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

Optics Letters

Extra resonances in time-domain four-wave mixing

John T. Fourkas, Rick P. Trebino, Mark A. Dugan, M. D. Fayer

Published May 15, 1993• 2 citations
Publisher

Abstract

We show that extra resonances, such as those caused in frequency-domain nonlinear wave mixing by pure dephasing or laser fluctuations, can also be induced by operation in the time domain. These pulse-length-induced extra resonances arise in transient-grating experiments when the laser pulses are short enough that a steady state cannot be achieved during the excitation process. We show theoretically that these resonances increase in strength with decreasing excitation pulse length until the pulse length becomes shorter than the dephasing time of the medium and quote an experimental example to support this interpretation.

DOI
10.1364/ol.18.000781

Related papers

Extra Resonances in Time-Domain Nonlinear Spectroscopies

John T. Fourkas, Rick P. Trebino, M. D. Fayer +1 more

Extra resonances between initially unpopulated excited states (IUES) or equally populated ground states (EPGS) have been studied extensively in the context of frequency-domain nonlinear spectroscopies such as Nearly-Degenerate Four-Wave Mixing (NDFWM)1. In the absence of strong laser fields2 or effects such as pure dephasing3, stochastic fluctuations in laser fields4, and laser transients5, the NDFWM extra resonances are either very weak (in the case of EPGS) or nonexistent (in the case of IUES). It is perhaps under-appreciated that "Fourier-transform" time- and frequency-domain FWM techniques do not necessarily provide the same information. For instance, under certain circumstances6, the NDFWM and transient grating (TG) techniques form such a pair, which would imply that TG extra resonances might disappear under the same experimental conditions in which they disappear in NDFWM. This assumption is belied by the TG data shown in Fig. 1. These data were taken by exciting and probing the D1 line of Na atoms in a cell in which there was no buffer gas and the Na pressure was low enough to preclude any significant number Na-Na collisions on the experimental time scale. Even in the absence of pressure-induced dephasing, these data exhibit strong extra resonances at both the 1.77-GHz ground-state hyperfine-splitting frequency and the 189-MHz excited-state hyperfine-splitting frequency. These data have prompted us to undertake a theoretical study of the nature of extra resonances in time-domain nonlinear spectroscopies, the preliminary results of which are discussed here. We show that time-domain extra resonances increase in strength with decreasing dephasing, and that IUES resonances exist even in the complete absence of pure dephasing. Finally, we show that IUES and EPGS extra resonances have a common origin in the time domain.

Nonlinear Optics•Jan 1, 1992•0 citations

Collision, fluctuation, and field-induced extra resonances

Yehiam Prior

Four wave mixing experiments are normally performed near atomic (molecular) resonances, when some of the input frequencies or their combinations are at resonance with the atomic transitions. If dephasing process are present, several new resonances appear, that may be traced directly to the influence of the dephasing processes. The origin of the ‘‘dephasing’’ may vary from collisions and other material relaxation processes, to field fluctuations, to higher order interactions in the wave mixing process. The source of these extra resonances is discussed, and specific results are shown for the various cases.

AIP conference proceedings•Jan 1, 1988•0 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

Transient Effects in Four-Wave Mixing

W. M. Schreiber, N. Chencinski

A formalism for four-wave mixing in the transient region, applicable to strong fields of short pulse duration, is developed. It is shown that transient effects can broaden resonance peaks and contribute to the appearance of extra resonances.

Shortwavelength: Physics with Intense Laser Pulses•Jan 1, 1993•0 citations

Nonlinear interaction of propagating short pulses in optically dense media

Opher Kinrot, Yehiam Prior

The optical density of a resonant medium significantly affects the output signal in time resolved nonlinear optical interactions. The resonant interaction with a medium reshapes any propagating short pulse, and the mutual interaction of several such pulses, as in four-wave mixing, must be treated self-consistently. We present a theoretical framework for the proper handling of the propagation of all pulses, input as well as generated, in the small area limit. For optically thick resonant absorbers, negative time delay signals are observed, and the apparent decay rate of the induced polarization is faster than the rate observed for thin samples. We experimentally measure degenerate four-wave mixing in an atomic medium as an example, and demonstrate the quality of the theoretical model by the excellent fit to measured signals over several orders of magnitude. The improved understanding enables us to provide a simple, but surprisingly accurate, estimate for the apparent decay rate in homogeneously broadened optically thick media: If the absorption is given by \ensuremath{\alpha}, the propagation length is L, and the transverse relaxation time is ${\mathit{T}}_{2}$, the apparent decay rate 2/${\mathit{T}}_{\mathit{a}}$ of a time resolved four-wave mixing signal is given by 2/${\mathit{T}}_{\mathit{a}}$=(2/${\mathit{T}}_{2}$)(1+\ensuremath{\alpha}L/2).

Physical Review A•Jun 1, 1995•24 citations

Dynamics of transient four-wave mixing of laser pulses in a resonant medium

V. V. Kabanov, Alexander S. Rubanov

The characteristic features of the conjugate wave's formation under transient four-wave mixing in a two-level medium are investigated. The phase modulations of the signal and conjugate waves induced in the four-wave mixing are not mutually conjugate and have the same sign. The fulfillment of the phase-conjugation for the phase modulated signal has been shown in particular to be connected with the envelope's deformation and the spectrum's change of signal pulses. The transient optical bistability connected with the nonlinear absorption's saturation in the quasi-cw four-wave mixing and with the inertia in the short pulse's regime is observed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 11, 1996•0 citations
We show that extra resonances, such as those caused in frequency-domain nonlinear wave mixing by pure dephasing or laser fluctuations, can also be induced by operation in the time domain. These pulse-length-induced extra resonances arise in transient-grating experiments when the laser pulses are short enough that a steady state cannot be achieved during the excitation process. We show theoretically that these resonances increase in strength with decreasing excitation pulse length until the pulse length becomes shorter than the dephasing time of the medium and quote an experimental example to support this interpretation.
Extra resonances between initially unpopulated excited states (IUES) or equally populated ground states (EPGS) have been studied extensively in the context of frequency-domain nonlinear spectroscopies such as Nearly-Degenerate Four-Wave Mixing (NDFWM)1. In the absence of strong laser fields2 or effects such as pure dephasing3, stochastic fluctuations in laser fields4, and laser transients5, the NDFWM extra resonances are either very weak (in the case of EPGS) or nonexistent (in the case of IUES). It is perhaps under-appreciated that "Fourier-transform" time- and frequency-domain FWM techniques do not necessarily provide the same information. For instance, under certain circumstances6, the NDFWM and transient grating (TG) techniques form such a pair, which would imply that TG extra resonances might disappear under the same experimental conditions in which they disappear in NDFWM. This assumption is belied by the TG data shown in Fig. 1. These data were taken by exciting and probing the D1 line of Na atoms in a cell in which there was no buffer gas and the Na pressure was low enough to preclude any significant number Na-Na collisions on the experimental time scale. Even in the absence of pressure-induced dephasing, these data exhibit strong extra resonances at both the 1.77-GHz ground-state hyperfine-splitting frequency and the 189-MHz excited-state hyperfine-splitting frequency. These data have prompted us to undertake a theoretical study of the nature of extra resonances in time-domain nonlinear spectroscopies, the preliminary results of which are discussed here. We show that time-domain extra resonances increase in strength with decreasing dephasing, and that IUES resonances exist even in the complete absence of pure dephasing. Finally, we show that IUES and EPGS extra resonances have a common origin in the time domain.
Four wave mixing experiments are normally performed near atomic (molecular) resonances, when some of the input frequencies or their combinations are at resonance with the atomic transitions. If dephasing process are present, several new resonances appear, that may be traced directly to the influence of the dephasing processes. The origin of the ‘‘dephasing’’ may vary from collisions and other material relaxation processes, to field fluctuations, to higher order interactions in the wave mixing process. The source of these extra resonances is discussed, and specific results are shown for the various cases.
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 optical density of a resonant medium significantly affects the output signal in time resolved nonlinear optical interactions. The resonant interaction with a medium reshapes any propagating short pulse, and the mutual interaction of several such pulses, as in four-wave mixing, must be treated self-consistently. We present a theoretical framework for the proper handling of the propagation of all pulses, input as well as generated, in the small area limit. For optically thick resonant absorbers, negative time delay signals are observed, and the apparent decay rate of the induced polarization is faster than the rate observed for thin samples. We experimentally measure degenerate four-wave mixing in an atomic medium as an example, and demonstrate the quality of the theoretical model by the excellent fit to measured signals over several orders of magnitude. The improved understanding enables us to provide a simple, but surprisingly accurate, estimate for the apparent decay rate in homogeneously broadened optically thick media: If the absorption is given by \ensuremath{\alpha}, the propagation length is L, and the transverse relaxation time is T2{\mathit{T}}_{2}T2​, the apparent decay rate 2/Ta{\mathit{T}}_{\mathit{a}}Ta​ of a time resolved four-wave mixing signal is given by 2/Ta{\mathit{T}}_{\mathit{a}}Ta​=(2/T2{\mathit{T}}_{2}T2​)(1+\ensuremath{\alpha}L/2).
The characteristic features of the conjugate wave's formation under transient four-wave mixing in a two-level medium are investigated. The phase modulations of the signal and conjugate waves induced in the four-wave mixing are not mutually conjugate and have the same sign. The fulfillment of the phase-conjugation for the phase modulated signal has been shown in particular to be connected with the envelope's deformation and the spectrum's change of signal pulses. The transient optical bistability connected with the nonlinear absorption's saturation in the quasi-cw four-wave mixing and with the inertia in the short pulse's regime is observed.