Numerical Modeling of Lattice Modes of Photonic-Crystal Lasers by Galerkin Method with Exact Matrix Elements

The paper is devoted to the mathematical modeling of the two-dimensional dielectric photonic-crystal resonators. The original eigenvalue problem for the Helmholtz operator on the plane is reduced to the nonlinear eigenvalue problem for the system of Muller boundary integral equations. The Galerkin m...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023, Vol.44 (1), p.325-340
Main Authors: Ketov, I. V., Spiridonov, A. O., Repina, A. I., Karchevskii, E. M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Boundary integral method
Crystal lattices
Eigenvalues
Emission analysis
Galerkin method
Geometry
Integral equations
Lattice vibration
Mathematical analysis
Mathematical Logic and Foundations
Mathematical models
Mathematics
Mathematics and Statistics
Numerical models
Operators (mathematics)
Photonic crystals
Probability Theory and Stochastic Processes
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Summary:The paper is devoted to the mathematical modeling of the two-dimensional dielectric photonic-crystal resonators. The original eigenvalue problem for the Helmholtz operator on the plane is reduced to the nonlinear eigenvalue problem for the system of Muller boundary integral equations. The Galerkin method with a trigonometric basis is applied to the system of Muller integral equations. The formulas defining the matrix elements of the obtained nonlinear algebraic eigenvalue problem are determined analytically. Using the program complex, based on the derived formulas, the lattice modes are looked for and threshold values and the direction of the laser emission are investigated.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223010183