Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Journal of Quantum Electronics

Theory of degenerate four-wave mixing in picosecond excitation-probe experiments

Brian S. Wherrett, Arthur L. Smirl, Thomas F. Boggess

Published Apr 1, 1983• 136 citations
Publisher

Abstract

A comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments is presented. Signals in both the probe and conjugate directions are discussed. The effects of recombination, nonradiative scattering, and spatial and orientational diffusion are included. The analysis is applied to both a molecular and a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. From the solid-state point of view, we show that state-filling, and in particular, anisotropic state-filling, can be identified from the configurational and time dependence of the detected signal, and thereby establish a theoretical explanation for our recent observations in germanium.

DOI
10.1109/jqe.1983.1071899

Related papers

Picosecond Transient Grating Measurements of Intra-well and Cross-well Transport in Multiple Quantum Wells

R. J. Manning, Alan Miller, David C. Herbert +2 more

The spatial confinement of carriers in semiconductor quantum well structures leads to resolvable excitonic features at room temperature. Saturation of these due to phase space filling gives rise to a very large non-linear refractive index [1,2]. We have used this non-linearity in GaAs/AlGaAs multiple quantum wells in two separate degenerate four wave mixing configurations. The two arrangements, forward travelling and counter-propagating (see fig.1), produce transient phase gratings across and parallel to the plane of the wells respectively. Time resolved measurements of the decay of these gratings allow comparison of intra-well and cross-well contributions to carrier diffusion, which is highly anisotropic, and reveal decay rates dependent upon the angle of the sample to the normal. In addition such experiments give carrier relaxation times and the intensity at which the excitonic non-linear refraction starts to saturate.

•Jul 1, 1988•0 citations

Orientational dependence of degenerate four-wave mixing in multiple-quantum-well structures

R. J. Manning, K. Woodbridge, Alan Miller +1 more

The transient grating technique is used to demonstrate how the temporal response of four-wave mixing in multiple-quantum-well structures depends on sample orientation. Variation of the decay times associated with the short-period grating in a phase-conjugate geometry between 40 and 500 psec is demonstrated in a GaAs/AlGaAs multiple-quantum-well structure and interpreted in terms of the large anisotropy in the carrier diffusion.

Optics Letters•Oct 1, 1988•9 citations

Transient analysis of four-grating copolarized four-wave mixing in saturable gain media with finite probe

K. S. Syed, Graham J. Crofts, Michael J. Damzen

We model transient copolarized degenerate four-wave mixing in a saturable gain medium, using pulses of duration much shorter than the population lifetime with a finite probe beam. Initially we describe a model to include the simultaneous existence of both the reflection and transmission gratings for arbitrary field strengths. Then we develop a model to include all four possible gratings, including standing-wave gratings between counterpropagating pump beams and the probe and conjugate beams. By use of two expansion methods for the higher-order grating terms it is possible to model regimes in which either one grating is arbitrarily strong or all four gratings are strong. Comparisons are made among models including one, two, and four gratings. Good agreement is found between the theoretical four-grating case and pulsed copolarized degenerate four-wave mixing experiments in laser-pumped Ti:sapphire for a finite probe beam.

Journal of the Optical Society of America B•Sep 1, 1996•13 citations

Extra resonances in four-wave mixing as a probe of exciton dynamics: The steady-state analog of the transient grating

Roger F. Loring, Shaul Mukamel

We present a microscopic theory of the nonlinear susceptibility χ(3) of a crystal composed of interacting two-level absorbers. The relationship between the signals in a steady-state four-wave mixing experiment and in a time-resolved transient grating experiment is established. In general, the steady-state signal is not simply the Fourier transform of the time-resolved signal, although such a relationship does hold under certain experimental conditions. We evaluate χ(3) for the Haken–Strobl model. χ(3) displays a dephasing-induced extra resonance, whose intensity and line shape are sensitive to the degree of exciton coherence. We also calculate χ(3) for a crystal of interacting three-level absorbers, under the assumption that population in the higher excited state relaxes rapidly to the lower excited state. We propose steady-state four-wave mixing as an alternative to the transient grating experiment in investigating the nature of exciton motion.

The Journal of Chemical Physics•Feb 1, 1986•19 citations

Broadband degenerate four-wave-mixing measurements

Stanislav G. Rozouvan

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.

Journal of the Optical Society of America B•Aug 1, 2000•2 citations

Characteristics of optical phase conjugation of picosecond pulses in semiconductor optical amplifiers

Jin Tang, K.A. Shore

Nondegenerate four-wave mixing (FWM) of picosecond optical pulses in semiconductor optical amplifiers is investigated theoretically, taking into account various carrier processes, probe depletion, and cross-gain modulation effects. Analytical solutions for greatly simplified coupled-wave mixing equations are obtained from which conditions where probe depletion and cross-gain modulation effects cannot be neglected are found. On the other hand, the frequency detuning dependence of optimum input pump pulse energy and shaping of output conjugate pulses are observed from numerical simulations. In particular, calculations show that the frequency symmetry of conjugate and probe pulses with respect to the pump pulse does not hold for optical pulse FWM. Two-photon absorption and ultrafast nonlinear refraction effects are shown to decrease the FWM conversion efficiency.

IEEE Journal of Quantum Electronics•Jul 1, 1999•26 citations
A comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments is presented. Signals in both the probe and conjugate directions are discussed. The effects of recombination, nonradiative scattering, and spatial and orientational diffusion are included. The analysis is applied to both a molecular and a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. From the solid-state point of view, we show that state-filling, and in particular, anisotropic state-filling, can be identified from the configurational and time dependence of the detected signal, and thereby establish a theoretical explanation for our recent observations in germanium.
The spatial confinement of carriers in semiconductor quantum well structures leads to resolvable excitonic features at room temperature. Saturation of these due to phase space filling gives rise to a very large non-linear refractive index [1,2]. We have used this non-linearity in GaAs/AlGaAs multiple quantum wells in two separate degenerate four wave mixing configurations. The two arrangements, forward travelling and counter-propagating (see fig.1), produce transient phase gratings across and parallel to the plane of the wells respectively. Time resolved measurements of the decay of these gratings allow comparison of intra-well and cross-well contributions to carrier diffusion, which is highly anisotropic, and reveal decay rates dependent upon the angle of the sample to the normal. In addition such experiments give carrier relaxation times and the intensity at which the excitonic non-linear refraction starts to saturate.
We model transient copolarized degenerate four-wave mixing in a saturable gain medium, using pulses of duration much shorter than the population lifetime with a finite probe beam. Initially we describe a model to include the simultaneous existence of both the reflection and transmission gratings for arbitrary field strengths. Then we develop a model to include all four possible gratings, including standing-wave gratings between counterpropagating pump beams and the probe and conjugate beams. By use of two expansion methods for the higher-order grating terms it is possible to model regimes in which either one grating is arbitrarily strong or all four gratings are strong. Comparisons are made among models including one, two, and four gratings. Good agreement is found between the theoretical four-grating case and pulsed copolarized degenerate four-wave mixing experiments in laser-pumped Ti:sapphire for a finite probe beam.
We present a microscopic theory of the nonlinear susceptibility χ(3) of a crystal composed of interacting two-level absorbers. The relationship between the signals in a steady-state four-wave mixing experiment and in a time-resolved transient grating experiment is established. In general, the steady-state signal is not simply the Fourier transform of the time-resolved signal, although such a relationship does hold under certain experimental conditions. We evaluate χ(3) for the Haken–Strobl model. χ(3) displays a dephasing-induced extra resonance, whose intensity and line shape are sensitive to the degree of exciton coherence. We also calculate χ(3) for a crystal of interacting three-level absorbers, under the assumption that population in the higher excited state relaxes rapidly to the lower excited state. We propose steady-state four-wave mixing as an alternative to the transient grating experiment in investigating the nature of exciton motion.
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.
Nondegenerate four-wave mixing (FWM) of picosecond optical pulses in semiconductor optical amplifiers is investigated theoretically, taking into account various carrier processes, probe depletion, and cross-gain modulation effects. Analytical solutions for greatly simplified coupled-wave mixing equations are obtained from which conditions where probe depletion and cross-gain modulation effects cannot be neglected are found. On the other hand, the frequency detuning dependence of optimum input pump pulse energy and shaping of output conjugate pulses are observed from numerical simulations. In particular, calculations show that the frequency symmetry of conjugate and probe pulses with respect to the pump pulse does not hold for optical pulse FWM. Two-photon absorption and ultrafast nonlinear refraction effects are shown to decrease the FWM conversion efficiency.