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Journal of the Optical Society of America B

Degenerate Four-Wave Mixing of Femtosecond Pulses in the Saturable Absorber of a Ring Dye Laser

Ian C. McMichael, Jean‐Claude Diels

Published Jan 1, 1984• 3 citations
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Abstract

The saturable absorber dye jet of a femtosecond ring dye laser provides an ideal candidate for the study of fast transients in de- generate four-wave mixing (DFWM). Since the counterpropagating pulses in the ring laser meet at the absorber jet, the problem of timing the DFWM pump pulses is solved. The energy of the pulses inside the cavity is such that the absorber is saturated. This meets one of the conditions for efficient DFWM in saturable media.1 Since the dye jet is thin, fast transients in DFWM are not masked by propagation effects.

Related papers

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

Transient effects in degenerate four-wave mixing in saturable absorbers

Yaron R. Silberberg, I. Bar‐Joseph

The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.

IEEE Journal of Quantum Electronics•Sep 1, 1981•60 citations

Degenerate four-wave mixing of femtosecond pulses in an absorbing dye jet

Jean‐Claude Diels, Ian C. McMichael

Intracavity measurements of degenerate four-wave mixing have been performed with femtosecond laser pulses to determine the phase relaxation time of the absorbing dye, diethyloxadicarbocyanine iodide (DODCI), in ethylene glycol. The influence of various broadening mechanisms (homogeneous, inhomogeneous, cross relaxation) and pulse parameters (frequency, pulse shape, phase modulation, and energy) is investigated. The dependence of the signal energy on probe delay is found to be strongly affected by the phase modulation of the pulse; hence determination of the phase relaxation time requires accurate diagnostics of the laser source. The rise of the signal provides an upper limit of 10 fsec for the phase relaxation time of the main absorption band of the dye DODCI. The decay of the signal is found to be related to the phase relaxation time of a two-photon absorption in the same dye. Accurate fitting of the data with the theory yields 50 ± 10 fsec for the dephasing time of the two-photon excitation in DODCI.

Journal of the Optical Society of America B•Apr 1, 1986•28 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

Temporal behavior of a conjugated beam by degenerate four-wave mixing in azo dyes

Sylvain Mailhot, Pierre Galarneau, Roger A. Lessard +1 more

Degenerate four-wave mixing (DFWM) is a simple method to achieve phase conjugation. It uses the third-order nonlinearity of the electric susceptibility to produce changes in the optical properties of materials. A dynamic grating is then induced. Such gratings might be used as fast optical memories in optical computing. Our aim is to find media with large nonlinear susceptibilities and fast response time. We report phase conjugation of 532-nm laser radiation by DFWM in dye solutions. The time dependence of the conjugated wave is investigated experimentally and compared to theoretical predictions. We have also studied the influence of the solvents, dye concentration, and pump intensity on the phase conjugated signal. The results are compared with those predicted by three nonlinear mechanisms. Thermally induced refractive-index changes, Kerr effect, and saturable absorption are considered.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Anisotropic properties of pulsed four-wave mixing in Cr^4+:YAG saturable absorbers

A. Brignon

A model of degenerate four-wave mixing (DFWM) in Cr4+:YAG saturable absorbers is given in the transient regime. Because of the presence of absorbing dipoles oriented along specific directions, the DFWM process exhibits an anisotropic behavior. The effects of pump beam fluences, relative polarization of the beams, crystal orientation, absorbance, excited-state absorption, and nonresonant losses are analyzed. The theoretical results are supported by DFWM experiments in Cr4+:YAG performed at 1.06 µm with nanosecond pulses.

Journal of the Optical Society of America B•Oct 1, 1996•27 citations
The saturable absorber dye jet of a femtosecond ring dye laser provides an ideal candidate for the study of fast transients in de- generate four-wave mixing (DFWM). Since the counterpropagating pulses in the ring laser meet at the absorber jet, the problem of timing the DFWM pump pulses is solved. The energy of the pulses inside the cavity is such that the absorber is saturated. This meets one of the conditions for efficient DFWM in saturable media.1 Since the dye jet is thin, fast transients in DFWM are not masked by propagation effects.
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.
The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.
Intracavity measurements of degenerate four-wave mixing have been performed with femtosecond laser pulses to determine the phase relaxation time of the absorbing dye, diethyloxadicarbocyanine iodide (DODCI), in ethylene glycol. The influence of various broadening mechanisms (homogeneous, inhomogeneous, cross relaxation) and pulse parameters (frequency, pulse shape, phase modulation, and energy) is investigated. The dependence of the signal energy on probe delay is found to be strongly affected by the phase modulation of the pulse; hence determination of the phase relaxation time requires accurate diagnostics of the laser source. The rise of the signal provides an upper limit of 10 fsec for the phase relaxation time of the main absorption band of the dye DODCI. The decay of the signal is found to be related to the phase relaxation time of a two-photon absorption in the same dye. Accurate fitting of the data with the theory yields 50 ± 10 fsec for the dephasing time of the two-photon excitation in DODCI.
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.
Degenerate four-wave mixing (DFWM) is a simple method to achieve phase conjugation. It uses the third-order nonlinearity of the electric susceptibility to produce changes in the optical properties of materials. A dynamic grating is then induced. Such gratings might be used as fast optical memories in optical computing. Our aim is to find media with large nonlinear susceptibilities and fast response time. We report phase conjugation of 532-nm laser radiation by DFWM in dye solutions. The time dependence of the conjugated wave is investigated experimentally and compared to theoretical predictions. We have also studied the influence of the solvents, dye concentration, and pump intensity on the phase conjugated signal. The results are compared with those predicted by three nonlinear mechanisms. Thermally induced refractive-index changes, Kerr effect, and saturable absorption are considered.
A model of degenerate four-wave mixing (DFWM) in Cr4+:YAG saturable absorbers is given in the transient regime. Because of the presence of absorbing dipoles oriented along specific directions, the DFWM process exhibits an anisotropic behavior. The effects of pump beam fluences, relative polarization of the beams, crystal orientation, absorbance, excited-state absorption, and nonresonant losses are analyzed. The theoretical results are supported by DFWM experiments in Cr4+:YAG performed at 1.06 µm with nanosecond pulses.