Propagation of whispering gallery modes in a microfiber coil having an n-fold helical symmetry is considered. The n-fold helically symmetric deformations of a coiled microfiber is similar to a long period grating introduced by periodic microfiber bending with the azimuthal angle period 2π/n. The considered modes are localized near a geodesic situated at the peripheral part of the microfiber surface. Using the perturbation theory, a simple condition for the stability of this geodesic is found. Violation of this condition happens in a small region localized near a point determined by the phase matching condition for the introduced long period grating. In the classical limit, the unstable region corresponds to the parametric resonance and stochastization of whispering gallery rays. Generally, this region corresponds to resonance intermode coupling, which may result either in the periodic transmission of radiation power between two modes or in the aperiodic wave parametric resonance, which causes simultaneous coupling and power transfer between numerous whispering gallery modes. The obtained results are important for engineering of miniature optical fiber coils and analysis of their propagation loss.
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