The waveguiding in thin planar structures with quadratic magneto-optical medium is analysed. The permittivity tensor elements with quadratic magneto-optical constants are specified. From synchronous condition for guided modes in layered system with magnetic ordering the dispersion relation of waveguide is presented. The reflection coefficients for s-polarized light at transversal, longitudinal, and polar configurations as incidence angle function are described. The influence of quadratic magneto-optical effect on the resonant character of the waveguiding term is described in detail. The theory covers the situation in which the optical response of the structure is linear in the amplitude of the incident wave.
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