Numerical modeling of on-threshold modes of eccentric-ring microcavity lasers using the Muller integral equations and the trigonometric Galerkin method

Oktyabrskaya, Alina O.; Repina, Anna I.; Spiridonov, Alexander O.; Karchevskii, Evgenii M.; Nosich, Alexander I.

doi:10.1016/j.optcom.2020.126311

Cited by 15 publications

(18 citation statements)

References 26 publications

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“…This corresponds to the effective refractive index of a 200-nm GaAs layer at the optical communication frequency [28]. According to Oktyabrskaya et al [28], we use the dimensionless…”

Section: Numerical Resultsmentioning

confidence: 99%

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Trade‐off between threshold gain and directionality of emission for modes of two‐dimensional eccentric microring lasers analysed using lasing eigenvalue problem

Repina

Oktyabrskaya

Spiridonov

et al. 2021

IET Microwaves Antenna & Prop

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This article discusses how a trade-off between the high directionality of emissions and low threshold gain can be achieved in active eccentric microring cavities. Our findings are based on the lasing eigenvalue problem formalism, considered using the method of analytical regularisation, and an extremely fast and accurate dedicated Galerkin method, applied to a set of associated Muller boundary integral equations. This method allows us to investigate symmetric and antisymmetric modes separately, on the threshold of nonattenuation in time emission. Numerical results show that the directivities of emission of working modes in a given frequency range, together with their threshold values of gain, are controlled by the size and location of the air hole in the cavity. The high efficiency of the developed code allows us to make an elementary optimisation of the considered cavity; this code is a promising engineering tool in the design of microring lasers.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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“…This corresponds to the effective refractive index of a 200-nm GaAs layer at the optical communication frequency [28]. According to Oktyabrskaya et al [28], we use the dimensionless…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Problem ( 14) could be solved numerically using a universal trigonometric Galerkin method, explained in Oktyabrskaya et al [28]. 2D cavities, in which one of the coordinate axes is the line of symmetry, are of particular practical interest.…”

Section: Galerkin Methods Based On the Symmetry Of The Problemmentioning

confidence: 99%

Trade‐off between threshold gain and directionality of emission for modes of two‐dimensional eccentric microring lasers analysed using lasing eigenvalue problem

Repina

Oktyabrskaya

Spiridonov

et al. 2021

IET Microwaves Antenna & Prop

Self Cite

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“…Together with an account of the symmetry, this made the calculations much faster and more stable. Additionally, the analysis of the numerical experiments in [19,20] demonstrated the exponential convergence of the Galerkin method.…”

Section: Introductionmentioning

confidence: 92%

“…Recently, for numerical simulation of more complicated 2D microcavity lasers, namely, active cavities with piercing holes [18], a modified version of the Muller BIEs, together with a trigonometric Galerkin discretization technique, was proposed [19,20]. Mathematically, this means that there is an additional region (the hole) inside the cavity domain, and hence, an additional boundary in the integral-equation formulation.…”

Section: Introductionmentioning

confidence: 99%

“…In [19,20], the authors investigated the directivities, spectra, and thresholds of the on-threshold modes of eccentric microring lasers. For such circular microcavity lasers with non-concentric circular air holes, explicit expressions for the matrix elements were obtained in [19,20]. Together with an account of the symmetry, this made the calculations much faster and more stable.…”

Section: Introductionmentioning

confidence: 99%

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Exponentially Convergent Galerkin Method for Numerical Modeling of Lasing in Microcavities with Piercing Holes

Spiridonov

Repina

Ketov

et al. 2021

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The paper investigates an algorithm for the numerical solution of a parametric eigenvalue problem for the Helmholtz equation on the plane specially tailored for the accurate mathematical modeling of lasing modes of microring lasers. The original problem is reduced to a nonlinear eigenvalue problem for a system of Muller boundary integral equations. For the numerical solution of the obtained problem, we use a trigonometric Galerkin method, prove its convergence, and derive error estimates in the eigenvalue and eigenfunction approximation. Previous numerical experiments have shown that the method converges exponentially. In the current paper, we prove that if the generalized eigenfunctions are analytic, then the approximate eigenvalues and eigenfunctions exponentially converge to the exact ones as the number of basis functions increases. To demonstrate the practical effectiveness of the algorithm, we find geometrical characteristics of microring lasers that provide a significant increase in the directivity of lasing emission, while maintaining low lasing thresholds.

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Accurate Simulation of On-Threshold Modes of Microcavity Lasers with Active Regions Using Galerkin Method

Repina

Oktyabrskaya

Ketov

et al. 2021

Lecture Notes in Computational Science and Engineering

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Numerical modeling of on-threshold modes of eccentric-ring microcavity lasers using the Muller integral equations and the trigonometric Galerkin method

Cited by 15 publications

References 26 publications

Trade‐off between threshold gain and directionality of emission for modes of two‐dimensional eccentric microring lasers analysed using lasing eigenvalue problem

Trade‐off between threshold gain and directionality of emission for modes of two‐dimensional eccentric microring lasers analysed using lasing eigenvalue problem

Exponentially Convergent Galerkin Method for Numerical Modeling of Lasing in Microcavities with Piercing Holes

Accurate Simulation of On-Threshold Modes of Microcavity Lasers with Active Regions Using Galerkin Method

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