Mathematical model of the optical vortex beams emission by the integrated microring resonator with grating

Abstract The paper proposes a novel mathematical model of emission and spatial distribution of the optical radiation that carries orbital angular momentum, i.e. optical vortex beams, by microring resonators (MRRs). The considered MRR features a diffraction grating formed by holes perforated on its surface, facilitating the emission of vortex beams. The emission process is analytically examined using the theory of scattering electromagnetic waves by permittivity inhomogeneities, applying the Rayleigh approximation. We use the vector representation of the electromagnetic fields utilizing the Kirchhoff–Helmholtz integral theorem to describe the field spatial distribution. Unlike already known ones, the proposed model considers the impact of the MRR and the diffraction grating parameters, including its inhomogeneities configuration, on the emitted field. Numerical simulations conducted using the Finite Difference Time Domain method in the Ansys Lumerical 2020 R2.4 environment support the validity of the proposed analytical model. The results we obtained enable us to identify the area with the highest energy flux density from the resonator at a specified distance analytically and with high accuracy. This capability can greatly streamline and enhance the development and optimization of vortex field emitters based on micro-ring resonators.