  We study the self interference effect of a resonator coupled with a bent
waveguide at two separated ports. Such interference effects are shown to be
similar for the cases of standing-wave and traveling-wave resonators, while in
the system of two separated resonators indirectly coupled via a waveguide, the
coupling forms and the related interference effects depend on which kind of
resonators is chosen. Due to the self interference, controllable optical
responses including tunable linewidth and frequency shift, and optical dark
state can be achieved. Moreover, we consider a self-interference photon-magnon
hybrid model and show phase-dependent Fano-like line shapes which have
potential applications in frequency sensing. The photon-magnon hybridization
can not only enhance the sensitivity and provide tunable working region, but
also enables optical readout of the magnetic field strength in turn. The
results in this paper provide a deeper insight into the self interference
effect and its potential applications.
