Extended model for optimizing high-order harmonic generation in absorbing gases

TL;DR

This paper extends a one-dimensional model to optimize high-order harmonic generation in absorbing gases, emphasizing the importance of pressure gradients and medium length for maximizing harmonic flux.

Contribution

The model is expanded from zeroth to first order to include media with linearly varying pressure profiles, providing new guidelines for harmonic flux optimization.

Findings

Steep pressure gradients at the medium's end enhance flux.

Increasing pressure at the start boosts harmonic flux and reduces medium length.

The extended model offers practical rules for optimizing harmonic generation.

Abstract

We report on an extended version of the one-dimensional model proposed by Constant \emph{et al.} [Phys. Rev. Lett 82(8), 1668 (1999)] to study phase matching of high-order harmonic generation in absorbing and dispersive medium. The model - expanded from zeroth to first order - can be used with media having a pressure profile varying linearly with propagation length. Based on the new formulas, the importance of having a generation medium that ends abruptly with a steep pressure gradient for achieving high flux is highlighted. In addition to further rule-of-thumb guidelines for harmonic-flux optimization, it is shown that having a steep increase of pressure in the beginning of the medium increases harmonic flux, while it also decreases the required medium length to reach the absorption-limited maximum.