McGurn A R
Department of Physics, Western Michigan University, Kalamazoo, MI 49008, USA.
J Phys Condens Matter. 2009 Dec 2;21(48):485302. doi: 10.1088/0953-8984/21/48/485302. Epub 2009 Oct 30.
The transmission of guided modes through a barrier of Kerr nonlinear optical media contained within a photonic crystal waveguide of linear dielectric media is studied in order to determine the effects of the dispersion of the incident waveguide modes on their barrier transmission coefficients. In McGurn (2008 Phys. Rev. B 77 115105) the conditions under which resonances exist in the guided mode transmission through the barrier were investigated for an incident waveguide mode having a single fixed frequency and a wavevector near the edge of the Brillouin zone. The transmission coefficient maxima were determined as functions of two parameters characterizing the Kerr nonlinearity of the barrier media and shown to exhibit a complex pattern in the two parameter space of the Kerr parameters, associated with various kinds of modes excited within the barrier. In the present paper the focus is on how the pattern of transmission resonance maxima in the two parameter Kerr parameter space is affected by varying the wavevector and frequency of the guided modes incident on the barrier. In addition, the effects of the barrier size on the pattern are determined. The focus of the paper is on affirming the classification scheme proposed in our previous papers upon the introduction of dispersive effects. The dynamical equations of our model are quite general, so it is expected that this scheme will be useful in studying the nonlinear dynamics of other nonlinear physical models which may or may not be based on photonic crystal waveguides.
研究了线性电介质光子晶体波导中包含的克尔非线性光学介质势垒对导模的传输，以确定入射波导模的色散对其势垒传输系数的影响。在McGurn（2008年，《物理评论B》77卷，115105页）中，对于具有单一固定频率且波矢靠近布里渊区边缘的入射波导模，研究了通过势垒的导模传输中存在共振的条件。确定了传输系数最大值作为表征势垒介质克尔非线性的两个参数的函数，并表明在克尔参数的二维参数空间中呈现出复杂的模式，这与势垒内激发的各种模式相关。在本文中，重点关注的是在二维克尔参数空间中，传输共振最大值的模式如何受到入射到势垒上的导模的波矢和频率变化的影响。此外，还确定了势垒尺寸对该模式的影响。本文的重点是在引入色散效应后，确认我们之前论文中提出的分类方案。我们模型的动力学方程非常通用，因此预计该方案将有助于研究其他可能基于或不基于光子晶体波导的非线性物理模型的非线性动力学。
