Fig. 1: Reversed Kerr phase matching.
From: Kerr reversal in Josephson meta-material and traveling wave parametric amplification
a Exaggerated dispersion relations of a weak probe tone in presence of pump at 8 GHz (green) and absence of pump (blue) in reversed Kerr TWPA at negative Kerr flux bias. The red arrows indicate the contribution of self phase modulation (SPM, at 8 GHz) and cross-phase modulation (XPM, at 6 and 10 GHz). The XPM experienced by the signal and idler waves is stronger than the SPM experienced by the pump wave, this allows signal, idler and pump to be colinear, i.e., satisfy the phase matching condition. Due to sign reversal of Kerr, self, and cross phase modulation processes cancel phase mismatch arising from curvature in dispersion (blue); which leads to perfect phase matching at 6 and 10 GHz (indicated with red-green points). Simulations of reversed Kerr phase matching and gain (b, c) using device parameters. The represented Δk values are phase mismatches at the output of the devices.
