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

Proceedings of the Academy of Sciences of the Estonian SSR Physics Mathematics

STEADY-STATE THIRD-ORDER NONLINEAR SPECTROSCOPY IN INHOMOGENEOUS MEDIA

Peeter Kukk, A. Freiberg

Published Jan 21, 1981• 0 citations
Publisher

Abstract

An analysis and model calculations are presented to clarity how both the electronic and vibrational inhomogeneities with no correlation between them influence the most relevant resonant steady-state third-order nonlinear optical mixing processes (CARS, CSRS, polarization spectroscopy and Raman gain (loss)).It is shown that all these processes may be divided into three groups: 1) processes yielding almost homogeneous spectra: both inhomogeneities are greatly reduced; 2) processes yielding quasihomo- geneous spectra: inhomogeneities are present, but the electronic one is not manifest in the spectrum; 3) processes yielding completely inhomogeneous spectra.The suppression of inhomogeneous broadening allows to study the excited electronic states and the ultrafast relaxation processes in inhomogeneous media more effectively than in linear spectroscopy. * About another steady-state frequency domain technique byhot luminescence measurements for the study of ultrafast energy relaxation see.e. g. f l4 ].ЁЁЗТТ NSV TEADUSTE AKADEEMIA TOIMETISED.30.

DOI
10.3176/phys.math.1981.4.08

Related papers

THEORETICAL ASPECTS OF FOUR-WAVE MIXING SPECTROSCOPY WITH MULTIPLE RESONANCES

J. L. Oudar

The use of multiresonant four-wave mixing processes in solid-state spectroscopy is analyzed in detail. Specific information on the excited states of solids can be obtained from such techniques, including the reduction of inhomogeneous broadening, study of transitions between excited states, determination of ultrafast relaxation times through measurements in the frequency domain.

•Jan 1, 1981•0 citations

Line Narrowing Effect in Fully Resonant Four Wave Mixing Spectroscopy in Solids

Hirotoshi Souma

We explain the utility of third-order nonlinear susceptibility, χ (3) (ω 2 ; ±ω 1 , \({\mp}\omega_{1}\), ω 2 ), for the observation of resonances with homogeneous widths from inhomogeneously broadened distributions in three-level systems related to Raman or two-photon allowed electronic transitions. The line narrowing and high resolution capabilities are demonstrated theoretically using a model for inhomogeneous distributions of transitions in which we regard an absorption spectrum as the composition of some inhomogeneously broadened substructures. The experimental methods to separate a signal having frequency ω 2 from ingoing beam at the same frequency are outlined.

Journal of the Physical Society of Japan•Sep 1, 1983•2 citations

Nonlinear spectroscopy by multiresonant four-wave mixing

J. L. Oudar, Y. Ron Shen

Four-wave mixing processes with double and triple resonances are discussed in detail. Explicit expressions for the resonant nonlinear susceptibilities of various cases are derived. It is shown that in some cases, four-wave mixing can yield a spectrum with reduced inhomogeneous broadening. Possible applications of multiresonant four-wave mixing as a spectroscopic technique are considered. They include high-resolution spectroscopy, deduction of transition matrix elements, study of transitions between excited states, measurement of longitudinal relaxation times, distinction between resonant Raman scattering and resonant fluorescence, etc. Selective polarization arrangement allows us to suppress the nonresonant background, separately measure the real and imaginary parts of the resonant nonlinear susceptibility, minimize the effects of absorption and laser intensity fluctuations, and greatly enhance the signal-to-noise ratio.

Physical Review A•Sep 1, 1980•144 citations

Study of ultra-fast relaxation processes by resonant Rayleigh-type optical mixing. I. Theory

Tatsuo Yajima, Hirotoshi Souma

A comprehensive theory of a new type of three-wave optical mixing (${\ensuremath{\omega}}_{3}=2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$) is given for the spectroscopic purpose of determining ultra-short relaxation times (picoseconds or less) associated with excited states of condensed matter. Two incident light frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are chosen so that they are both resonant with an inhomogeneously broadened optical transition and $|{\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}|$ is in the vicinity of inverse relaxation times. The theory is developed for its major application to broad-band electronic transitions. The nonlinear susceptibility ${\ensuremath{\chi}}_{R}^{(3)}$ for this process (named resonant Rayleigh-type mixing) is calculated by a density-matrix formalism with the model of a two-level atomic system incorporating the distribution of resonance frequencies and longitudinal (${T}_{1}$) and transverse (${T}_{2}$) relaxation times. The result shows a frequency characteristic depending only on ${T}_{1}$, ${T}_{2}$, and ${\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}$ in a broad-band limit, which serves for the determination of ${T}_{1}$ and ${T}_{2}$ in the frequency domain. The analysis is further extended to include the various effects as follows. The calculation of the saturation effect in the lowest order reveals that it modifies the shape of the frequency characteristic of the nonlinear susceptibility but does not affect seriously the determination of relaxation times. The effect of spectral cross relaxation within the inhomogeneous broadening is incorporated by a generalized density-matrix formalism. The resultant ${\ensuremath{\chi}}_{R}^{(3)}$ consists of two terms. The dominant term is the same as before except that ${T}_{1}$ is replaced by a combined relaxation time ${T}_{1}^{\ensuremath{'}}={({T}_{1}^{\ensuremath{-}1}+{T}_{3}^{\ensuremath{-}1})}^{\ensuremath{-}1}$, where ${T}_{3}$ is the cross-relaxation time. The other term originates from the inverse spectral-diffusion process. The effect of other energy levels located between the two levels under study is analyzed with a simple three-level model. The resultant ${\ensuremath{\chi}}_{R}^{(3)}$ also consists of two terms, the dominant one being the same as that for the two-level model except that ${T}_{1}^{\ensuremath{-}1}$ should be interpreted as total population decay rate of the upper level. For accurate derivation of ${\ensuremath{\chi}}_{R}^{(3)}$ from experiment, we discuss the interference between the resonant and nonresonant susceptibility terms and the light-wave propagation effect. Finally, the close analogy between this type of optical mixing and the photon echo is discussed.

Physical Review A•Jan 1, 1978•146 citations

Saturation effects in resonant coherent anti-Stokes Raman spectroscopy of inhomogeneously broadened media

François Ouellette, Marguerite-Marie Denariez

The effects of pump field intensity are investigated for resonant coherent anti-Stokes Raman spectroscopy (CARS) in inhomogeneously broadened media. It is shown that the CARS line, although Doppler broadened for low intensity, is narrowed to its natural linewidth as intensity is increased and that higher order selectively saturating processes become dominant. Splitting effects are also discussed. Analog results are found for "double electronic resonances."

Canadian Journal of Physics•Oct 1, 1982•23 citations

Nonlinear spectra of a homogeneously and inhomogeneously broadened two-level system

Amenaida Ferrer Marcano, O. M. C. Salazar, J. L. Paz +2 more

Polarization and Rayleigh type optical mixing spectra of a homogeneously and inhomogeneously broadened two-level system are calculated. We show that the nonlinear signal has contributions from the population pulsation and saturation effect. In the homogeneous system these effects can induce an asymmetric spectrum when the probe frequency is different from the resonant value. In the inhomogeneous system the spectral response is always symmetric independent of the probe frequency value. Line saturation and dynamic stark splitting are substantially reduced in the inhomogeneous case. The mentioned differences can be used to identify the type of broadening of a given spectral line.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
An analysis and model calculations are presented to clarity how both the electronic and vibrational inhomogeneities with no correlation between them influence the most relevant resonant steady-state third-order nonlinear optical mixing processes (CARS, CSRS, polarization spectroscopy and Raman gain (loss)).It is shown that all these processes may be divided into three groups: 1) processes yielding almost homogeneous spectra: both inhomogeneities are greatly reduced; 2) processes yielding quasihomo- geneous spectra: inhomogeneities are present, but the electronic one is not manifest in the spectrum; 3) processes yielding completely inhomogeneous spectra.The suppression of inhomogeneous broadening allows to study the excited electronic states and the ultrafast relaxation processes in inhomogeneous media more effectively than in linear spectroscopy. * About another steady-state frequency domain technique byhot luminescence measurements for the study of ultrafast energy relaxation see.e. g. f l4 ].ЁЁЗТТ NSV TEADUSTE AKADEEMIA TOIMETISED.30.
We explain the utility of third-order nonlinear susceptibility, χ (3) (ω 2 ; ±ω 1 , ∓ω1{\mp}\omega_{1}∓ω1​, ω 2 ), for the observation of resonances with homogeneous widths from inhomogeneously broadened distributions in three-level systems related to Raman or two-photon allowed electronic transitions. The line narrowing and high resolution capabilities are demonstrated theoretically using a model for inhomogeneous distributions of transitions in which we regard an absorption spectrum as the composition of some inhomogeneously broadened substructures. The experimental methods to separate a signal having frequency ω 2 from ingoing beam at the same frequency are outlined.
Four-wave mixing processes with double and triple resonances are discussed in detail. Explicit expressions for the resonant nonlinear susceptibilities of various cases are derived. It is shown that in some cases, four-wave mixing can yield a spectrum with reduced inhomogeneous broadening. Possible applications of multiresonant four-wave mixing as a spectroscopic technique are considered. They include high-resolution spectroscopy, deduction of transition matrix elements, study of transitions between excited states, measurement of longitudinal relaxation times, distinction between resonant Raman scattering and resonant fluorescence, etc. Selective polarization arrangement allows us to suppress the nonresonant background, separately measure the real and imaginary parts of the resonant nonlinear susceptibility, minimize the effects of absorption and laser intensity fluctuations, and greatly enhance the signal-to-noise ratio.
A comprehensive theory of a new type of three-wave optical mixing (${\ensuremath{\omega}}_{3}=2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$) is given for the spectroscopic purpose of determining ultra-short relaxation times (picoseconds or less) associated with excited states of condensed matter. Two incident light frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are chosen so that they are both resonant with an inhomogeneously broadened optical transition and $|{\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}|$ is in the vicinity of inverse relaxation times. The theory is developed for its major application to broad-band electronic transitions. The nonlinear susceptibility ${\ensuremath{\chi}}_{R}^{(3)}$ for this process (named resonant Rayleigh-type mixing) is calculated by a density-matrix formalism with the model of a two-level atomic system incorporating the distribution of resonance frequencies and longitudinal (T1{T}_{1}T1​) and transverse (T2{T}_{2}T2​) relaxation times. The result shows a frequency characteristic depending only on T1{T}_{1}T1​, T2{T}_{2}T2​, and ${\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}$ in a broad-band limit, which serves for the determination of T1{T}_{1}T1​ and T2{T}_{2}T2​ in the frequency domain. The analysis is further extended to include the various effects as follows. The calculation of the saturation effect in the lowest order reveals that it modifies the shape of the frequency characteristic of the nonlinear susceptibility but does not affect seriously the determination of relaxation times. The effect of spectral cross relaxation within the inhomogeneous broadening is incorporated by a generalized density-matrix formalism. The resultant ${\ensuremath{\chi}}_{R}^{(3)}$ consists of two terms. The dominant term is the same as before except that T1{T}_{1}T1​ is replaced by a combined relaxation time ${T}_{1}^{\ensuremath{'}}={({T}_{1}^{\ensuremath{-}1}+{T}_{3}^{\ensuremath{-}1})}^{\ensuremath{-}1}$, where T3{T}_{3}T3​ is the cross-relaxation time. The other term originates from the inverse spectral-diffusion process. The effect of other energy levels located between the two levels under study is analyzed with a simple three-level model. The resultant ${\ensuremath{\chi}}_{R}^{(3)}$ also consists of two terms, the dominant one being the same as that for the two-level model except that ${T}_{1}^{\ensuremath{-}1}$ should be interpreted as total population decay rate of the upper level. For accurate derivation of ${\ensuremath{\chi}}_{R}^{(3)}$ from experiment, we discuss the interference between the resonant and nonresonant susceptibility terms and the light-wave propagation effect. Finally, the close analogy between this type of optical mixing and the photon echo is discussed.
Polarization and Rayleigh type optical mixing spectra of a homogeneously and inhomogeneously broadened two-level system are calculated. We show that the nonlinear signal has contributions from the population pulsation and saturation effect. In the homogeneous system these effects can induce an asymmetric spectrum when the probe frequency is different from the resonant value. In the inhomogeneous system the spectral response is always symmetric independent of the probe frequency value. Line saturation and dynamic stark splitting are substantially reduced in the inhomogeneous case. The mentioned differences can be used to identify the type of broadening of a given spectral line.