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IEEE Journal of Quantum Electronics

Polarization-decoupled Brillouin-enhanced four-wave mixing

W.A. Schroeder, Michael J. Damzen, M. H. R. Hutchinson

Published Mar 1, 1989• 19 citations
Publisher

Abstract

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.>

DOI
10.1109/3.18561

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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 the results of an experimental investigation of a polarization-decoupled Brillouin-enhanced four-wave mixing (BEFWM) configuration used for short-pulse high-resolution imaging. In this geometry, the four-wave mixing medium is carbon disulphide (CS2) and the counterpropagating pump is generated from the forward pump by stimulated Brillouin scattering in a second CS2 cell. This configuration produced a good quality, high resolution (∼9 μm) phase conjugate image of a United States Air Force test chart, correcting for aberrations in the system.
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.
The technique of polarization-decoupled Brillouin-enhanced four-wave mixing is known for its high-reflectivity, high-quality phase conjugation. The treatment accounts for the transverse structure of the pump and signal beams within a waveguide in the paraxial approximation, assuming a steady-state acoustic wave and assuming that many transverse modes of the waveguide are excited by the four mixing waves. The zeroth-order equations are obtained for the polarization states of the signal and conjugate beams by dropping all phase-mismatch terms. Under the stated assumptions, the phase-mismatched terms are found to make only a small contribution. A first-order solution accounts for phase-mismatch terms and determines the loss of conjugation fidelity as a function of the angular spread of the pump laser beam, the pump-signal angle, the pump intensities, and the pump mutual fidelity.>
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.
We report on an investigation of Brillouin-enhanced four-wave mixing which provides phase conjugate reflectivities greater than 104. Theoretical modeling shows that the phase conjugate intensity grows with time until limited by pump depletion, and the main effect of varying the signal power is to increase the time delay before the conjugate beam reaches peak intensity. This is confirmed experimentally, and the maximum peak reflectivity is limited by the length of the laser pulses used in the experiment.