A novel supercell overlapping method is developed to analyze the photonic crystal fibers (PCFs). The electric field is decomposed using the localized Hermite-Gaussian functions, and the dielectric constant of the PCF missing the central air hole is considered as the sum of two different periodic dielectric structures of virtual perfect photonic crystals (PCs). The structures of both virtual PCs are expanded in cosine functions. From the wave equations and the orthonormality of Hermite-Gaussian functions,the propagation characteristics of the PCF, such as the mode field distribution,the effective area, the birefringence, and the dispersion properties, are obtained. There are fewer computations, and all the elements of the eigenvalue equation are analytical. We are convinced that this novel method is accurate and efficient due to the numerical calculation processes and its results.
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