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Pure and Applied Optics Journal of the European Optical Society Part A

Transient and time-resolved four-wave mixing with collinear pump and probe pulses using the heterodyne technique

Antonio Mecozzi, Jesper Mørk

Published Mar 1, 1998• 3 citations
Publisher

Abstract

We review the recently proposed heterodyne technique for four-wave mixing experiments with collinear and co-polarized pulses. We discuss issues related to the parameters of the nonlinear dynamics of the sample that can be extracted by this technique.
DOI
10.1088/0963-9659/7/2/023

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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.
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We treat the problem of four-wave resonant mixing of ultrashort laser pulses in gaseous media. We show that for some transitions, for example, quadrupole transitions, the polarization effects can be strongly manifested. For four-wave two-photon resonant mixing we find that the signal-wave plane rotation depends on the parameters of the resonant medium and the pulses mixed. We show that for long pump pulses and short signal pulses in the ultrashort-pulse time domain the angle of rotation of the plane of polarization of the signal plane can reach several dozen degrees. We show that the effect of altering the state of polarization of the short signal pulse can be used for measuring its shape and duration. Since the polarization measurements are precise and the proposed regimes of four-wave mixing do not depend on phase and amplitude fluctuations of the measuring pulse, the polarization four-wave mixing technique can be more accurate than the technique widely used for such purposes, measurement of the second-order intensity correlation function. We also discuss new nonlinear spectroscopy for measuring fast resonant susceptibilities (in particular, second-order polarizabilities) of the medium, based on the rotation of the polarization plane or the polarization ellipse of the signal pulse.
The use of phase-locked pulses in various spectroscopic techniques related to the third-order polarization P(3) is analyzed. Using correlation function expressions for the nonlinear response function, we clarify the interrelationship among several photon echo, pump–probe, and spontaneous light emission techniques, without alluding to any specific model for the material system. By combining phase-locked pulses and heterodyne detection it becomes possible to probe separately the real and imaginary parts of the nonlinear response function. Combining two phase-locked pulse excitation with time-resolved detection of the spontaneous light emission allows direct separation of the Raman and fluorescence contributions.