Optimized method of lines for non-linear waveguide problems

Spiller Waldemar

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Optimized method of lines for non-linear waveguide problems

机译：Optimized method of lines for non-linear waveguide problems

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摘要

The Method of Lines is a semi-analytical versatile tool for the solution of partial differential equations. For the analysis of spatial complex linear waveguide structures, this method is combined with impedance/admittance and field transformation, as well as with finite differences. This paper extends this approach to the treatment of structures with non-linear dielectric materials. The non-linear generalized transmission line equations are derived. An iterative algorithm based on the impedance/admittance transformation with the field transformation obtains efficient and self-consistent solutions. For demonstration, a non-linear stripe waveguide is considered. The Kerr non-linearity was investigated, though the general case is treatable. As a criterion for the correctness of the algorithm, a second harmonic generation as well as a bidirectional, spatially, and temporally energy exchange between the harmonics was examined. The specific limiting factors for the algorithm were explored. The approach can be used for any spatial structure, including, for instance, photonic crystal waveguides and metamaterials.

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来源
《Optical and Quantum Electronics》 |2022年第9期|共22页
作者
Spiller Waldemar;
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作者单位

FernUniversitat;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
中图分类光学;
关键词
Method of lines (MoL); Non-linear generalized transmission line equations; Impedance; admittance transformation; Finite differences; Non-linear waveguides; Second-order non-linear phenomena; Self-consistent solutions; EFFICIENT;

Optimized method of lines for non-linear waveguide problems

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