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

Abstract

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.

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

“…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.…”

“…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.…”

“…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.…”

“…The main idea of the present work is to provide, using results of [21], a rigorous proof of convergence of the Galerkin method proposed previously in [19,20] for the numerical modeling of lasers with piercing holes, and to derive the accuracy estimates for the approximate eigenvalues and eigenfunctions. Our consideration, similar to [8], is based on the fundamental results of the theory of holomorphic operator-valued functions.…”

Guest Editorial: Method of analytical regularisation for new frontiers of applied electromagnetics

“…Repina et al[1] shows an efficient engineering tool for the design and optimisation of promising microring lasers. It is based on the Muller Boundary Integral Equation and the entire-domain Galerkin discretisation method, adapted to the study of on-threshold modes of the open cavities with active regions.In the paper 'Magnetic field penetration through a circular aperture in a perfectly conducting plate excited by a coaxial loop' by Lovat et al[2], the first-kind singular integral equation in the Hankel transform domain is analytically regularised by means of the application of the Abel integral-transform technique.…”