Superprism effect and light refraction and propagation in photonic crystals

Photonic crystal based devices received attention in recent years. Based on the superprism effect in photonic crystals, beam steering devices can be made with properties sensitively dependent on the wavelength and incident angle of light. One stumbling block for designing superprism-based demultiplexers is that current numerical methods have difficulties in simulating a practical superprism device with commonly available computational facilities. Examining the superprism effect in a more general perspective, we previously developed a rigorous theory to solve the photonic crystal refraction problem for any surface orientation and any lattice type. This paper will compare our theory with other methods with regard to computational workload to demonstrate the advantages of our theory. Excellent agreement of numerical results with the transfer matrix method is also demonstrated. Heuristic discussions on the beam width variation and energy conservation are presented. A technique for direct computation of the dispersion surface is compared with the methods that combine a photonic band solver with certain interpolation or 1D-searching techniques.