A three-dimensional (3-D) beam propagation method is described for the analysis of nonlinear optical fibers, where the finite element and finite difference methods are, respectively, utilized for discretizing the fiber cross section and the propagation direction. For efficient evaluation of wide-angle beam propagation, Pade approximation is applied to the differential operator along the propagation direction. In order to improve the efficiency and accuracy of solutions, isoparametric elements and numerical integration formulae derived by Hammer et al. are introduced. The propagation characteristics of nonlinear optical fibers with linear core and nonlinear cladding are analyzed, and unique features of nonlinear guided-wave propagation are investigated. Furthermore, all-optical logic gates with practical, 3-D geometry consisting of optical fibers and a nonlinear film are proposed, and their operations of Boolean arithmetric are demonstrated.
Akira Niiyama and Masanori Koshiba, "Three-Dimensional Beam Propagation Analysis of Nonlinear Optical Fibers and Optical Logic Gates," J. Lightwave Technol. 16, 162- (1998)