Different time scales in plasmonically enhanced high-order harmonic generation

TL;DR

This paper explores how inhomogeneous media affect high-order harmonic generation, revealing that slow and fast oscillations interplay to extend the harmonic cutoff energy, with potential for analytical description under certain conditions.

Contribution

It introduces a phase-space analysis of harmonic generation in inhomogeneous media and demonstrates how slow oscillations influence the harmonic cutoff, providing new insights into the dynamics involved.

Findings

Inhomogeneity causes specific features in harmonic spectra.

Slow oscillations can extend the harmonic cutoff energy.

Analytical descriptions are possible for small inhomogeneity parameters.

Abstract

We investigate high-order harmonic generation in inhomogeneous media for reduced dimensionality models. We perform a phase-space analysis, in which we identify specific features caused by the field inhomogeneity. We compute high-order harmonic spectra using the numerical solution of the time-dependent Schr\"odinger equation, and provide an interpretation in terms of classical electron trajectories. We show that the dynamics of the system can be described by the interplay of high-frequency and slow-frequency oscillations, which are given by Mathieu's equations. The latter oscillations lead to an increase in the cutoff energy, and, for small values of the inhomogeneity parameter, take place over many driving-field cycles. In this case, the two processes can be decoupled and the oscillations can be described analytically.