Dispersive effects in ultrafast non-linear phenomena

TL;DR

This paper explores how causality and dispersion relations influence ultrafast nonlinear optical responses, revealing intrinsic delays in Kerr effects through theoretical analysis and experimental measurements in GaAs.

Contribution

It applies dispersive formalism to nonlinear phenomena, demonstrating causality-induced effects in ultrafast Kerr response and experimentally confirming intrinsic phase-amplitude lag.

Findings

Causality affects ultrafast Kerr dynamics.

Experimental evidence of phase lag in GaAs.

Dispersive effects are crucial in nonlinear optical analysis.

Abstract

It is a basic principle that an effect cannot come before the cause. Dispersive relations that follow from this fundamental fact have proven to be an indispensable tool in physics and engineering. They are most powerful in the domain of linear response where they are known as Kramers-Kronig relations. However when it comes to nonlinear phenomena the implications of causality are much less explored, apart from several notable exceptions. Here in this work we demonstrate how to apply the dispersive formalism to analyse the ultrafast nonlinear response in the context of the paradigmatic nonlinear Kerr effect. We find that the requirement of causality introduces a noticeable effect even under assumption that Kerr effect is mediated by quasi-instantaneous off-resonant electronic hyperpolarizability. We confirm this by experimentally measuring the time resolved Kerr dynamics in GaAs by means of a hybrid pump-probe Mach-Zehnder interferometer and demonstrate the presence of an intrinsic lagging between amplitude and phase responses as predicted by dispersive analysis. Our results describe a general property of the time-resolved nonlinear processes thereby highlighting the importance of accounting for dispersive effects in the nonlinear optical processes involving ultrashort pulses.