Theory for the Dependence of Optical Second Harmonic Generation Intensity on Non-equilibrium Electron Temperatures at Metal Surfaces

TL;DR

This paper develops a theoretical model to understand how optical second harmonic generation (SHG) intensity depends on non-equilibrium electron temperatures at metal surfaces, revealing that SHG is more sensitive to hot electrons than linear optics.

Contribution

The paper introduces a new theoretical framework linking electron temperature to SHG intensity, emphasizing the role of nonlinear susceptibility over Fresnel coefficients, and extends analysis to Au and Ag.

Findings

SHG intensity decreases monotonically with increasing electron temperature in Cu.

SHG can be enhanced or reduced depending on frequency and electron temperature.

SHG is more sensitive to hot electrons than linear optical response.

Abstract

We present a theory for the electron-temperature dependence $T_{el}$ of optical second harmonic generation (SHG). Such an analysis is required to study the dynamics of metallic systems with many hot electrons not at equilibrium with the lattice. Using a tight-binding theory for the nonlinear susceptibility \cwtel and the Fresnel coefficients we present results for the SHG intensity \iwtel for a Cu monolayer. In the case of linear optical response we find that the intensity will decrease monotonously for increasing $T_{el}$. In agreement with experiment we find a frequency range where \iwtel may be enhanced or reduced depending on electron temperature. Note, \cwtel rather than the Fresnel coefficients determines essentially the temperature dependence. Our theory yields also that SHG probes effects due to hot electrons more sensitively than linear optics. We also discuss the $T_{el}$-dependence of SHG for Au and Ag.