Optical eigenmodes in plane arrays of cylindrical waveguides. Analysis by means of multiple Mie scattering formalism and phenomenological model

We consider a plane periodical array of parallel cylindrical waveguides with evanescent coupling between them. A new method for calculating the isofrequency curves based on the multiple Mie scattering formalism (MMSF) is developed. This method is compared with the phenomenological model. The derivation of the phenomenological model by means of the MMSF is performed. The formulae for calculation of parameters of the phenomenological model are derived, such as propagation constants and coupling constants.