Analytical solutions of coupled-mode equations for microring resonators

摘要

We present a study on analytical solutions of coupled-mode equations for microring resonators with an emphasis on occurrence of all-optical EIT phenomenon, obtained by using a cofactor. As concrete examples, analytical solutions for a $3 imes 3$ linearly distributed coupler and a circularly distributed coupler are obtained. The former corresponds to a non-degenerate eigenvalue problem and the latter corresponds to a degenerate eigenvalue problem. For comparison and without loss of generality, analytical solution for a $4 imes 4$ linearly distributed coupler is also obtained. This paper may be of interest to optical physics and integrated photonics communities.