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.