Scale-invariant nonlinear optics in gases

TL;DR

This paper demonstrates that many nonlinear optical phenomena in gases are scale-invariant when spatial coordinates, gas density, and pulse energy are scaled appropriately, enabling flexible manipulation of nonlinear processes.

Contribution

The authors develop a general scale-invariance model for (3+1)D wave equations in gases, validated through numerical simulations and experiments.

Findings

Nonlinear optical effects in gases are scale-invariant with proper scaling.

The model applies to high-order harmonic generation and filamentation.

Experimental verification confirms the theoretical predictions.

Abstract

Nonlinear optical methods are becoming ubiquitous in many areas of modern photonics. They are, however, often limited to a certain range of input parameters, such as pulse energy and average power, since restrictions arise from, for example, parasitic nonlinear effects, damage problems and geometrical considerations. Here, we show that many nonlinear optics phenomena in gaseous media are scale-invariant if spatial coordinates, gas density and laser pulse energy are scaled appropriately. We develop a general scaling model for (3+1)-dimensional wave equations, demonstrating the invariant scaling of nonlinear pulse propagation in gases. Our model is numerically applied to high-order harmonic generation and filamentation as well as experimentally verified using the example of pulse post-compression via filamentation. Our results provide a simple recipe for up-or downscaling of nonlinear processes in gases with numerous applications in many areas of science.