Iterative nonlinear beam propagation method and its application in nonlinear devices

Abstract

In this thesis, an iterative nonlinear beam propagation method is introduced and applied to optical devices. This method is based on Hamiltonian ray tracing and the Wigner distribution function. First, wave propagation simulation using Hamiltonian ray tracing is illustrated and verified with different examples. Based on this, the iterative method is presented for beam propagation in nonlinear media, which is validated with common Kerr effect phenomena such as self-focusing and spatial solitons. As the application to the analysis of nonlinear optical devices, this method is applied to nonlinear Lineburg lens. It is found that the nonlinear Liineburg lens is able to compensate the focal shift caused by the diffraction of Gaussian illumination. The iterative nonlinear beam propagation method is computationally efficient and provides much physical insights into the wave propagation. Since it is based on Hamiltonian ray tracing, a ray diagram can be easily obtained which contains the evolution of generalized radiances. Besides bulk nonlinear media, this method provides a systematic approach to beam propagation problem in complex media such as nonlinear photonic crystals and metamaterials. Also, it is applicable to both coherent and partially coherent illumination. Therefore, this method has potential applications in the design and analysis of nonlinear optical devices and systems.