Topological aspects in nonlinear optical frequency conversion

TL;DR

This paper explores how topological concepts can impose additional constraints on nonlinear optical frequency conversion, revealing topological phase transitions in multi-frequency processes at classical and quantum levels.

Contribution

It introduces the idea that topology provides a new degree of freedom to understand and constrain nonlinear frequency conversion beyond traditional conservation laws.

Findings

Topological phase transitions can occur in frequency conversion processes.

Topological constraints influence multi-frequency conversion beyond conservation laws.

Classical and quantum level phenomena exhibit topological phase transitions.

Abstract

Nonlinear optical frequency conversion, observed more than half a century ago, is a corner stone in modern applications of nonlinear and quantum optics. It is well known that frequency conversion processes are constrained by conservation laws, such as momentum conservation that requires phase matching conditions for efficient conversion. However, conservation laws alone could not fully capture the features of nonlinear frequency conversion. Here it is shown that topology can provide additional constraints in nonlinear multi-frequency conversion processes. Unlike conservation laws, a topological constraint concerns with the conserved properties under continuous deformation, and can be regarded as a new indispensable degree of freedom to describe multi-frequency processes. We illustrate such a paradigm by considering sum frequency generation under a multi-frequency pump wave, showing that, akin topological phases in topological insulators, topological phase transitions can be observed in the frequency conversion process both at classical and quantum level.