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17 February 2003 Polynomial Expansion of Fields for Extraction of Eigenmodes in Layered Waveguides
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Proceedings Volume 4833, Applications of Photonic Technology 5; (2003) https://doi.org/10.1117/12.474744
Event: Applications of Photonic Technology 5, 2002, Quebec City, Canada
Abstract
In this article, polynomial expansion approach for extraction of guided and leaky modes in layered waveguides in which loss and gain can be present simultaneously is proposed. To verify the method, results of analysis of a typical test case have been compared to the other references, proving a good agreement. Polynomial expansion is a nonharmonic expansion and does not involve harmonic functions or intrinsic modes of homogenous layers. This approach has the benefit of leading to algebraic dispersion equations rather than transcendental dispersion equation; therefore, it will be easier to solve compared with other methods such as argument principle method (APM), reflection pole method (RPM) or wavevector density method (WDM), which are solving the transcendental equation via integral methods. Besides, algebraic dispersion equation will be obtained without any numerical stability problem, while ordinary transcendental dispersion equation, which is usually derived by transfer matrix method, is difficult to obtain due to stability problem in multiplying transfer matrices.
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Khashayar Mehrany and Bizhan Rashidian "Polynomial Expansion of Fields for Extraction of Eigenmodes in Layered Waveguides", Proc. SPIE 4833, Applications of Photonic Technology 5, (17 February 2003); https://doi.org/10.1117/12.474744
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