A numerical method is presented for determining the transmittance of long-period (LP) fiber-gratings having arbitrary azimuthal/radial refractive index variations. The method uses coupled-mode theory and includes both the sine and cosine character of the LP modes. The model treats interactions between the fundamental LP01 mode and high-azimuthal-order cladding modes. The method utilizes the transfer matrix method to model cylindrical layers both in the core and the cladding regions.
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