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Open AccessArticle

Mathematical and Numerical Modeling of On-Threshold Modes of 2-D Microcavity Lasers with Piercing Holes

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Laboratory of Computational Technologies and Computer Modeling, Kazan Federal University, 18 Kremlevskaya st., 420008 Kazan, Russia
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Department of Applied Mathematics, Kazan Federal University, 18 Kremlevskaya st., 420008 Kazan, Russia
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Laboratory of Micro and Nano Optics, Institute of Radio-Physics and Electronics NASU, vul. Proskury 12, 61085 Kharkiv, Ukraine
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(3), 101; https://doi.org/10.3390/axioms8030101
Received: 31 July 2019 / Revised: 18 August 2019 / Accepted: 19 August 2019 / Published: 1 September 2019
This study considers the mathematical analysis framework aimed at the adequate description of the modes of lasers on the threshold of non-attenuated in time light emission. The lasers are viewed as open dielectric resonators equipped with active regions, filled in with gain material. We introduce a generalized complex-frequency eigenvalue problem for such cavities and prove important properties of the spectrum of its eigensolutions. This involves reduction of the problem to the set of the Muller boundary integral equations and their discretization with the Nystrom technique. Embedded into this general framework is the application-oriented lasing eigenvalue problem, where the real emission frequencies and the threshold gain values together form two-component eigenvalues. As an example of on-threshold mode study, we present numerical results related to the two-dimensional laser shaped as an active equilateral triangle with a round piercing hole. It is demonstrated that the threshold of lasing and the directivity of light emission, for each mode, can be efficiently manipulated with the aid of the size and, especially, the placement of the piercing hole, while the frequency of emission remains largely intact. View Full-Text
Keywords: microcavity laser; eigenvalue problem; active microcavity; boundary integral equation; Nyström method microcavity laser; eigenvalue problem; active microcavity; boundary integral equation; Nyström method
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Spiridonov, A.O.; Karchevskii, E.M.; Nosich, A.I. Mathematical and Numerical Modeling of On-Threshold Modes of 2-D Microcavity Lasers with Piercing Holes. Axioms 2019, 8, 101.

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