Thresholds of lasing and modal patterns of a limacon cavity analysed with Muller's integral equations

Smotrova, E.I.; Nosich, Alexander I.

doi:10.1109/lfnm.2011.6144962

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…Some preliminary results of this analysis have been published in contributed conference papers [34][35][36]; however, they are presented here in a more complete and convincing manner. Special attention is paid to the connection of the rate of convergence with the contour smoothness.…”

Section: Introductionmentioning

confidence: 92%

Spectra, thresholds, and modal fields of a kite-shaped microcavity laser

et al. 2013

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We investigate the lasing spectra, threshold gain values, and emission directionalities for a two-dimensional microcavity laser with a "kite" contour. The cavity modes are considered accurately using the linear electromagnetic formalism of the lasing eigenvalue problem with exact boundary and radiation conditions. We develop a numerical algorithm based on the Muller boundary integral equations discretized using the Nystrom technique, which has theoretically justified and fast convergence. The influence of the deviation from the circular shape on the modal characteristics is studied numerically for the modes polarized in the cavity plane, demonstrating opportunities of directionality improvement together with preservation of a low threshold. These advantageous features are shown for the perturbed whispering-gallery modes of high-enough azimuth orders. Other modes can display improved directivities while suffering from drastically higher threshold levels. Experiments based on planar organic microcavity lasers confirm the coexistence of Fabry-Perot-like and whispering-gallery-like modes in kite-shaped cavities and show good agreement with the predicted far-field angular diagrams.

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Section: Introductionmentioning

confidence: 92%

Spectra, thresholds, and modal fields of a kite-shaped microcavity laser

et al. 2013

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“…Now, following [41], p. 69, we present the Nyström method for numerical solution of nonlinear eigenvalue problem (14). Note that this method was applied, in the simplest form, in [16] and then sophisticated in [17], to take full account of possible symmetry lines of a 2-D cavity.…”

Section: Nyström Methodsmentioning

confidence: 99%

“…, 2n − 1. Applying approximations (33) and equating both sides of the functional equality following from (14) on the mesh points Ξ h , we reduce (14) to the following finite-dimensional nonlinear eigenvalue problem:…”

Section: Nyström Methodsmentioning

confidence: 99%

“…Such observations lied in the core of the lasing eigenvalue problem (LEP) approach, suggested in [9][10][11] and applied to the on-threshold analysis of lasing modes of 2-D circular [10][11][12][13], and non-circular cavities: Limacon [14], ellipse [15], kite [16], square and other regular polygons [17]. As is easy to see, a presence of both active regions with gain material and lossy regions with absorptive material can be taken into account, in LEP, without any difficulty.…”

Section: Introductionmentioning

confidence: 99%

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

Spiridonov

Karchevskii

Nosich³

2019

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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.

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