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

Degenerate four-wave mixing of c-w h-f laser beams in h-f absorption cell. Technical report

H. Mirels, John G. Coffer, Jay M. Bernard, R. A. Chodzko

Published Aug 6, 1990• 0 citations
OpenAlex

Abstract

Phase conjugation of a cw hydrogen fluoride (HF) laser beam has been investigated experimentally and theoretically using resonant degenerate four-wave mixing (DFWM) in an HF gas absorption cell. A single-line single-mode HF laser, operating on P1(8), P1(9),or P1(10) transitions, provided total (forward plus backward) pump beam intensities of 130, 600, and 400 W/sq. cm., respectively, in the HF absorption cell. A probe beam intensity of the order of 10 W/sq. cm. was also provided. Conjugate reflection of the probe beam was investigated as a function of gas cell pressure and as a function of frequency detuning from line center. The variation of reflectivity with gas cell pressure at fixed laser beam intensity indicated a peak reflectivity of the order of .0001 at pressures from 2 to 4 Torr. Measurement of conjugate beam intensity, as a function of frequency detuning from the line center,provided a signal with a full width at half maximum (FWHM) of about 30 MHz. The latter is of the order of the homogeneous width, for HF at the test pressure, and may be compared to the Doppler width delta nu sub d = 300 MHz for the medium. An Analytical model is presented which provides theoretical estimatesmore » for the variation of reflectivity with pressure. Effects of diffusion, thermal conduction, pump depletion, and a nonuniform (Gaussian) profile are considered. Theoretical estimates for peak reflectivity agree with experiments to within a factor of about 2.« less

Related papers

Measurement of cw HF laser resonant degenerate four-wave mixing in an absorbing HF gas

John G. Coffer, R. A. Chodzko, Jay M. Bernard +1 more

Continuous wave (cw) phase conjugation of a HF laser beam has been observed using resonant degenerate four-wave mixing in a HF gas absorption cell. A HF laser was operated in the P1(8) transition to provide total (forward plus backward) pump beam and probe beam intensities of about 400 and 30 W/cm2, respectively, in the cell. Conjugate reflectivities were measured as a function of HF pressure and frequency detuning from line center. Reflectivities of the order of 10−4 were measured at HF gas pressures of the order of 2 Torr when the laser frequency was tuned near line center.

Applied Physics Letters•Apr 16, 1990•3 citations

Phase conjugation in CO2 laser medium: theory and experiment

А. А. Ионин, А. А. Котков, Anatolii P. Napartovich +2 more

Phase conjugation (PC) processes at degenerate four-wave mixing (DFWM) in the active medium of a pulsed e-beam controlled discharge CO2-laser were studied both experimentally and theoretically. The experiment was carried out with the following parameters: laser gas mixture CO2:N2:He=1:2:4, gas pressure 0.3 bar, active medium length 1.2 m, resonator length 12 m (17.7 m for single line laser), interaction angle ~10 mrad at DFWM without optical delay between probe wave and co-propagating pump one. Integral PC reflectivity (PCR) strongly depends on such parameters as: specific input energy (Fig. 1); intensity ratio for probe J3 and co-propagating pump J1 wave (Fig.2); coherency of the laser radiation, that varied by rotation of mutual polarization or with optical delay between probe wave and co-propagating pump one; geometry of DFWM; output mirror reflectance Rout (8-80%) (PCR was maximum with Rout of 8% but best quality of PC signal was observed with Rout =80%); gas mixture composition and pressure, being maximum for a mixture with a low fraction of helium and at higher pressure (up to 0.6 bar). A periodical dependence of PCR on optical delay between probe and co-propagating pump wave with periods 10−3 and 10−5 m was observed. The PCR did not depend on spectral content and a degree of linear polarization of the laser radiation.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1998•0 citations

Phase-conjugate characteristics of SF 6 by degenerate four-wave mixing at 10.6 μm

Bangwei Cai, Baida Lü, Xiang Sean Zhou +1 more

Degenerate-four-wave mixing (DFWM) is an important technique for the generation of phase-conjugate wave, to which much attention has been paid. In this paper. a tunalile CW CO2 1.aser is used as the pump sourse and gaseous SF6 as the nonlinear medium, the dependence of reflectivity of phase-conjugate wave generated by DFWM on the pump intensity, the pressure in SF6, the angle between the pump and probe beams as welt as the potarization of the optical fields etc, is investigated experimentatty and exptained theoretically. Peak reftectivity of 2.1x101 is abtained at P=4 Torr in the gaseous SF6. In the Doppler-free phase-conjugate spectrum of SF6 five absorption dips are observed and the spectral resolving power is measured to be about 3 MHz.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 1, 1990•0 citations

Theory of saturated line shapes in phase-conjugate emission by resonant degenerate four-wave mixing in Doppler-broadened three-level systems

Daniel Bloch, M. Ducloy

We present a theoretical study of phase-conjugate (PC) emission by backward degenerate four-wave mixing (DFWM) processes in a resonant gas medium. In this study, high-intensity (pump) saturation and Doppler broadening are simultaneously taken into account. We develop a general formalism to deal with the saturation effects in the case of a three-level atom (with degenerate frequencies) and obtain analytical expressions of the PC field amplitude (after integration over the velocity distribution) under the following conditions: (1) the probe beam and one of the pump beams have intensities weak enough to be treated at the lowest perturbation order, whereas the other pump intensity is arbitrarily high; (2) the probe crosses the standing pump wave at grazing incidence. It is shown that the saturation induced by the forward pump (copropagating with the probe beam) leads to entirely different behavior of the nonlinear susceptibility from that induced by the backward pump (counterpropagating with the probe beam). This saturation anisotropy is specific to the inhomogeneous broadening of the gas medium, which is also responsible for the frequency splitting experimentally observed in the intensity line shape of the PC emission for large pump intensities. At saturation, this splitting is theoretically shown to be proportional to the Rabi frequency, with a proportionality coefficient critically dependent on the relaxation processes; in the case of a single-relaxation model, the splitting is equal to 1.5 times the Rabi frequency. The PC intensity line shape is demonstrated to be of dispersive origin in the case of backward saturation, whereas for forward saturation, narrow structures are predicted in both real and imaginary parts of the nonlinear susceptibility, also leading to the intensity line-shape splitting. One also finds that the reflectivity of PC mirrors based on resonant DFWM strongly depends on the origin of the saturation. For a saturating forward pump, the PC emission intensity tends toward zero with increasing pump intensities, and it reaches a finite (nonzero) limit in the case of backward saturation. Most of these predictions have been observed experimentally [ BlochD., Phys. Rev. Lett.49, 719 ( 1982)].

Journal of the Optical Society of America•May 1, 1983•67 citations

Degenerate four-wave mixing spectroscopy with short-pulse lasers: theoretical analysis

Thomas A. Reichardt, Robert P. Lucht

The use of picosecond lasers for degenerate four-wave mixing (DFWM) diagnostics of atmospheric pressure flames has been suggested as a means of overcoming the complicated collision-rate dependence of the DFWM signal in the nanosecond-laser pulse-length regime. In this paper DFWM spectroscopy in the regime in which the laser pulse length (τL) is less than the characteristic collisional time (τC) is investigated theoretically. DFWM signal levels for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integration of the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and by summing of the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision broadened and Doppler broadened are considered. DFWM signal generation for these two types of resonances in the fully transient regime (τL≪τC) is strikingly different. For a homogeneously broadened resonance, the DFWM signal persists long after the laser beam has passed through the medium. The decay rate of the DFWM signal is determined by the collision rate in the medium, and the integrated DFWM signal is still dependent on the collision rate even in this fully transient regime. However, when the Doppler broadening of the resonance is much greater than the collisional broadening, the DFWM signal decays with a fall time close to that of the laser pulse. For τL≪τC, we find that it is the laser spectral width, rather than the collisional width, that dictates the range of velocity groups with which the pulses effectively interact. The signal decays with a fall time close to that of the laser pulse because the excited velocity groups radiate out of phase with one another. In a medium in which the Doppler width is much greater than the collisional width, the DFWM reflectivity is independent of collision rate for τL≪τC, but the signal level is dependent on the Doppler width. Finally, we investigate the effect of different laser pulse lengths on reflectivity saturation curves for resonances with different levels of Doppler broadening.

Journal of the Optical Society of America B•Dec 1, 1996•17 citations

Theory of degenerate four-wave mixing in resonant Doppler-broadened systems - I. Angular dependence of intensity and lineshape of phase-conjugate emission

M. Ducloy, Daniel Bloch

We present in this paper a theoretical study of the angular dependence of phase-conjugate emission via resonant degenerate four-wave mixing (FWM) in Doppler-broadened gas media. The nonlinear optical polarization is calculated through an expansion of the atomic density matrix up to the third order in the incident fields. One finds that, when the incident frequency is resonant for a single-photon transition, both strength and lineshape of the phase-conjugate emission strongly depend on the angle 0 between standing pump wave and probe wave. The emission intensity, maximum at grazing incidences, decreases rapidly by several orders of magnitude when 0 increases. Simultaneously the emission linewidth increases from homogeneous to Doppler width. Similar effects are predicted for nearly-degenerate FWM (different pump and probe frequencies). In particular, one shows that the bandwidth of the equivalent optical reflection filter undergoes a Doppler-broadening linearly increasing with sin θ. On the opposite, none of the above effects is predicted in two-photon-resonant FWM which does not exhibit any angular dependence.

Journal de physique•Jan 1, 1981•74 citations
Phase conjugation of a cw hydrogen fluoride (HF) laser beam has been investigated experimentally and theoretically using resonant degenerate four-wave mixing (DFWM) in an HF gas absorption cell. A single-line single-mode HF laser, operating on P1(8), P1(9),or P1(10) transitions, provided total (forward plus backward) pump beam intensities of 130, 600, and 400 W/sq. cm., respectively, in the HF absorption cell. A probe beam intensity of the order of 10 W/sq. cm. was also provided. Conjugate reflection of the probe beam was investigated as a function of gas cell pressure and as a function of frequency detuning from line center. The variation of reflectivity with gas cell pressure at fixed laser beam intensity indicated a peak reflectivity of the order of .0001 at pressures from 2 to 4 Torr. Measurement of conjugate beam intensity, as a function of frequency detuning from the line center,provided a signal with a full width at half maximum (FWHM) of about 30 MHz. The latter is of the order of the homogeneous width, for HF at the test pressure, and may be compared to the Doppler width delta nu sub d = 300 MHz for the medium. An Analytical model is presented which provides theoretical estimatesmore » for the variation of reflectivity with pressure. Effects of diffusion, thermal conduction, pump depletion, and a nonuniform (Gaussian) profile are considered. Theoretical estimates for peak reflectivity agree with experiments to within a factor of about 2.« less
Continuous wave (cw) phase conjugation of a HF laser beam has been observed using resonant degenerate four-wave mixing in a HF gas absorption cell. A HF laser was operated in the P1(8) transition to provide total (forward plus backward) pump beam and probe beam intensities of about 400 and 30 W/cm2, respectively, in the cell. Conjugate reflectivities were measured as a function of HF pressure and frequency detuning from line center. Reflectivities of the order of 10−4 were measured at HF gas pressures of the order of 2 Torr when the laser frequency was tuned near line center.
Phase conjugation (PC) processes at degenerate four-wave mixing (DFWM) in the active medium of a pulsed e-beam controlled discharge CO2-laser were studied both experimentally and theoretically. The experiment was carried out with the following parameters: laser gas mixture CO2:N2:He=1:2:4, gas pressure 0.3 bar, active medium length 1.2 m, resonator length 12 m (17.7 m for single line laser), interaction angle ~10 mrad at DFWM without optical delay between probe wave and co-propagating pump one. Integral PC reflectivity (PCR) strongly depends on such parameters as: specific input energy (Fig. 1); intensity ratio for probe J3 and co-propagating pump J1 wave (Fig.2); coherency of the laser radiation, that varied by rotation of mutual polarization or with optical delay between probe wave and co-propagating pump one; geometry of DFWM; output mirror reflectance Rout (8-80%) (PCR was maximum with Rout of 8% but best quality of PC signal was observed with Rout =80%); gas mixture composition and pressure, being maximum for a mixture with a low fraction of helium and at higher pressure (up to 0.6 bar). A periodical dependence of PCR on optical delay between probe and co-propagating pump wave with periods 10−3 and 10−5 m was observed. The PCR did not depend on spectral content and a degree of linear polarization of the laser radiation.
Degenerate-four-wave mixing (DFWM) is an important technique for the generation of phase-conjugate wave, to which much attention has been paid. In this paper. a tunalile CW CO2 1.aser is used as the pump sourse and gaseous SF6 as the nonlinear medium, the dependence of reflectivity of phase-conjugate wave generated by DFWM on the pump intensity, the pressure in SF6, the angle between the pump and probe beams as welt as the potarization of the optical fields etc, is investigated experimentatty and exptained theoretically. Peak reftectivity of 2.1x101 is abtained at P=4 Torr in the gaseous SF6. In the Doppler-free phase-conjugate spectrum of SF6 five absorption dips are observed and the spectral resolving power is measured to be about 3 MHz.
We present a theoretical study of phase-conjugate (PC) emission by backward degenerate four-wave mixing (DFWM) processes in a resonant gas medium. In this study, high-intensity (pump) saturation and Doppler broadening are simultaneously taken into account. We develop a general formalism to deal with the saturation effects in the case of a three-level atom (with degenerate frequencies) and obtain analytical expressions of the PC field amplitude (after integration over the velocity distribution) under the following conditions: (1) the probe beam and one of the pump beams have intensities weak enough to be treated at the lowest perturbation order, whereas the other pump intensity is arbitrarily high; (2) the probe crosses the standing pump wave at grazing incidence. It is shown that the saturation induced by the forward pump (copropagating with the probe beam) leads to entirely different behavior of the nonlinear susceptibility from that induced by the backward pump (counterpropagating with the probe beam). This saturation anisotropy is specific to the inhomogeneous broadening of the gas medium, which is also responsible for the frequency splitting experimentally observed in the intensity line shape of the PC emission for large pump intensities. At saturation, this splitting is theoretically shown to be proportional to the Rabi frequency, with a proportionality coefficient critically dependent on the relaxation processes; in the case of a single-relaxation model, the splitting is equal to 1.5 times the Rabi frequency. The PC intensity line shape is demonstrated to be of dispersive origin in the case of backward saturation, whereas for forward saturation, narrow structures are predicted in both real and imaginary parts of the nonlinear susceptibility, also leading to the intensity line-shape splitting. One also finds that the reflectivity of PC mirrors based on resonant DFWM strongly depends on the origin of the saturation. For a saturating forward pump, the PC emission intensity tends toward zero with increasing pump intensities, and it reaches a finite (nonzero) limit in the case of backward saturation. Most of these predictions have been observed experimentally [ BlochD., Phys. Rev. Lett.49, 719 ( 1982)].
The use of picosecond lasers for degenerate four-wave mixing (DFWM) diagnostics of atmospheric pressure flames has been suggested as a means of overcoming the complicated collision-rate dependence of the DFWM signal in the nanosecond-laser pulse-length regime. In this paper DFWM spectroscopy in the regime in which the laser pulse length (τL) is less than the characteristic collisional time (τC) is investigated theoretically. DFWM signal levels for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integration of the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and by summing of the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision broadened and Doppler broadened are considered. DFWM signal generation for these two types of resonances in the fully transient regime (τL≪τC) is strikingly different. For a homogeneously broadened resonance, the DFWM signal persists long after the laser beam has passed through the medium. The decay rate of the DFWM signal is determined by the collision rate in the medium, and the integrated DFWM signal is still dependent on the collision rate even in this fully transient regime. However, when the Doppler broadening of the resonance is much greater than the collisional broadening, the DFWM signal decays with a fall time close to that of the laser pulse. For τL≪τC, we find that it is the laser spectral width, rather than the collisional width, that dictates the range of velocity groups with which the pulses effectively interact. The signal decays with a fall time close to that of the laser pulse because the excited velocity groups radiate out of phase with one another. In a medium in which the Doppler width is much greater than the collisional width, the DFWM reflectivity is independent of collision rate for τL≪τC, but the signal level is dependent on the Doppler width. Finally, we investigate the effect of different laser pulse lengths on reflectivity saturation curves for resonances with different levels of Doppler broadening.
We present in this paper a theoretical study of the angular dependence of phase-conjugate emission via resonant degenerate four-wave mixing (FWM) in Doppler-broadened gas media. The nonlinear optical polarization is calculated through an expansion of the atomic density matrix up to the third order in the incident fields. One finds that, when the incident frequency is resonant for a single-photon transition, both strength and lineshape of the phase-conjugate emission strongly depend on the angle 0 between standing pump wave and probe wave. The emission intensity, maximum at grazing incidences, decreases rapidly by several orders of magnitude when 0 increases. Simultaneously the emission linewidth increases from homogeneous to Doppler width. Similar effects are predicted for nearly-degenerate FWM (different pump and probe frequencies). In particular, one shows that the bandwidth of the equivalent optical reflection filter undergoes a Doppler-broadening linearly increasing with sin θ. On the opposite, none of the above effects is predicted in two-photon-resonant FWM which does not exhibit any angular dependence.