Green's Function Analysis of Electromagnetic Wave Propagation in Photonic Crystal Devices Using Complex Images Technique

An integral equation method employing complex images Green's functions is developed for analyzing different devices fabricated in 2-D dielectric photonic crystals. The integral equation is written in terms of the unknown equivalent current sources flowing on the surfaces of the periodic 2-D cylinders. The method of moments is then employed to solve for the unknown current distributions. The required Green's function of the problem is represented in terms of a finite summation of complex images instead of the conventional slowly converging infinite series. It is shown that when the field-point is far from the periodic sources, it is just sufficient to consider the contribution of the propagating poles in the structure. This will result in a summation of plane waves that has an even smaller size compared with the conventional complex images Green's function. This will enable us to analyze the dielectric periodic structures efficiently and accurately. The method is applied to a number of waveguide structures and its results are compared with the existing literature.