Abstract
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.
© 2010 IEEE
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