# COUPLING COEFFICIENTS OF DIFFERENT SPHERICAL DIELECTRIC MICRORESONATORS

## DOI:

https://doi.org/10.20535/2411-2976.12018.49-57## Keywords:

infrared range, integrated optics, optical filter, bandstop filter, bandpass filter, microresonator.## Abstract

**Background.** Nowadays, further increase of processing and transmission speed of information is associated with the development of hybrid integrated circuits, combining electrical and optical components. One of the important constituent parts of future optical integrated circuits are filters that can be conveniently implemented using so-called disc microresonators with whispering gallery oscillations. Technically, the problem of manufacturing such filters in the infrared and even in the visible wavelength range has been solved, but calculation of parameters and tuning of multilink filters is impossible without further development of the theory of their building. The development of such a theory is based on the electrodynamic modeling of processes that occur in complex systems of coupled microcavities, coupled with transmission line. At present, the study of filters that built on different microresonators hasn’t been carried out.**Objective.** The aim of the research is to construct the theory of electromagnetic wave scattering of the integral optical transmission lines on systems of coupled diversiform optical microresonators with whispering gallery modes, as well as

development of mathematical models of filters constructed using various disk microresonators, and investigation of new structures of coupled microresonators with acceptable scattering characteristics.**Methods.** To construct a mathematical model of filters, an approximate solution of the Maxwell equations based on perturbation theory is used. The application of perturbation theory made it possible to find a solution to the problem of calculating the S-matrix of the filter in an analytical form.**Results.** An electrodynamic model for the scattering of optical transmission line waves by a system of coupled diversiform microresonators made of different dielectrics is developed. New structures of microresonators, realizing bandpass and bandstop filters, are investigated and their scattering characteristics are calculated.**Conclusions.** The theory of scattering of electromagnetic waves by systems of coupled diversiform optical microresonators is expanded. A new definition of the coupling coefficients of different microresonators is given. New filter models are constructed.**Keywords:** infrared range; integrated optics; optical filter; bandstop filter; bandpass filter; microresonator.

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