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

The Journal of Chemical Physics

Microscopic theory of the transient grating experiment

Roger F. Loring, Shaul Mukamel

Published Nov 1, 1985• 21 citations
Publisher

Abstract

We present the first fully microscopic theory of the generation of the transient grating signal from a crystal of interacting molecules. We derive a general expression for the signal, measured at a time immediately after a short probe pulse, in terms of the exciton Green function. This expression agrees with previous calculations of the grating signal, in which the experiment was treated as a diffraction process. It is also shown that the temporal profile of the signal pulse is, in general, different from that of the probe pulse. This result is inconsistent with the usual diffraction picture. Our treatment of this experiment as a transient four-wave mixing process rather than as a diffraction process allows us to derive an expression for the signal in terms of equilibrium correlation functions of the dipole operator. Using this formulation, we discuss the relationship of this experiment to other nonlinear spectroscopic techniques.

DOI
10.1063/1.449050

Related papers

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

Femtosecond coherent fields induced by many-particle correlations in transient four-wave mixing

W. Schäfer, D. S. Kim, Jagdeep Shah +5 more

We present a unified microscopic approach to four-wave mixing (FWM) in semiconductors on an ultrashort time scale. The theory is valid for resonant excitation in the vicinity of the excitonic resonance and at low densities. The most important many-particle effects, i.e., static and dynamical exciton-exciton interaction as well as biexcitonic effects are incorporated. The internal fields resulting from these interaction processes give rise to pronounced many-particle effects in FWM signals. Our results explain the dependence of FWM signals on the polarization geometry, especially if biexcitons contribute. Time-resolved (TR) FWM experiments show that the diffraction of the interaction induced fields dominate the FWM signals completely. This dominance of the interaction induced field at low temperatures is true regardless of density, detuning, or polarization geometry. While spectrally resolved FWM (-FWM) shows biexcitonic or bound excitonic contributions under various experimental conditions, TR-FWM is always completely delayed, peaking roughly at the dephasing time after both beams passed through. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Jun 15, 1996•105 citations

Pulse-propagation-induced higher orders of diffraction in transient four-wave mixing with semiconductors

B. Lummer, J.‐M. Wagner, R. Heitz +3 more

Higher orders of diffraction observed in a transient four-wave mixing experiment with acceptor-bound exciton complexes in CdS are analyzed in terms of pulse propagation. The description is based on a mean-field correction to the driving electric field in the optical Bloch equations, which are shown to generally lack higher-order diffraction for two-pulse self-diffraction. A propagation-induced sequence of stimulated echoes diffracted at the population grating dominates at least the second order of diffraction. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Dec 15, 1996•10 citations

Chirped four-wave mixing

Koos Duppen, Foppe de Haan, Erik T. J. Nibbering +1 more

We will demonstrate that four-wave mixing with linearly chirped (phase-modulated) pulses is a unique tool for obtaining information on the dynamics and level structure of a system. Especially, it will be shown that the transient-grating-scattering type of experiment with chirped pulses provides an immediate answer to the question of whether the dynamics of a system occurs on a fast and/or slow time scale. In addition, we present compelling evidence that chirped four-wave mixing in a molecular system is a viable method for measuring excited-state vibrational frequencies. Double-sided Feynman diagrams are used for a third-order perturbative calculation of two-level four-wave-mixing effects and chirped coherent Raman scattering. The diagrams provide a visual representation of the quantum-mechanical pathways that the system can take as a result of the different field interactions. The number of quantum-mechanical pathways that contribute to the signal is shown to depend on the chirp rate compared to the time scale(s) of the system dynamics. A stochastic model is used to describe the optical dynamics of the system. The resulting expressions for the third-order nonlinear polarization are so complex that numerical calculations are necessary to simulate the time dependence of the optical response. It will also be shown that our theoretical results in the appropriate limits converge to those obtained for impulsive or continuous-wave excitation.

Physical Review A•Jun 1, 1993•65 citations

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

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

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.

IEEE Journal of Quantum Electronics•Apr 1, 1983•136 citations
We present the first fully microscopic theory of the generation of the transient grating signal from a crystal of interacting molecules. We derive a general expression for the signal, measured at a time immediately after a short probe pulse, in terms of the exciton Green function. This expression agrees with previous calculations of the grating signal, in which the experiment was treated as a diffraction process. It is also shown that the temporal profile of the signal pulse is, in general, different from that of the probe pulse. This result is inconsistent with the usual diffraction picture. Our treatment of this experiment as a transient four-wave mixing process rather than as a diffraction process allows us to derive an expression for the signal in terms of equilibrium correlation functions of the dipole operator. Using this formulation, we discuss the relationship of this experiment to other nonlinear spectroscopic techniques.
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.
We present a unified microscopic approach to four-wave mixing (FWM) in semiconductors on an ultrashort time scale. The theory is valid for resonant excitation in the vicinity of the excitonic resonance and at low densities. The most important many-particle effects, i.e., static and dynamical exciton-exciton interaction as well as biexcitonic effects are incorporated. The internal fields resulting from these interaction processes give rise to pronounced many-particle effects in FWM signals. Our results explain the dependence of FWM signals on the polarization geometry, especially if biexcitons contribute. Time-resolved (TR) FWM experiments show that the diffraction of the interaction induced fields dominate the FWM signals completely. This dominance of the interaction induced field at low temperatures is true regardless of density, detuning, or polarization geometry. While spectrally resolved FWM (-FWM) shows biexcitonic or bound excitonic contributions under various experimental conditions, TR-FWM is always completely delayed, peaking roughly at the dephasing time after both beams passed through. \textcopyright{} 1996 The American Physical Society.
Higher orders of diffraction observed in a transient four-wave mixing experiment with acceptor-bound exciton complexes in CdS are analyzed in terms of pulse propagation. The description is based on a mean-field correction to the driving electric field in the optical Bloch equations, which are shown to generally lack higher-order diffraction for two-pulse self-diffraction. A propagation-induced sequence of stimulated echoes diffracted at the population grating dominates at least the second order of diffraction. \textcopyright{} 1996 The American Physical Society.
We will demonstrate that four-wave mixing with linearly chirped (phase-modulated) pulses is a unique tool for obtaining information on the dynamics and level structure of a system. Especially, it will be shown that the transient-grating-scattering type of experiment with chirped pulses provides an immediate answer to the question of whether the dynamics of a system occurs on a fast and/or slow time scale. In addition, we present compelling evidence that chirped four-wave mixing in a molecular system is a viable method for measuring excited-state vibrational frequencies. Double-sided Feynman diagrams are used for a third-order perturbative calculation of two-level four-wave-mixing effects and chirped coherent Raman scattering. The diagrams provide a visual representation of the quantum-mechanical pathways that the system can take as a result of the different field interactions. The number of quantum-mechanical pathways that contribute to the signal is shown to depend on the chirp rate compared to the time scale(s) of the system dynamics. A stochastic model is used to describe the optical dynamics of the system. The resulting expressions for the third-order nonlinear polarization are so complex that numerical calculations are necessary to simulate the time dependence of the optical response. It will also be shown that our theoretical results in the appropriate limits converge to those obtained for impulsive or continuous-wave excitation.
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.