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

Physical Review A

Four-wave mixing in optically dense media

Opher Kinrot, Yehiam Prior

Published Sep 1, 1994• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.r1999

Related papers

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

Effects of coherent polarization interactions on time-resolved degenerate four-wave mixing

Karl Leo, Martin Wegener, J. Shah +5 more

We report the first observation of coherent polarization interactions in dense media in time-resolved degenerate four-wave mixing in semiconductors. For near-resonant ultrashort-optical-pulse excitation, these interactions lead to a diffracted signal at negative delay times, with a slope half that for positive delay times. At higher intensities, two temporal maxima appear in the diffracted signal, in agreement with many-body theory.

Physical Review Letters•Sep 1, 1990•296 citations

FWM in optically dense medía

Opher Kinrol, Yehiam Prior

We show, both experimentally and theoretically, that short-pulse reshaping clue to propagation leads to the formation of negative-time-delay signals in four-wave mixing (FWM) and to apparent signal decay that is not given by the dephasing or the population-decay rates. Recently, pulse reshaping due to coherent propagation was used to estimate dephasing times in CD, and ZnP·. (Ref. 1), and negative time-delay response in FWM in quantum wells was reported and was explained in terms of higher-order susceptibilities interfering with the third-order FWM process.2

•May 8, 1994•0 citations

Self-diffraction in optically dense media

M. Belov, M. A. Selifanov, Edward A. Manykin

We investigate the phenomenon of self-diffraction in optically dense media for those cases where it is necessary to take into account the inverse effect of the medium on the field. Our study is based on a numerical analysis of the Maxwell–Bloch equations. This analysis reveals that, as the concentration of two-level systems increases, an anomalous response of four-wave mixing arises. This response is associated with the appearance of a self-diffraction signal in the negative-delay region and also with a faster decay of coherence in the system.

Soviet Journal of Quantum Electronics•Nov 30, 1992•0 citations

Optical pulse integration and chirp reversal in degenerate four-wave mixing

John H. Marburger

A simple theory shows that phase modulation on a pulse may be reversed in time (e.g., positive chirp to negative) by degenerate four-wave mixing in an optically thin nonlinear medium. In thick media, the reflected pulse field is not truly time reversed, but is proportional to the time integral of the conjugate incident field.

Applied Physics Letters•Mar 15, 1978•55 citations

Degenerate Four Wave Mixing of Short and Ultrashort Light Pulses

Ian C. McMichael

This dissertation presents experimental and theoretical studies of transient degenerate four wave mixing (DFWM) in organic dyes. Chapter 1 is an introduction to DFWM. Chapter 2 describes DFWM experiments that were performed in the gain medium of a dye laser. Chapter 3 presents the theory of DFWM of short pulses in three level saturable media. Chapter 4 presents DFWM experiments of femtosecond pulses in the saturable absorber of a passively modelocked ring dye laser. Chapter 5 presents the theory of DFWM of ultrashort pulses in resonant media.

•Aug 1, 1984•1 citation
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 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).
We show, both experimentally and theoretically, that short-pulse reshaping clue to propagation leads to the formation of negative-time-delay signals in four-wave mixing (FWM) and to apparent signal decay that is not given by the dephasing or the population-decay rates. Recently, pulse reshaping due to coherent propagation was used to estimate dephasing times in CD, and ZnP·. (Ref. 1), and negative time-delay response in FWM in quantum wells was reported and was explained in terms of higher-order susceptibilities interfering with the third-order FWM process.2
We investigate the phenomenon of self-diffraction in optically dense media for those cases where it is necessary to take into account the inverse effect of the medium on the field. Our study is based on a numerical analysis of the Maxwell–Bloch equations. This analysis reveals that, as the concentration of two-level systems increases, an anomalous response of four-wave mixing arises. This response is associated with the appearance of a self-diffraction signal in the negative-delay region and also with a faster decay of coherence in the system.
This dissertation presents experimental and theoretical studies of transient degenerate four wave mixing (DFWM) in organic dyes. Chapter 1 is an introduction to DFWM. Chapter 2 describes DFWM experiments that were performed in the gain medium of a dye laser. Chapter 3 presents the theory of DFWM of short pulses in three level saturable media. Chapter 4 presents DFWM experiments of femtosecond pulses in the saturable absorber of a passively modelocked ring dye laser. Chapter 5 presents the theory of DFWM of ultrashort pulses in resonant media.