Iterative finite difference beam propagation method analysis of nonlinear optical waveguide excitation problem

Abstract

AbstractThe beam propagation method (BPM), used widely for analyzing optical waveguides and optical circuits, is also being applied to devices that include nonlinear materials. However, in the analysis of nonlinear optical devices using the conventional BPM, in many cases it is assumed that the field intensity distribution does not change within the step length in propagation direction. Therefore, for accurate calculation, the step size in the propagation direction must be extremely small, which results in long calculation times.Therefore, this paper proposes and formulates a numerical method where the solution is forced to converge by the iterative calculation of a difference equation over each propagation step of the Crank‐Nicolson BPM method. Using this method, first, we analyzed the case where the fundamental TE mode propagates in the dielectric slab waveguide that has a Kerr‐like nonlinear cladding. By calculating the emission angle of the optical beam into the cladding, the present method is compared with the conventional method. After it is demonstrated that this present method is effective, the dependency of the optical beam emission angle for the incident power is shown. Furthermore, the effect of the beamwidth on the excitation is analyzed in the case where a nonlinear stationary wave is excited by a Gaussian beam and the interesting results are proved.