Nonparaxial beam propagation in nonlinear optical medium.

摘要

Beam propagation methods (BPMs) have long been powerful tools for research in various fields of optics. However, studies on the traditional BPMs based on paraxial approximation exposed their inevitable limitations in dealing with beams of large divergence angles, which are quite common in integrated optics, nonlinear optics and other cases where beam size undergoes drastic change. Thus nonparaxial BPMs are essential ways for investigations in those areas. The Lanczos method based on Krylov subspace technique had been proposed for solving nonparaxial beam propagation problems. Although we have improved the Lanczos method by applying cylindrical coordinates instead of Cartesian coordinates as well as limiting high frequency components, its application is still confined to beam propagation in lossless media under a small divergence angle and low resolution. As a remedy, we have developed a modified Arnoldi method (MAM) based on a new Krylov subspace that can handle beam propagation in various media with high resolution and large divergence angle. The complex Pade approximation and Zolotarev approximation were investigated for square root operation. The former one was adopted to construct MAM with both discrete Fourier basis and discrete Bessel basis. Tests have been carried out on linear propagations, nonlinear soliton propagation as well as Gaussian beam propagation in a grade-index fiber, which demonstrated the superiority of MAM over the original BPMs. The application of MAM to the study of ultra-short pulse propagation in a nonlinear dispersive medium revealed the asymmetric pulse split pattern. As a preparation for the future work, we introduced reliable bidirectional beam propagation techniques that are essential for modeling of propagation in photonic crystal structure.