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IEEE Journal of Quantum Electronics

Thermally induced degenerate four-wave mixing

Hanna J. Hoffman

Published Apr 1, 1986• 26 citations
Publisher

Abstract

Time-dependent aspects of thermally stimulated degenerate four-wave mixing (DFWM) in absorbing liquid solutions have been theoretically investigated through a coupled electromagnetic-hydrodynamic theory originally formulated to study stimulated scattering processes. The various time scales involved in the interaction (including those characteristic of acoustic modes and thermalization effects) are identified and relevant laser and media parametrical relations are sorted out. Suitable approximation regimes are then outlined, corresponding to specific experimental situations of interest and allowing for relatively simple and tractable analytic relations to be derived. In particular, the effects of finite rise time of thermalization were studied and found to lead to a possibly strong angular dependence in the conjugate reflectivity. Acoustic modes and their influence on the process efficiency were also investigated. The calculations culminate in a set of guidelines for optimizing conjugation efficiencies, through judicious choice of dye-solvent combinations, "read" pump time delays, experimental arrangements, and laser pulse parameters.

DOI
10.1109/jqe.1986.1072992

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Experimental investigations of thermally stimulated degenerate four-wave mixing

Hanna J. Hoffman, Patrick E. Perkins

Results of experimental investigations aimed at testing efficiency-related aspects of thermally induced degenerate four-wave mixing in absorbing solutions are reported. The effects of fluorescence, read beam time delay, and forward beam angle variations are measured and shown to strongly influence the achievable thermal grating diffraction efficiency. In particular, a strong decrease of conjugation efficiency is observed as a function of increasing angle between the forward beams. Conjugate beam diffraction efficiencies as high as 17 percent were measured for the dye RhB in acetone. Based on our observations, we predict that still higher conjugation efficiencies will be feasible under optimal conditions with the thermal grating mechanism.

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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.

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Degenerate four-wave mixing and phase conjugation of pulsed CO2 laser radiation on transient gratings inside its own inverted medium

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Degenerate four-wave mixing (DFWM) and phase conjugation (PC) of pulsed CO2 laser radiation on transient gratings inside its own laser medium have been studied both experimentally and theoretically. The operational mode of the e-beam controlled discharge CO2 laser has been chosen in such a way (CO2:N2:He equals 1:2:4, p equals 0.28 atm, tin equals 30 microsecond(s) ) that the laser pulse length ((tau) out approximately 10 - 20 microsecond(s) ) is comparable with an effective relaxation time of the upper laser level ((tau) rel approximately 15 - 30 microsecond(s) ). The time-history of the CO2 laser and PC signal pulses, and PC reflectivity have been thoroughly investigated for different cavity Q factors and specific electrical energy inputs. It has been shown, that the formation of the PC signal under the intracavity DFWM on gain (amplitude) and thermal (phase) gratings is characterized by a complicated time history that reflects the main relaxation processes taking place inside the inverted medium. A feature of the transient PC process inside the laser active medium is the dependence of the effective relaxation time of the upper laser level on the intensity of pumping waves. PC reflectivity has been obtained by numerical calculations. A comparison of the theoretical and experimental data confirms the contribution of two different mechanisms of grating formation under DFWM inside the active medium of the CO2 laser.

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Degenerate four-wave mixing (DFWM) and phase conjugation (PC) of pulsed carbon-dioxide laser radiation on transient gratings inside its own laser medium have been studied both experimentally and theoretically. The operational mode of the e-beam controlled discharge carbon-dioxide laser has been chosen in such a way (CO2:N2:He equals 1:2:4, p equals 0.28 atm, tin equals 30 microseconds) that the laser pulse length (tauout approximately 10 - 20 microseconds) is comparable with an effective relaxation time of the upper laser level (taurel approximately 15 - 30 microseconds). The time-history of the carbon-dioxide laser and pc signal pulses, and pc reflectivity have been thoroughly investigated for different cavity Q factors and specific electrical energy inputs. It has been shown, that the formation of the PC signal under the intracavity DFWM on gain (amplitude) and thermal (phase) gratings is characterized by a complicated time history that reflects the main relaxation processes taking place inside the inverted medium. A feature of the transient pc process inside the laser active medium is the dependence of the effective relaxation time of the upper laser level on the intensity of pumping waves. Pc reflectivity has been obtained by numerical calculations. A comparison of the theoretical and experimental data confirms the contribution of two different mechanisms of grating formation under DFWM inside the active medium of the carbon-dioxide laser.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 26, 1996•0 citations

Degenerate Four Wave Mixing With Pulsed Lasers Theory And Applications

P. Ewart

Resonant Degenerate Four Wave Mixing, DFWM, is a nonlinear optical process arising from the third order susceptibility X(3). Resonance enhancement of X(3)in absorbing media makes the process useful for spectroscopic applications[1]. In many situations pulsed, high power lasers are used which have broad spectral bandwiths. The stochastic fluctuations of amplitude and phase associated with this bandwidth complicates the theoretical description in such cases. An averaging of the atom-field interaction is required simultaneously over the temporal and spatial variations of the fields. A solution has been found in the broad bandwidth limit which uses an appropriate decorrelation approximation. Theoretical and experimental results will be presented for the effects of laser bandwidth on the power dependence and temporal behaviour of resonant DFWM[2].

Digest on Nonlinear Optics: Materials, Phenomena and Devices•Jan 1, 1990•0 citations
Time-dependent aspects of thermally stimulated degenerate four-wave mixing (DFWM) in absorbing liquid solutions have been theoretically investigated through a coupled electromagnetic-hydrodynamic theory originally formulated to study stimulated scattering processes. The various time scales involved in the interaction (including those characteristic of acoustic modes and thermalization effects) are identified and relevant laser and media parametrical relations are sorted out. Suitable approximation regimes are then outlined, corresponding to specific experimental situations of interest and allowing for relatively simple and tractable analytic relations to be derived. In particular, the effects of finite rise time of thermalization were studied and found to lead to a possibly strong angular dependence in the conjugate reflectivity. Acoustic modes and their influence on the process efficiency were also investigated. The calculations culminate in a set of guidelines for optimizing conjugation efficiencies, through judicious choice of dye-solvent combinations, "read" pump time delays, experimental arrangements, and laser pulse parameters.
Results of experimental investigations aimed at testing efficiency-related aspects of thermally induced degenerate four-wave mixing in absorbing solutions are reported. The effects of fluorescence, read beam time delay, and forward beam angle variations are measured and shown to strongly influence the achievable thermal grating diffraction efficiency. In particular, a strong decrease of conjugation efficiency is observed as a function of increasing angle between the forward beams. Conjugate beam diffraction efficiencies as high as 17 percent were measured for the dye RhB in acetone. Based on our observations, we predict that still higher conjugation efficiencies will be feasible under optimal conditions with the thermal grating mechanism.
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.
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.
Degenerate four-wave mixing (DFWM) and phase conjugation (PC) of pulsed CO2 laser radiation on transient gratings inside its own laser medium have been studied both experimentally and theoretically. The operational mode of the e-beam controlled discharge CO2 laser has been chosen in such a way (CO2:N2:He equals 1:2:4, p equals 0.28 atm, tin equals 30 microsecond(s) ) that the laser pulse length ((tau) out approximately 10 - 20 microsecond(s) ) is comparable with an effective relaxation time of the upper laser level ((tau) rel approximately 15 - 30 microsecond(s) ). The time-history of the CO2 laser and PC signal pulses, and PC reflectivity have been thoroughly investigated for different cavity Q factors and specific electrical energy inputs. It has been shown, that the formation of the PC signal under the intracavity DFWM on gain (amplitude) and thermal (phase) gratings is characterized by a complicated time history that reflects the main relaxation processes taking place inside the inverted medium. A feature of the transient PC process inside the laser active medium is the dependence of the effective relaxation time of the upper laser level on the intensity of pumping waves. PC reflectivity has been obtained by numerical calculations. A comparison of the theoretical and experimental data confirms the contribution of two different mechanisms of grating formation under DFWM inside the active medium of the CO2 laser.
Degenerate four-wave mixing (DFWM) and phase conjugation (PC) of pulsed carbon-dioxide laser radiation on transient gratings inside its own laser medium have been studied both experimentally and theoretically. The operational mode of the e-beam controlled discharge carbon-dioxide laser has been chosen in such a way (CO2:N2:He equals 1:2:4, p equals 0.28 atm, tin equals 30 microseconds) that the laser pulse length (tauout approximately 10 - 20 microseconds) is comparable with an effective relaxation time of the upper laser level (taurel approximately 15 - 30 microseconds). The time-history of the carbon-dioxide laser and pc signal pulses, and pc reflectivity have been thoroughly investigated for different cavity Q factors and specific electrical energy inputs. It has been shown, that the formation of the PC signal under the intracavity DFWM on gain (amplitude) and thermal (phase) gratings is characterized by a complicated time history that reflects the main relaxation processes taking place inside the inverted medium. A feature of the transient pc process inside the laser active medium is the dependence of the effective relaxation time of the upper laser level on the intensity of pumping waves. Pc reflectivity has been obtained by numerical calculations. A comparison of the theoretical and experimental data confirms the contribution of two different mechanisms of grating formation under DFWM inside the active medium of the carbon-dioxide laser.
Resonant Degenerate Four Wave Mixing, DFWM, is a nonlinear optical process arising from the third order susceptibility X(3). Resonance enhancement of X(3)in absorbing media makes the process useful for spectroscopic applications[1]. In many situations pulsed, high power lasers are used which have broad spectral bandwiths. The stochastic fluctuations of amplitude and phase associated with this bandwidth complicates the theoretical description in such cases. An averaging of the atom-field interaction is required simultaneously over the temporal and spatial variations of the fields. A solution has been found in the broad bandwidth limit which uses an appropriate decorrelation approximation. Theoretical and experimental results will be presented for the effects of laser bandwidth on the power dependence and temporal behaviour of resonant DFWM[2].