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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 01 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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Abstruct-An efficient numerical method is presented for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides. The method is applicable to any lossless and/or lossy (dielectric, semiconductor, metallic) waveguide structure. The method is based on the argument principle theorem and is capable of extracting all of the zeros of any analytic function in the complex plane. It is applied in the present work to solving the multilayer waveguide dispersion equation derived from the well known thin-film transfer matrix theory. Excellent agreement is found with seven previously published results and with results from two limiting cases where the propagating constants can be obtained analytically.

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