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

Abstract

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.

Test of accuracy of the generalized boundary conditions in the scattering by thin dielectric strips

“…In the 2D case, such derivation can be found in [20,21] and the resulting equations have the following form: 11 12 ( ) ( , ') ( ') ' …”

“…is the limit value of the normal derivative of the total field function on the closed contour k k H , and of their first-order and second-order normal derivatives [19][20][21][22].…”

“…As known [20,21], if L is a Lyapunov curve then the kernel functions have only logarithmic singularities, and (8), (9) together are a Fredholm second kind IE. This guarantees convergence of conventional MM schemes of its solution.…”

“…They can serve as a source of reference data if, besides of guaranteed convergence, they are free from the spurious real-valued eigenvalues [18]. This is true for the Muller BIE (MBIE) that is actually a pair of coupled Fredholm second-kind IEs [19][20][21][22].…”

“…Here, the Nystrom-type meshless discretization using interpolation polynomials and quadrature formulas is known as efficient solution technique [20,21]. We have adapted it for a piecewise smooth contour of our strip scatterer.…”