Since the introduction of Photonic Crystals in early 1980s, there has been many attempt to use its bandgap properties for other applicators. Photonic Crystal Fibers (PCFs) are one of the successful applications among them. In this dissertation, we derived the Boundary Integral Equations, which based on Huygen's principal and the Green's function and simulate the basics dispersion and loss profile for Photonic Crystal Fiber including air-silica fibers, photonic bandgap fibers, and super-structured fiber. This formulation is very flexible for the geometry and each hole index. And the real and imaginary part of propagation constant, which is related to the confinement loss, can be found using any complex root searching method.; Integral equation usually yields a large dense matrix system. Thus, fast solver is required to handle practical problem. The fast solver for the layered media based on hankel transformation of spectral Green's function which is developed by W. Cai and multilevel fast multipole method with partial numerical results are presented. Finally, as a physical application, a volume integral equation for the QD in the layered media is formulated with the Green's function.
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