Purcell enhancement of the parametric down-conversion in two-dimensional nonlinear materials

TL;DR

This paper develops a quantum-electrodynamic model to analyze Purcell-enhanced parametric down-conversion in 2D nonlinear materials within nanostructures, revealing significant reductions in instability thresholds due to strong confinement and dissipation effects.

Contribution

It introduces a rigorous Heisenberg-Langevin approach for modeling nonlinear quantum processes in dissipative 2D nanostructures, providing analytic expressions for key quantities.

Findings

Strong reduction in parametric instability threshold in 2D materials

Analytic formulas for spontaneous signal power and instability threshold

Comparison showing advantages over conventional nonlinear devices

Abstract

Ultracompact nonlinear optical devices utilizing two-dimensional (2D) materials and nanostructures are emerging as important elements of photonic circuits. Integration of the nonlinear material into a subwavelength cavity or waveguide leads to a strong Purcell enhancement of the nonlinear processes and compensates for a small interaction volume. The generic feature of such devices which makes them especially challenging for analysis is strong dissipation of both the nonlinear polarization and highly confined modes of a subwavelength cavity. Here we solve a quantum-electrodynamic problem of the spontaneous and stimulated parametric down-conversion in a nonlinear quasi-2D waveguide or cavity. We develop a rigorous Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. Within a relatively simple model, we take into account the nonlinear coupling of the quantized cavity modes, their interaction with a dissipative reservoir and the outside world, amplification of thermal noise and zero-point fluctuations of the electromagnetic field, and other relevant effects. We derive closed-form analytic results for relevant quantities such as the spontaneous parametric signal power and the threshold for parametric instability. We find a strong reduction in the parametric instability threshold for 2D nonlinear materials in a subwavelength cavity and provide a comparison with conventional nonlinear photonic devices.