1 March 2006 Resonant effect analysis at finite one-dimensional anisotropic photonic crystal band edges
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Abstract
Using the transfer matrix method to analyze a 1D anisotropic photonic crystal usually involves a 4×4 matrix, which means for any given ω and β (the Snell quantity nsinθ), four eigenvalues of K can be found. Based on the degeneracy of K, the band edge in the dispersion curves can be divided into two types. One is the regular band edge (R.B.E) which has degeneracy of the order 2 and another is the degenerate band edge (D.B.E) which has fourth order degeneracy. It was predicted that in the case of a transmission resonance in the vicinity of the D.B.E, the resonant field intensity enhancement is proportional to N4, where N is the total number of periods, while in the case of a regular band edge, the field intensity enhancement is proportional to N2. Based on this prediction, we have calculated the band edge resonant effect of a novel D.B.E photonic crystal structure with a unit cell having two misaligned in-plane anisotropic layers and one isotropic layer. By making a comparison among different anisotropic materials, we have found that the giant resonant effects in the vicinity of the D.B.E also need a large anisotropy of the materials. However, whether the anisotropy is large or small, the field intensity enhancement is approximately proportional to N4 once the number of the periods is large enough to cause the strong enough resonance effect inside the structure. We believe this DBE resonant effect will have applications requiring slow-light and in nonlinear optics.
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Yang Cao, Yang Cao, Michael A. Fiddy, Michael A. Fiddy, } "Resonant effect analysis at finite one-dimensional anisotropic photonic crystal band edges", Proc. SPIE 6128, Photonic Crystal Materials and Devices IV, 61281I (1 March 2006); doi: 10.1117/12.646056; https://doi.org/10.1117/12.646056
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