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Journal of the Optical Society of America B

Observation and compensation of frequency detuning in high-reflectivity Brillouin enhanced four-wave mixing

John R. Ackerman, Paul S. Lebow

Published May 1, 1991• 8 citations
Publisher

Abstract

Details of the frequency relationships among interacting beams in Brillouin enhanced four-wave mixing (BEFWM) are examined. A new technique using two individually injection-seeded single-mode lasers allows for precise control and knowledge of the relative wavelengths of the interacting beams. This is compared with the standard frequency-shifting technique employing a single laser in conjunction with stimulated Brillouin scattering (SBS) frequency shifters. A continuously tunable frequency difference ranging over many gigahertz is achieved, resulting in a valuable tool for the investigation of nondegenerate four-wave mixing processes such as BEFWM. Two variations of BEFWM are studied: ωpump1 − ωpump2 = 0 with noncollinear pumps; and ωpump1 − ωpump2 = ωSBS with collinear pumping. Resonance spectra of BEFWM gain versus probe–pump frequency shift show a significant detuning in the frequency for the gain maximum from the expected Brillouin shift for the former case. When the probe–pump frequency is tuned in compensation for this detuning, improvements in BEFWM phase conjugation are realized in comparison with more conventional techniques using SBS frequency shifting.

DOI
10.1364/josab.8.001028

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IEEE Journal of Quantum Electronics•Jul 1, 1987•15 citations
Details of the frequency relationships among interacting beams in Brillouin enhanced four-wave mixing (BEFWM) are examined. A new technique using two individually injection-seeded single-mode lasers allows for precise control and knowledge of the relative wavelengths of the interacting beams. This is compared with the standard frequency-shifting technique employing a single laser in conjunction with stimulated Brillouin scattering (SBS) frequency shifters. A continuously tunable frequency difference ranging over many gigahertz is achieved, resulting in a valuable tool for the investigation of nondegenerate four-wave mixing processes such as BEFWM. Two variations of BEFWM are studied: ωpump1 − ωpump2 = 0 with noncollinear pumps; and ωpump1 − ωpump2 = ωSBS with collinear pumping. Resonance spectra of BEFWM gain versus probe–pump frequency shift show a significant detuning in the frequency for the gain maximum from the expected Brillouin shift for the former case. When the probe–pump frequency is tuned in compensation for this detuning, improvements in BEFWM phase conjugation are realized in comparison with more conventional techniques using SBS frequency shifting.
Brillouin enhanced four-wave mixing (BEFWM) is a judicious combination of SBS and FWM processes. Very high phase conjugate reflectivity (>106) has been reported. Various conditions have been presented that lead to these high reflectivities, but all those discussions are based on a single mode laser. Here we report the experimental results of BEFWM with a multimode laser. The laser mode spacing is 0.15 GHz, which is larger than the linewidth of the acoustic phonon (0.1 GHz), so we can neglect the gratings that are not resonant with the acoustic frequency. We observed that the phase conjugate reflectivity is smaller for the multimode pump. Assume there is no coupling between modes through BEFWM and each mode interacts with the nonlinear medium independently. It has been shown that the reflectivity will decrease as the input pump power decreases. Thus the reflectivity of a single mode pump is higher than the resultant reflectivity from a multimode pump. Further examination of the temporal profiles of the probe and phase conjugate pulses in the multimode case shows that the pulse modulation depth is decreased in the phase conjugate pulse.
It has previously been shown that Brillouin enhanced four-wave mixing can lead to large phase conjugate reflectivities for moderate laser powers.1,2 However, in the geometry considered by previous workers the pumps have equal frequency and hence the conjugate signal is shifted in frequency with respect to the probe. We have conducted an experimental and theoretical study of Brillouin-enhanced four-wave mixing for the different case in which the two pump waves differ in frequency by twice the Brillouin frequency of the four-wave mixing medium, and in which the probe wave frequency is halfway between those of the pump waves. In this case, the phase conjugate wave has the same frequency as the probe. Reflectivities > 100 % have been measured. Experimental results are compared to those of a theory that includes the effects of phase mismatch, pump depletion, and the finite response time of the medium.
The results of an experimental investigation of a new geometry for producing phase conjugation by Brillouin-enhanced four-wave mixing are presented. In this geometry, the four-wave mixing medium is carbon disulfide, and the backward-going pump wave is created from the transmitted forward-going pump wave by stimulated Brillouin scattering (SBS) in glycerol. The two pump waves are hence phase conjugates of each other, and the quality of the phase-conjugation process is not degraded even by the use of an aberrated pump wave. The probe wave is created by SBS in carbon disulfide, which has a Brillouin frequency half that of glycerol, and the conjugate wave is therefore generated at the same frequency as the probe. Since the pump and signal waves differ in frequency by the Brillouin frequency of the carbon disulfide four-wave mixing medium, high reflectivities (approximately 2000%) are obtained as a result of Brillouin resonance enhancement.
Brillouin enhanced four-wave mixing (BEFWM) is a judicious combination of SBS and FWM processes. In the traditional BEFWM experiments, two cells are used: one generates SBS, the other provides four-wave mixing. We demonstrated the generation of a phase conjugate signal by single cell BEFWM with focusing geometry. A single cell containing the optical nonlinear medium was used simultaneously for conventional SBS and FWM. Experiments were performed by using either CS2 or TiCl4 as the nonlinear medium; both have large Brillouin gain but differ greatly in their nonlinear indices of refraction. Thus the mechanism for four-wave mixing is shown to be Brillouin nonlinearity. In this experiment, the phase matching condition was satisfied and the frequency of the phase conjugate signal was not shifted from that of the master input beam. The operating regime of the experiment was far below the threshold of instability, which accounts for the low reflectivity that we observed. This single cell configuration is more compact and the optical alignment is easier than in the conventional BEFWM, in which two nonlinear cells are used.
An experimental and theoretical investigation of a polarization-decoupled form of Brillouin-enhanced four-wave mixing (BEFWM) is undertaken. Analytical steady-state solutions are found and numerical simulations of the transient regime including pump depletion are made. Experimental investigations of the BEFWM process were carried out in the liquids acetone and CS/sub 2/. Reflectivities, greater than unity, are readily observed. The variation of the transient reflectivity as a function of pump intensities and frequency detuning is studied. In the case of CS/sub 2/ it is shown that the Kerr effect makes a significant contribution to the interaction and numerical simulations, including Kerr effects, to produce good agreement with the experimental results.>
We present a theoretical treatment of four-wave mixing (FWM) in a Brillouin-active medium for the case in which the pump waves differ in frequency by approximately twice the Brillouin frequency shift of the medium and in which the probe-wave frequency is approximately the arithmetic mean of the frequencies of the two pump waves. Under these conditions, the conjugate wave produced by the FWM process has the desirable property of being at the same frequency as the probe. We derive the coupled amplitude equations describing this interaction. We solve these equations analytically in the limit of negligible pump depletion and find that large phase conjugate reflectivities are readily achievable. The coupled amplitude equations are solved numerically for the general case, and it is found that large power transfer from the pumps to the output wave is possible. The output wave is shown to be a nearly perfect phase conjugate of the probe wave, even far into the regime where pump depletion effects are important. Our formalism predicts the existence of a parametric instability in the propagation of the pump waves, but good performance is predicted before the onset of this instability.