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Optics Letters

Transient four-wave mixing with a collinear pump and probe

Antonio Mecozzi, Jesper Mørk, Martin Rudolf Hofmann

Published Jul 15, 1996• 15 citations
Publisher

Abstract

We propose a new heterodyne scheme for performing time-resolved four-wave mixing experiments with collinear pump and probe beams. The method is not limited by phase-matching requirements and permits the investigation of thick samples and waveguide devices such as semiconductor optical amplifiers.
DOI
10.1364/ol.21.001017

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We demonstrate that the transient coherent nonlinearity (coherent artifact) affecting the pump-probe response of semiconductor optical amplifiers can be experimentally separated from the incoherent transient. The technique is based on measuring the mirror component of the coherent artifact which is a background-free four--wave mixing signal at a different frequency with respect to the transmitted probe in a heterodyne detection scheme. Measurements on amplifiers of different length reveal strong deviations from the commonly expected symmetric shape of the coherent artifact in case of long waveguides.
We give the first analysis of heterodyne experiments that includes the propagation along the waveguide. Under the assumption that the material polarization is adiabatically eliminated we derive simple analytic expressions for the coherent coupling term, exact for Gaussian pulses and a good approximation for other shapes. We find that the measured signal does not display any phase dependence close to zero pump–probe delay. A four-wave mixing band is identified in the heterodyne signal, and a new class of experiments is proposed by analogy with the spatial case.
The new experimental research on the four-wave mixing (FWM) phenomena described here consists in launching three optical waves (pump, probe, and test) into a semiconductor optical amplifier and measuring the test beam transmission and the conversion efficiency of the new wave generated to one side of the test beam. It allows for an excellent identification of the nonlinear phenomena involved in the FWM process. The analysis principle is based on the modulation of the gain curve for each of the three effects considered: spectral hole burning, carrier heating, and carrier density pulsation. Experimental and theoretical results are presented.
Abstract This tutorial provides a joint theoretical and experimental overview of heterodyne wave mixing spectroscopy, focusing mainly on four-wave mixing (FWM). This powerful and versatile time-resolved nonlinear optical spectroscopy technique enables the investigation of individual localized single photon emitters, as well as microscopy of extended samples, e.g. two-dimensional transition metal dichalcogenides. Starting with the fundamental theory of optically driven two-level systems, we motivate the utility of wave mixing spectroscopy via a discussion on homogeneous and inhomogeneous linewidths which can be independently measured using FWM. We then provide a detailed overview of the heterodyne wave mixing setup operated by one of the authors (JK) at Institut Néel in Grenoble, supported by theoretical modeling of the signal detection process. Throughout the paper we elaborate on important benefits of heterodyne wave mixing spectroscopy, e.g. background-free detection, measurement of the full signal field including amplitude and phase, and investigation of coupling mechanisms in few-level systems. Within the context of the latter point we discuss the significance of two-dimensional FWM spectra. This tutorial is dedicated to students, young researchers, as well as experts in the field of nonlinear spectroscopy in general and FWM in particular. It explains the fundamental concepts and building blocks required to operate a heterodyne wave mixing experiment both from the experimental and theoretical side. This joint approach is helpful for theoreticians who want to accurately and quantitatively model wave mixing signals, as well as for experimentalists who aim to interpret their recorded data.