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This paper discusses an alternative method for calculating modal parameters in optical fibers such as propagation constants, transverse distributions, and anisotropy, due to linear and nonlinear phenomena acting as perturbations caused by doped silica regions. This method is based on a Hamiltonian formulation of the Helmholtz equation and the stationary perturbation theory, which allows a full-vectorial description of the electric field components when linear anisotropic inhomogeneities and Kerr nonlinearity are included. Linear and nonlinear parameters can be found for each propagating mode, and its accuracy has been successfully tested when compared to numerical calculations from the vector finite element method, and the results are published in the literature. This method facilitates the calculation of the spatial-distributed perturbation effects on individual electric field components for each propagating mode.

Analysis of Spatially Doped Fused Silica Fiber Optic by Means of a Hamiltonian Formulation of the Helmholtz Equation