A spectral phase modulation transfer function for dispersive four-wave mixing

TL;DR

This paper introduces a spectral phase-modulation transfer function for dispersive four-wave mixing, enabling indirect UV pulse phase control through a linear operator framework that relates input spectral phase to output phase transfer efficiency.

Contribution

It develops a spectral phase-response kernel and defines a spectral phase-modulation transfer function (SPMTF) to analyze phase transfer in dispersive four-wave mixing, linking pump dispersion to phase transfer bandwidth.

Findings

Pump chirp influences phase transfer bandwidth.

SPMTF curves vary with pump group-delay dispersion.

Framework aids in optimizing phase transfer conditions.

Abstract

Indirect control of ultraviolet (UV) pulse phase through nonlinear frequency conversion is attractive when direct UV pulse shaping is limited by material loss, dispersion, and damage threshold. Here we cast dispersive four-wave mixing (DFWM) as a pump-conditioned spectral kernel and show that, in a locally one-to-one mapping regime, the signal-to-idler conversion admits a practical transfer function description. Starting from the exact frequency domain expression, we rewrite the idler field as a linear operator acting on the conjugated signal spectrum, with a two-frequency kernel set by the pump self-convolution and phase matching. Linearization around a reference operating point then yields a spectral phase-response kernel for small input perturbations. By probing this response with sinusoidal spectral-phase modulation of different spatial frequencies, we define a spectral phase-modulation transfer function (SPMTF), an MTF-like measure of the phase-transfer bandwidth of the nonlinear interaction. Simulations with different pump group-delay dispersion (GDD) values produce distinct SPMTF curves, showing that pump chirp directly controls how much fine spectral-phase structure survives the conversion. This framework provides a simple way to compare operating conditions and identify regimes favorable for programmable NIR-to-UV phase transfer.