The coil optical resonator (COR) is an optical microfiber coil tightly wound on an optical rod. The resonant behavior of this all-pass device is determined by evanescent coupling between the turns of the microfiber. This paper investigates the uniform COR with N turns. Its transmission characteristics are surprisingly different from those of the known types of resonators and of photonic crystal structures. It is found that for certain discrete sequences of propagation constant and interturn coupling, the light is completely trapped by the resonator. For N →∞, the COR spectrum experiences a fractal collapse to the points corresponding to the second order zero of the group velocity. For a relatively small coupling between turns, the COR waveguide behavior resembles that of a SCISSOR (side-coupled integrated spaced sequence of resonators), while for larger coupling it resembles that of a CROW (coupled resonator optical waveguide).
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