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.
E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, "Transmission Characteristics of Long-Period Fiber Gratings Having Arbitrary Azimuthal/Radial Refractive Index Variations," J. Lightwave Technol. 21, 218- (2003)