Characteristic band gap structures of high dielectric contrast photonic crystals
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Characteristic band gap structures of high dielectric contrast photonic crystals Sheng D. Chao and Hsin Y. Peng Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan ABSTRACT Conventional photonic crystals exhibit low-lying full band gaps for the dielectric contrast smaller than 15. As the dielectric contrast increases, the band gap patterns change characteristics and exhibit interesting properties. In particular, the dispersion curves near the band gap region become concentrated to the middle band frequencies and exhibit an overall red shift in frequency. For a dielectric column photonic crystal made of a hexagonal lattice of circular cylinders, the maximum full band gap was found at the dielectric contrast as high as 27.5, which is attainable by using ceramics materials. The gap opens at high-lying bands, has simultaneous TM and TE band edges, and exhibit flattened dispersion curves near the band edges. INTRODUCTION A photonic crystal is a structure with periodically modulated dielectric constants and the most interesting feature is the existence of photonic band gaps [1-6]. A forbidden frequency range, or a band gap, for which no wave propagation is allowed, can appear as a spectral dip in the transmission spectrum. Band gaps are sensitive to the variations of materials and geometric parameters of a photonic crystal. Because the band gaps might open for different polarizations, recent efforts have been spent on searching for large full band gaps. Ideally, the gaps opened at different k points should overlap as much as possible to yield full band gaps. It is thus required that gaps are large and centered at neighboring frequencies. One possibility is to let the Brillouin zone to be of spherical shape [7]. This is why many previous works focus on hexagonal lattice. Moreover, there is an empirical rule of thumb based on the comparative study of square lattice with either column or air type rods [8]. The rule says that TM band gaps favor high dielectric inclusion regions while TE band gaps favor connected dielectric networks. However, a closer look at the original study and the mathematical analysis shows that this conclusion works only for low-lying bands or at least one being the lowest band. Besides, the conclusion is based on observing the field distributions post priori. In our previous study [9] we observe an interesting rule: full band gaps open when both the TM and TE band gaps have the same band edges. If the rule works, it is useful to decide which direction we should follow to find the full band gap. For example, if in a trial calculation it happens that the TM and TE gaps do not share the same band edges, we must adjust the available geometric and materials parameters to match their band edges. Recently, several studies have shown that the band gap opening of high dielectric contrast photonic crystals is closely related to the Mie scattering, at least for the TM mode [10-11]. These studies open the way to fabricate high dielectric constant materials which fully employ the concept
