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Applied Optics

Properties of transient degenerate four-wave mixing involving the relaxation effect: an investigation

Guang Lan, Dianyuan Fan

Published Jul 15, 1987• 1 citation
Publisher

Abstract

A series of phenomenological relaxation equations have been introduced to describe the formation and decay of a grating. The influences of medium relaxation on the transient properties of degenerate four-wave mixing were studied theoretically and experimentally. As we studied the backward wave shape, the accumulation and smoothing effects were observed. The theory agreed well with the experimental results.

DOI
10.1364/ao.26.002843

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A series of phenomenological relaxation equations have been introduced to describe the formation and decay of a grating. The influences of medium relaxation on the transient properties of degenerate four-wave mixing were studied theoretically and experimentally. As we studied the backward wave shape, the accumulation and smoothing effects were observed. The theory agreed well with the experimental results.
We show that four-wave mixing in optically dense media is very different than in an optically thin medium. In time-resolved degenerate four-wave mixing we experimentally observe ``negative'' time delay response, fast decay rates at short delay times, and broad shoulders at long delays. The observations are explained very well in terms of pulse propagation effects, and a theoretical framework is presented for the analysis of the nonlinear interaction. We treat both the incident and generated fields self-consistently, and solve for the interaction of short pulses with a resonantly absorbing medium. The implications for the extraction of relaxation rates from four-wave-mixing experiments involving ultrashort pulses in optically dense matter are discussed.
The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.
The nonlinear signal in a degenerate four-wave mixing experiment as a result of diffraction of a spatially distributed third-order nonlinearity is studied theoretically. The approach has been applied for the case of monochromatic and ultrashort pulses. As a consequence, the degenerate four-wave mixing signal is found to be independent of light-coherence parameters and cannot be explained as a product of diffraction on a dynamic grating. In this model only the fast component of the signal (the coherent artifact) is related directly to third-order nonlinear processes. The main features (the origins, temporal shapes, dependencies of pump intensity, and modulation effects) of the coherent artifact and a slow-decay component are discussed theoretically and experimentally.
We present a time-resolved study of the diffracted pulse in degenerate four-wave mixing experiments with short-response-time materials. The first step is the validation of a theoretical model that takes into account the temporal characteristics of the energy level (relaxation time T1 and dephasing time T2) and of the incident pulse (duration and spectral phase) in a simple particular case. Two methods are used for characterizing the diffracted beam: the amplitude correlation with the reference pulse and the spectrum intensity measurements. We discuss the experimental results, which show good agreement with the theoretical model and evidence the strong influence of the incident pulse characteristics.
A set of coupled equations is derived and used to analyze transient coherent degenerate four-wave mixing (DFWM) in a two-level system. The numerical results show that in the case of near-resonance, intense pumping, and short pulses, the properties of degenerate four-wave mixing have interesting coherent interaction characteristics, such as quasi-periodicity in the pump pulse area, probe pulse areas, and energy reflectivity, oscillatory behavior of the DFWM pulse, and generation of a DFWM signal in the case of delayed incidence, where the three incident pulses do not overlap in the medium.>