General analytic theory of classical collinear three wave mixing in a monolithic cavity

TL;DR

This paper develops a comprehensive analytic theory for classical three wave mixing in monolithic cavities, applicable to various designs and processes, validated by experimental data and extendable to phase modulation effects.

Contribution

It provides the first general analytic model for three wave mixing in monolithic cavities, covering multiple processes and design configurations, including linear and nonlinear regions.

Findings

Model agrees with experimental spectra

Reversing linear and nonlinear regions alters output

Model can incorporate phase modulation effects

Abstract

Integrated, monolithic nonlinear cavities are of high interest in both classical and quantum optics experiments for their high efficiency and stability. However, a general, analytic theory of classical three wave mixing in such systems that encompasses multiple monolithic designs, including both linear and nonlinear regions, as well as any three-wave mixing process has not yet been fully developed. In this paper, we present the analytic theory for a general, classical three wave mixing process in a cavity with arbitrary finesse and non-zero propagation losses, encompassing second harmonic, sum frequency and difference frequency generation - SHG, SFG and DFG respectively. The analytic expression is derived under the sole assumption of low single-pass conversion efficiency (or equivalently operating in the non-depleted pump regime). We demonstrate remarkable agreement between the presented model and the experimentally obtained highly complex second-harmonic spectrum of a titanium-diffused lithium niobate waveguide cavity that includes both a linear and nonlinear section. We then show the effect that reversing the linear and nonlinear regions has on the output spectrum, highlighting the importance of system design. Finally, we demonstrate that the model can be extended to include the effect of phase modulation applied to the cavity.