Transmission characteristics of long-period fiber gratings having arbitrary azimuthal/radial refractive index variations

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.