Yuan Lijun, Lu Ya Yan
College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China.
Opt Express. 2013 May 20;21(10):11952-64. doi: 10.1364/OE.21.011952.
Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime.
非线性光学效应可通过光子晶体微腔得到增强，并用于开发具有低功耗要求的实用超紧凑型光学器件。时域有限差分法是模拟非线性光学器件的标准数值方法，但在精度和效率方面存在局限性。本文针对非线性效应集中在微腔中的非线性光学器件，开发了一种严格且高效的频域数值方法。该方法通过一个严格且数值计算得到的边界条件来替代微腔外部的线性问题，然后在微腔周围的小区域内迭代求解非线性问题。由于问题规模显著减小，迭代方法的收敛更容易实现。针对具有克尔非线性的特定二维光子晶体波导 - 腔系统，利用能够利用结构几何特征的数值方法给出了该方法。该方法能够计算出在强非线性区域呈现光学双稳现象的多个解。
