Quantized Nonlinear Gaussian-Beam Dynamics $-$ Tailoring Multimode Squeezed-Light Generation

TL;DR

This paper develops a second quantization framework for complex multimode Gaussian beam dynamics in nonlinear optics, enabling detailed analysis and tailoring of spatial mode structures and their quantum properties in processes like four-wave mixing.

Contribution

It introduces a comprehensive second quantization method for multi-transverse-spatial mode Gaussian beams, advancing beyond spectral and angular analyses to include complex transverse mode structures.

Findings

Simulated four-wave mixing and parametric down-conversion schemes.

Demonstrated ability to elucidate and tailor multi-transverse-spatial mode structures.

Enhanced understanding of quantum properties of multimode squeezed light.

Abstract

We present a general, second quantization procedure for multi-transverse-spatial mode Gaussian beam dynamics in nonlinear interactions. Previous treatments have focused on the spectral density and angular distribution of spatial modes. Here we go a layer deeper by investigating the complex transverse-spatial mode in each angular-spatial mode. Furthermore, to implement the theory, we simulate four-wave mixing and parametric down-conversion schemes, showing how one can elucidate and tailor the underlying multi-transverse-spatial mode structure along with it's quantum properties.