Theory of multiwave mixing within the superconducting kinetic-inductance traveling-wave amplifier

摘要

We present a theory of parametric mixing within the coplanarwaveguide (CPW) of a superconducting nonlinearkinetic-inductance traveling-wave (KIT) amplifier engineered with periodic dispersion loadings. This is done byfirst developing a metamaterial band theory of the dispersion-engineered KIT using a Floquet-Bloch constructionand then applying it to the description of mixing of the nonlinear RF traveling waves. Our theory allows us tocalculate signal gain versus signal frequency in the presence of a frequency stop gap, based solely on loadingdesign. We present results for both three-wave mixing (3WM), with applied dc bias, and four-wave mixing(4WM), without dc. Our theory predicts an intrinsic and deterministic origin to undulations of 4WM signalgain with signal frequency, apart from extrinsic sources, such as impedance mismatch, and shows that suchundulations are absent from 3WM signal gain achievable with dc. Our theory is extensible to amplifiers basedon Josephson junctions in a lumped LC-ladder transmission line (TWPA).