The Theory Of Photonic Crystal Design And Algorithm Research

Periodic dielectrics (metals), or photonic crystals, allow the propagation of light to be controlled in otherwise difficult or impossible ways, and offer many inspiring and fire-new ideas to material scientists, physicists, and electronic engineers. Photonic crystal structures are promising building blocks for miniature photonic integrated circuits, which synthesize such functions as collecting, disposing, and transfering messages. They will surely bring on great innovations in the fields of optics, optoelectronics, and information industry.Many applications of photonic crystals are based on photonic band gaps, and it would thus be very interesting to design a photonic crystal with the largest band gap for a given dielectric contrast. In chapter 2, a two-stage genetic algorithm is developed to design a two-dimensional photonic crystal of a square lattice with the maximal absolute band gap. As numerical examples, the genetic algorithm gives both an istropic structure and an anisotropic struture with a relative width of the absolute band gap several times larger than those reported before.A photoinc crystal can be a perfect mirror for light from any direction, with any polarization, within a specified frequency range. It is natural to assume that a necessary condition for such omnidirectional reflection is that the crystal exhibit a complete three-dimensional photonic band gap. However, recent research shows that, in fact, a one-dimensional( 1D) photonic crystal will suffice. In chapter 3, a genetic algorithm is developed to design a 1D photonic crystal with the maximal omnidirectional band gap. Numerical examples not only demonstrate the effectivity of such a genetic algorithm approach, but also lead to a general experiential law of designing such an omnidirectional ID photonic crystal.Plane wave expansion method is widely used in calculating the band gaps of photonic crystals. In chapter 4, two kinds of linear operators are introduced to calculate analytically the Fourier coefficients of complicated photonic crystals fromsimple structures. The present method is much faster and more accurate than those conventional ones.