For the analysis of light propagation in photonic guided-wave ring microresonators, leaky-mode solvers for bent channel waveguides are often used. In the analytical approach, the leaky mode field is expressed in terms of cylindrical functions of complex arguments and a complex order which plays a role of the ( azimuthal) propagation constant. In this contribution we present a modified approach which takes into account the circular symmetry of the structure. We calculate the eigenmodes of a lossy microresonator as modes with complex eigenfrequencies. In this approach, the eigenmodes are described by cylindrical functions of an integer order and a complex argument. Similarities and differences of both approaches are demonstrated using simple examples of 2D ( planar) structures. References: 15
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