Exponentially Converging NystrÖm Methods Applied to the Integral-Integrodifferential Equations of Oblique Scattering/Hybrid Wave Propagation in Presence of Composite Dielectric Cylinders of Arbitrary Cross Section

Tsalamengas, J.L.

doi:10.1109/tap.2007.908833

Cited by 27 publications

(19 citation statements)

References 19 publications

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“…Then, applying the second Green's formula to the functions G j ⃗ r; ⃗r 0 and U j , we obtain (see also [37])…”

Section: B Reduction To the Muller Boundary Integral Equationsmentioning

confidence: 99%

“…Discretization Using the Quadratures As mentioned, there are several approaches to a reasonable discretization of BIEs. One of the most efficient discretization techniques is the method of quadratures, also known as the Nystrom method [32,33,37,40,41]. This method is based on the approximation of smooth unknown functions by certain polynomials and the replacement of the integrals with approximate sums using the appropriate quadrature formulas.…”

Section: B Reduction To the Muller Boundary Integral Equationsmentioning

confidence: 99%

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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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“…Then, applying the second Green's formula to the functions G j ⃗ r; ⃗r 0 and U j , we obtain (see also [37])…”

Section: B Reduction To the Muller Boundary Integral Equationsmentioning

confidence: 99%

Section: B Reduction To the Muller Boundary Integral Equationsmentioning

confidence: 99%

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

et al. 2013

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“…One of the most efficient discretization techniques is the method of quadratures, also known as the Nystrom method [16]- [18]. This method is based on the replacement of the integrals with approximate sums using the appropriate quadrature formulas.…”

Section: Discretization Of Integral Equationsmentioning

confidence: 99%

Directional light emission from a kite-shaped microcavity laser

Smotrova

Nosich

2011

2011 13th International Conference on Transparent Optical Networks

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The lasing modes in a thin kite-shaped active microcavity are considered as solutions to a specifically tailored two-dimensional (2-D) linear eigenvalue problem for the Maxwell equations with exact boundary and radiation conditions. This problem is reduced to the set of Muller's boundary integral equations discretized using the adequate quadrature formulas. The eigenvalues are found numerically as the roots of the corresponding determinantal equation. The results of the study of mode lasing thresholds, spectra and light emission directivities are presented.

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“…This latter method is based on the replacement of the integrals with approximate sums using the appropriate quadrature formulas. As some of the kernel functions have logarithmic singularities, it is convenient to represent all of the kernels in (3) and (4) in such a way that these singularities are extracted [8], [9]. Then the integrals are approximated by two different quadrature rules for the regular and singular parts with the same equidistant set of points.…”

Section: Discretisation Of Integral Equationsmentioning

confidence: 99%

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

Smotrova

Nosich

2011

2011 11th International Conference on Laser and Fiber-Optical Networks Modeling (LFNM)

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Abstract:We consider the lasing characteristics of the natural modes in a limacon active microcavity. The modes are the solutions to the two-dimensional (2-D) linear eigenproblem for the Maxwell equations with exact boundary conditions and radiation condition at infinity. This problem is reduced equivalently to the set of Muller's integral equations of the Fredholm second kind and discretized using the exponentially convergent quadrature formulas. The numerical studies of lasing thresholds and modal field patterns of the whispering-gallery modes are presented. They demonstrate that the directionality of emission from a cavity deformed from the circle can be enhanced in several times using relatively small deformations. However this is achieved at the expense of higher threshold values.

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Exponentially Converging NystrÖm Methods Applied to the Integral-Integrodifferential Equations of Oblique Scattering/Hybrid Wave Propagation in Presence of Composite Dielectric Cylinders of Arbitrary Cross Section

Cited by 27 publications

References 19 publications

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

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

Directional light emission from a kite-shaped microcavity laser

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

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