A modified beam propagation method to model second harmonic generation in optical fibers

A finite-difference implementation of the beam propagation method (BPM) is used to solve the paraxial, scalar wave equation with a nonlinear source term. A transparent boundary condition capable of handling asymmetric modes is incorporated in the finite-difference algorithm. This nonlinear BPM is used to model the generation and propagation of second harmonic light in an optical fiber which has been prepared for second harmonic generation (SHG) by the formation of a _χ⁽²⁾ grating. This method can be used to predict the guided mode in which the generated second harmonic light propagates based on the modes of the writing (fundamental and second harmonic) and reading (fundamental only) light. The effects of self-phase modulation (SPM) and cross-phase modulation (XPM) are included in the model