, "Homogenization of a set of parallel fibers," J. of Waves in Random Media, Vol. 7, 245-256, 1997.

7. Datta, S., C. T. Chan, K. M. Ho, and C. M. Soukoulis, "Effective dielectric constant of periodic composite structures," Phys. Rev. B, Vol. 48, No. 20, 14936-14943, 1993.

8. Halevi, P., A. A. Krokhin, and J. Arriaga, "Photonic crystal optics and homogenization of 2D periodic composites," Phys. Rev. Lett., Vol. 82, No. 4, 719-722, 1999.

9. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2062, 1987.

10. Joannopoulos, J., R. Meade, and J. Winn, Photonic Crystals, Princeton Press, Princeton, NJ, 1995.

11. De La Rue, R. C. and T. F. Kraus, "Strategies for the fabrication of photonic microstructures in semiconductors," Microcavities and photonic bandgaps Kluwer Acad. Pub., 175-192, Netherlands, 1996.

12. Maystre, D., "Electromagnetic study of photonic band gaps," Pure Appl. Opt., 3, 975-993, 1994.

13. Felbacq, D., G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A, Vol. 11, No. 9, 2526-2538, 1994.

14. Maystre, D., G. Tayeb, and D. Felbacq, "Theoretical study of photonic band gap structures," Optics for Science and New Technology, ED. J. Chang, J. Lee, S. Lee, and C. Nam, Vol. 2778, 740-743, SPIE, 1996.

15. Zolla, F., D. Felbacq, and B. Guizal, "A remarkable diffractive property of photonic quasi-crystals," Optics Commun., Vol. 148, 6-10, 1998.

16. Felbacq, D., B. Guizal, and F. Zolla, "Wave propagation in one-dimensional photonic crystals," Optics Commun., Vol. 152, 119-126, 1998.

17. Felbacq, D., B. Guizal, and F. Zolla, "Limit analysis of the diffraction of a plane wave by a stratified periodic medium," J. Math. Phys., Vol. 39, No. 9, 4604-4607, 1998.

18. Cadilhac, M. and R. Petit, "On the diffraction problem in electromagnetic theory: a discussion based on concepts of functional analysis including an example of practical application," Huygens’ Principle 1690-1990: Theory and Applications, H. Blok, H. A. Ferwerda, and H. K. Kuiken (editors), Elsevier Science Publishers B.V., 1992.

19. Zolla, F., R. Petit, and M. Cadilhac, "Electromagnetic theory of diffraction by a system of parallel rods: the method of fictitious sources," J. Opt. Soc. Am. A, Vol. 11, No. 3, 1087-1096, 1994.

20. Petit, R. and F. Zolla, "The method of fictitious sources as applied to the conical diffraction by a homogeneous rod," J. of Electromagnetic Waves and Applications, Vol. 8, No. 1, 1-18, 1994.

21. Derrick, G. H., R. C. Mc Phedran, D. Maystre, and M. Neviere, "Crossed gratings: a theory and its applications," Appl. Phys., Vol. 18, 39-52, 1979.

22. Mc Phedran, R. C., G. H. Derrick, and L. C. Botten, "Theory of crossed gratings," Electromagnetic Theory of Gratings, Springer-Verlag, Berlin, edited by R. Petit, 1980.

23. Schwartz, L., Theorie des Distributions, 142-143, Hermann, Paris, 1966.

24. Reed, M. and S. Simon, Methods of Modern Mathematical Physics, Academic Press, New York, 1978.

25. Cessenat, M., "Mathematical methods in electromagnetism," World Scientific, Vol. 41, 1996.

26. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, 1990.

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