High-gain squeezing in lossy resonators: An asymptotic-field approach

We present a method for describing nonlinear electromagnetic interactions in integrated photonic devices utilizing an asymptotic-in (-out) field formalism. Our method expands upon previous continuous wave asymptotic treatments by describing the evolution nonperturbatively for an arbitrary pulsed input. This is presented in the context of a squeezing interaction within an integrated micro-ring resonator side coupled to an input-output waveguide, but is readily generalizable to other integrated structures, while including a variety of (nonsqueezing) third-order interactions. An example of a single-pump, nondegenerate squeezing interaction is studied, which is shown to match well with standard coupled-mode treatments for high-finesse resonators, as well as previous perturbative treatments dealing with the generation of pairs with low probability.