Temporal modulation of second harmonic generation in ferroelectrics by a pulsed electric field

TL;DR

This paper explores how pulsed electric fields modulate second harmonic generation in ferroelectrics, revealing complex relationships involving electric field derivatives and phase behavior, supported by theoretical derivations and simulations.

Contribution

It introduces a nonlinear response theory that accounts for electric field derivatives and phase effects, challenging the traditional proportionality assumption between polarization change and SH intensity.

Findings

Electric field derivatives influence SH modulation.

SH intensity can be out of phase with the electric field.

Proportionality between polarization change and SH intensity can break down.

Abstract

We revisit the relationship between electric polarization modulation $\Delta P$ in ferroelectrics induced by a low-frequency pulsed electric field and the corresponding second harmonic intensity modulation $\Delta I_{\mathrm{SH}}$. Using nonlinear response theory, we derive their time-domain expressions linear in the pulse amplitude, revealing that not only the electric field but also its time derivative contributes to $\Delta I_{\mathrm{SH}}$. Furthermore, even when the time-derivative component is negligible, $\Delta I_{\mathrm{SH}}$ can be in antiphase with the pulsed field and thus with $\Delta P$. These theoretical predictions are further supported by real-time simulations of a model for electronic ferroelectrics. Our results demonstrate that the commonly assumed relation $\Delta P \propto \Delta I_{\mathrm{SH}}$ can break down under certain conditions, reflecting the complex-valued and frequency-dependent nature of nonlinear dynamical susceptibilities.