Mathematical and Numerical Analysis of the Generalized Complex-Frequency Eigenvalue Problem for Two-Dimensional Optical Microcavities

DOI10.1137/19M1261882zbMath1452.65318OpenAlexW3082228679MaRDI QIDQ5123480

A. O. Oktyabrskaya, E. M. Karchevskij, A. O. Spiridonov, Alexander I. Nosich

Publication date: 29 September 2020

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1261882

zbMATH Keywords

nonlinear eigenvalue problemNyström methodmicrocavity laserMüller boundary integral equations

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Lasers, masers, optical bistability, nonlinear optics (78A60) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Boundary element methods for boundary value problems involving PDEs (65N38) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (4)

Numerical modeling of lattice modes of photonic-crystal lasers by Galerkin method with exact matrix elements ⋮ Resonance frequencies of arbitrarily shaped dielectric cylinders ⋮ Muller boundary integral equations in the microring lasers theory ⋮ Accurate simulation of on-threshold modes of microcavity lasers with active regions using Galerkin method

Cites Work

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• Rational eigenvalue problems and applications to photonic crystals
• Eigenvibrations of a beam with elastically attached load
• Multidimensional weakly singular integral equations
• Ausstrahlungsbedingungen für die Wellengleichung
• Linear integral equations.
• Inverse acoustic and electromagnetic scattering theory.
• Rigorous formulation of the lasing eigenvalue problem as a spectral problem for a Fredholm operator function
• Perturbation theory for linear operators.
• Convergence of infinite element methods for scalar waveguide problems
• Meromorphic families of compact operators
• Convergence of Hardy Space Infinite Elements for Helmholtz Scattering and Resonance Problems
• Combined boundary integral equations for acoustic scattering-resonance problems
• STABILITY OF ACOUSTIC PROPAGATION IN 2D DUCT FLOWS: A LOW FREQUENCY APPROACH
• Residual Inverse Iteration for the Nonlinear Eigenvalue Problem
• The convergence rate of approximate methods in the eigenvalue problem when the parameter appears non-linearly
• On the discrete approximation of eigenvalue problems with holomorphic parameter dependence
• Approximation in eigenvalue problems for holomorphic fredholm operator functions I
• Approximation in eigenvalue problems for holomorphic fredholm operator functions Ii (Convergence Rate)
• Mathematical Analysis of the Generalized Natural Modes of an Inhomogeneous Optical Fiber
• Boundary Integral Equations for Calculating Complex Eigenvalues of Transmission Problems
• Integral Equation Methods in Scattering Theory

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