Electromagnetic study of photonic band gaps

Using a rigorous integral theory of diffraction gratings, we investigate the properties of two-dimensional photonic crystals made with lossless dielectric materials using a model where the crystal is represented by a finite stack of dielectric grids of infinite extension. After studying the influence of the thickness of the crystal, we analyse the variations of the properties of the gap with the filling ratio, the index of dielectric, the geometry of the crystal, the shape of the rods, the polarization and finally with a contrast inversion. The validity of this multi-grid model is checked by varying the angle of incidence, which appears to have a significant influence. Some surprising properties emerge from these results, in particular the fact that contrast inversion has opposite effects according to whether the incident wave is s or p polarized. Finally, we give a very simple empirical rule that enables one to predict with a good precision the location of the centres of the gaps.

[1]  A. D. Boardman 編: Electromagnetic Surface Modes, John Wiley, Chichester and New York, 1982, x+776ページ, 23.5×16cm, 29,050円. , 1983 .

[2]  M. Nieto-Vesperinas,et al.  Effects of total internal reflection on the reflectivities of dielectric gratings , 1992 .

[3]  Daniel Maystre,et al.  A new general integral theory for dielectric coated gratings , 1978 .

[4]  Chan,et al.  Existence of a photonic gap in periodic dielectric structures. , 1990, Physical review letters.

[5]  D. Maystre,et al.  Selected papers on diffraction gratings , 1993 .

[6]  Rangarajan,et al.  Optimal structures for classical wave localization: An alternative to the Ioffe-Regel criterion. , 1988, Physical review. B, Condensed matter.

[7]  Alexei A. Maradudin,et al.  Two-dimensional photonic band structures , 1991 .

[8]  E. Yablonovitch,et al.  Photonic band structure: The face-centered-cubic case. , 1989, Physical review letters.

[9]  Zhang,et al.  Theory of photon bands in three-dimensional periodic dielectric structures. , 1990, Physical review letters.

[10]  Schultz,et al.  Microwave propagation in two-dimensional dielectric lattices. , 1991, Physical review letters.

[11]  Daniel Maystre,et al.  Theoretical Study of the Anomalies of Coated Dielectric Gratings , 1986 .

[12]  Ross C. McPhedran,et al.  Lossy Lamellar Gratings in the Quasistatic Limit , 1982 .

[13]  Leung,et al.  Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media. , 1990, Physical review letters.