Abstract
A new kind of birefringence is found in a two-dimensional (2D) flat perfect photonic crystal (PhC). It is different from the one in the normal biaxial crystal, but qualitative, and comes from the positive and negative refraction in the 2D flat perfect PhC. The quantitative relationship between the refractive index and the incident angle are plotted, by the analysis of the equal-frequent surface (EFS) of the perfect PhC. The plot is consisted of three branches---the main across 0° to 45.53° of the incident angle, the upper across 33.3° to 38.53° and the lower across 38.53° to 45.53°. The upper reveals the positive refraction; the lower and the main reveal the negative ones. The finite-difference time-domain (FDTD) simulations are performed, and the relevantly quantitative measurement validates the quantitative relationship by the analysis of the EFS, but a 2.67° shift to the bigger incident angle. A novel beam guiding is observed, which is resulted not from the guiding in a defect photonic crystal (PhC) but from the negative refraction in a two-dimensional (2D) flat perfect PhC slab.
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