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Analytic solutions to the wave equation for saturable Kerr media with application to nonlinear directional couplers.

机译：饱和Kerr介质波动方程的解析解及其在非线性定向耦合器中的应用。

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摘要

Much work has been done to find exact analytic solutions for the electric field of modes in various structures in terms of Jacobian elliptic functions, valid when the intensity-dependent refractive index obeys the Kerr model. This is unrealistic for multiple quantum well (MQW) structures even at moderate power levels due to the saturation of the nonlinearity. This has prompted interest in solving the nonlinear wave equation for modes in saturating materials.;To date, finding the power dependent modes of simple three layer structures in saturable materials has been accomplished in the literature, however either approximate techniques have been employed, such as coupled mode theory, valid only in the limit that the field distribution does not change appreciably over the full range of possible guided wave powers, or an exact technique is used which only derives a dispersion relation from which the effective index of a mode may be found, but no solution of the electric field problem itself has been attempted. Instead, the electric field distribution must be found using a numerical finite difference technique on the wave equation itself.;In this thesis, original exact analytic expressions for the electric field solving the nonlinear wave equation including saturation effects for a lossless saturable Kerr-like medium are, for the first time, found. These solutions are then applied to the coupling layer of a nonlinear directional coupler as a numerical example of their use, both to find the TE power-dependent guided modes of the structure and to determine the corresponding electric field profile of the modes via power-dependent dispersion relations.;The critical power, defined in the literature to be the level of input power above which 100% of the power can not be switched between the guides of a coupler, is shown in this thesis to be the result of a mathematical misinterpretation in both saturable media as well as in nonsaturable Kerr media, leading to the conclusion that the phenomenon of critical power does not actually exist.;Finally, absorptive losses are considered. Differing attenuation coefficients for the symmetric and antisymmetric TE mode leads to less than 100% power transfer at any input power. However, for light which is polarized perpendicular to the plane of the MQW layers (TM modes of the coupler) the hh-exciton absorption peak is almost not active, therefore the hh-exciton completely dominates the absorption spectrum. Hence when the excitation wavelength is close to the hh-exciton peak, the TM mode does not suffer from high absorption, therefore a distinctly different coupling behavior exists for the TM mode as compared with the TE mode, predicting polarization dependent switching in this device.
机译：已经进行了许多工作，以根据雅可比椭圆函数找到各种结构中模态电场的精确解析解，当强度相关的折射率服从Kerr模型时有效。由于非线性的饱和，即使在中等功率水平下，这对于多量子阱（MQW）结构也是不现实的。这引起了人们对求解饱和材料中模态的非线性波动方程的兴趣。迄今为止，文献中已经完成了在饱和材料中找到简单的三层结构的功率相关模态的研究，但是已经采用了近似技术，例如耦合模式理论，仅在以下范围内有效：场分布在可能的导波功率的整个范围内不会发生明显变化，或者使用一种精确的技术，仅得出一种色散关系，从中可以找到模式的有效指标，但尚未尝试解决电场问题本身。取而代之的是，必须在波动方程本身上使用数值有限差分技术来找到电场分布。；本文中，电场的原始精确解析表达式解决了非线性波动方程，包括对无损可饱和克尔类介质的饱和效应第一次被发现。然后，将这些解决方案应用于非线性定向耦合器的耦合层，作为其使用的数值示例，既可以找到结构的TE功率相关导模，也可以通过功率相关来确定模式的相应电场分布色散关系。临界功率，在文献中定义为输入功率的水平，高于该水平时，不能在耦合器的导轨之间切换100％的功率，这是数学错误解释的结果在饱和介质和非饱和Kerr介质中，都得出了实际上不存在临界功率现象的结论。最后，考虑了吸收损耗。对称和反对称TE模式的衰减系数不同，导致在任何输入功率下的功率传输都小于100％。但是，对于垂直于MQW层平面（耦合器的TM模式）偏振的光，hh激子吸收峰几乎不起作用，因此hh激子完全占据了吸收光谱。因此，当激发波长接近hh激子峰时，TM模式不会受到高吸收，因此与TE模式相比，TM模式存在明显不同的耦合行为，从而预测了该设备中偏振相关的开关。

著录项

  • 作者

    Begin, John David.;

  • 作者单位

    Technical University of Nova Scotia (Canada).;

  • 授予单位 Technical University of Nova Scotia (Canada).;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 1995
  • 页码 215 p.
  • 总页数 215
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 耳科学、耳疾病;
  • 关键词

  • 入库时间 2022-08-17 11:49:35

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