Second-order filtering and sensing with partially coupled traveling waves in a single resonator

The counterpropagating waves in a single traveling-wave cavity can be partially coupled by means of a small perturbation such as a notch. When it is side coupled to a waveguide, this single cavity yields a general second-order (Chebyshev) reflection response in the waveguide, which is useful for narrow-bandwidth reflecting applications. In a different application, the cavity amplifies small reflections induced by external perturbations, thus finding use in ultrafine sensing. Amplification factors as great as ${10}^{12}$ are predicted for the highest-$Q$ microsphere resonators. The analytic theory of these devices is presented.