No 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.

No abstract

We present new method for the numerical reconstruction of the variable refractive index of multi-layered circular weakly guiding dielectric waveguides using the measurements of the propagation constants of their eigenwaves. Our numerical examples show stable reconstruction of the dielectric permittivity function ε for random noise level using these measurements.

This paper investigates an eigenvalue problem for the Helmholtz equation on the plane modeling the laser radiation of two-dimensional microdisk resonators. It was reduced to an eigenvalue problem for a holomorphic Fredholm operator-valued function A(k) . For its numerical solution, the Galerkin method was proposed, and its convergence was proved. Namely, a sequence of the finite-dimensional holomorphic operator functions A n (k) that converges regularly to A(k) was constructed. Further, it was established that there is a sequence of eigenvalues k n of the operator-valued functions A n (k) converging to k 0 for each eigenvalue k0 of the operator-valued function A(k) . If {kn}n∈N is a sequence of eigenvalues of the operator-valued functions A n (k) converging to a number of k 0 , then k 0 is an eigenvalue of A(k) . The estimates for the rate of convergence of {k n } n∈N to k 0 depend either on the order of the pole k0 of the operator-valued function A −1 (k) , or on the algebraic multiplicities of all eigenvalues of A n (k) in a neighborhood of k 0 , or on the number of different eigenvalues of An(k) in this neighborhood. The reasoning is based on the fundamental results of the theory of holomorphic operator-valued functions and is important for the theory of microdisk lasers, because it significantly expands the class of devices interesting for applications that allow mathematical modeling based on numerical methods that are strictly justified.