Local comb generation in nonlinear TiN superconducting resonators

Low loss superconducting nonlinear resonators are extensively used for qubit readout as well as photon detectors. These devices are typically capacitively coupled to a launch line. When driven at high power, a shift in resonant frequency is observed due to the kinetic inductance of the TiN superconductor. At higher power, the resonant frequency mixes with the drive tone to produce a series of peaks that are observed to be equally spaced at the detuning frequency, i.e. a ``local comb.'' The full circuit analysis of this system is derived. The renormalized resonant frequency is obtained and the local comb is derived from a first order successive approximation.