Resonant effect analysis at finite one-dimensional anisotropic photonic crystal band edges

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Using the transfer matrix method to analyze a 1D anisotropic photonic crystal usually involves a 4×4 matrix, which means for any given &#969; and &#946; (the Snell quantity nsin&#952;), four eigenvalues of <i>K</i> can be found. Based on the degeneracy of <i>K</i>, 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.