Nonperturbative effects in second harmonic generation

TL;DR

This paper develops a nonperturbative Floquet-Keldysh theory to analyze second-harmonic generation in two-band systems, revealing new saturation behaviors driven by resonance processes.

Contribution

It introduces a novel nonperturbative theoretical framework for SHG, highlighting distinct saturation regimes and their resonance origins in realistic materials.

Findings

Identifies a transition from quadratic to linear E dependence in SHG response.

Discovers a saturation regime where SHG becomes independent of field amplitude.

Validates theoretical predictions with numerical Floquet calculations on monolayer GeS.

Abstract

Second-harmonic generation (SHG) is a quintessential probe of inversion symmetry breaking in condensed matter. While perturbative $\chi^{(2)}$ processes are well-documented, the nonperturbative regime under intense driving remains largely unexplored. In this Letter, we develop a nonperturbative Floquet-Keldysh theory to describe SHG in two-band systems. Our analysis reveals the emergence of two distinct types of nonperturbative saturation: a transition from the conventional $E^2$ scaling to a linear $E$ dependence, and a stronger saturation regime where the SHG response becomes independent of the field amplitude. These behaviors are analytically shown to be governed by one-photon and two-photon resonance processes, respectively. By applying our formalism to a tight-binding model of monolayer GeS, we demonstrate that these specific scaling behaviors are observable in realistic materials and are fully consistent with large-scale numerical Floquet-matrix calculations.