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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Phase Conjugation In The Forward Direction With Thin Na Vapor Cells

C. V. Heer, N. C. Griffen

Published Nov 13, 1980• 1 citation

Abstract

During the study of focusing and phase conjugation of photon echoes it became apparent that similar effects occur for either simultaneous pulses or continuous laser radiation. These effects are apparent in the simple two level atom theory in which the stimulated electric dipole is proportional for steady state to [EQUATION] where the electric field amplitude E = A eiφ + B . A(x,z) and φ(x,z) are the amplitude and phase of the signal wave and B is the amplitude of a plane carrier wave. The phase conjugate wave A e-1φ is generated by the A2 + B2 + 2 AB cosφ term in the denominator. Phase conjugation is limited to physically thin cells and a 1 mm Na cell limits the angular spread to ± 20 milliradians. Current experiments with a 2 mm thick Na cell will be discussed. For two laser beams at angle θ, radiation at the phase conjugate -θ, and at higher angles ± 2θ, ±3θ, etc. are observed. Limited phase conjugation such as focusing of a curved wavefront has been observed. More extensive phase conjugation results will be reported.

DOI: 10.1117/12.957781

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Kei Hagiwara, Atsushi Okamoto, Hiroyuki Kaneko +2 more

With progress in phase conjugate optics, studies on forward four-wave mixing have been actively carried out. From the practical optical system design point of view, it is important to understand the angular dependence of phase conjugate intensity when pumping beams with limited spot size are used, especially with beam separation taken into consideration. In this paper, the angular dependence of phase conjugate intensity distribution is theoretically analyzed for the first time, in forward four-wave mixing when an optical Kerr medium is used. First, the phase conjugate intensity is calculated for a nonlinear medium thinner than the overlapping region of two pumping beams, where the intensity is relatively low. The results are used to calculate the output angle of the phase conjugate beam against the z-axis and the azimuth angle in the x-y plane. Then, a similar analysis is conducted for a medium sufficiently thick to cover the interaction region of two pumping beams. The differences between the above two cases are described and comparison with plane-wave pumping is made. Finally, the effects of spot size and curvature variation with Gaussian beam pumping on conjugate beam intensity are discussed for the case of a thick medium. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 2, 80(4): 67–75, 1997

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During the study of focusing and phase conjugation of photon echoes it became apparent that similar effects occur for either simultaneous pulses or continuous laser radiation. These effects are apparent in the simple two level atom theory in which the stimulated electric dipole is proportional for steady state to [EQUATION] where the electric field amplitude E = A eiφ + B . A(x,z) and φ(x,z) are the amplitude and phase of the signal wave and B is the amplitude of a plane carrier wave. The phase conjugate wave A e-1φ is generated by the A2 + B2 + 2 AB cosφ term in the denominator. Phase conjugation is limited to physically thin cells and a 1 mm Na cell limits the angular spread to ± 20 milliradians. Current experiments with a 2 mm thick Na cell will be discussed. For two laser beams at angle θ, radiation at the phase conjugate -θ, and at higher angles ± 2θ, ±3θ, etc. are observed. Limited phase conjugation such as focusing of a curved wavefront has been observed. More extensive phase conjugation results will be reported.

Various aspects of optical phase conjugation are discussed: the properties of the conjugate wave, its potential applications, the basic conjugation methods, and a brief history of the question. The theory for phase conjugation in stimulated scattering is set forth in detail. The basic experimental results on this conjugation method are also discussed in detail. Phase conjugation occurs because that configuration of the back-scattered field which has the conjugate wavefront is amplified to the greatest extent (at a doubled gain) in the intense speckle-inhomogeneous conjugate wave in a medium in which stimulated scattering occurs. Because of the large overall amplification in stimulated scattering, all the other, uncorrelated, configurations of the spontaneously scattered nucleating waves are amplified by a factor of 107 less and are discriminated against. The intervals of values of the various parameters in which the conjugate configuration (the specklon) exists are discussed theoretically, as is the effect of nonlinear selection and saturation on phase conjugation in stimulated scattering. There is a review of experimental results on the first observation of the effect, on the measurement of the angular structure of the uncorrelated waves and of the extent to which they are discriminated against, on the phase fluctuations of the conjugate wave, on the conjugation of subthreshold and depolarized radiation, and on phase conjugation in stimulated scattering in focused beams and for other scattered-wave amplification mechanisms.

We have used a two-wave mixing gain process in sodium vapor to construct a self-pumped phase conjugator. This was done by forming a resonator around a quartz sodium cell equipped with Brewster angle windows. A pump beam is then directed into the sodium cell at a small angle to the longitudinal axis of the resonator. At sufficiently high cw pump intensities, the ac-Stark effect pro- vides sufficient gain to achieve oscillation. Although this gain is unidirectional it occurs on the wings of the sodium resonance so that the backward traveling optical field in the resonator does not experience loss due to sodium absorption. The counterpropagating optical fields in the resonator interact with the pump in an internal four- wave mixing process to produce a fourth optical field (phase conjugate to the pump field). Our experiment was conducted at the sodium D2 resonance. The pump laser was a 699 autoscan single frequency ring dye laser providing pump intensities up to several hundred watts per square centimeter.

With progress in phase conjugate optics, studies on forward four-wave mixing have been actively carried out. From the practical optical system design point of view, it is important to understand the angular dependence of phase conjugate intensity when pumping beams with limited spot size are used, especially with beam separation taken into consideration. In this paper, the angular dependence of phase conjugate intensity distribution is theoretically analyzed for the first time, in forward four-wave mixing when an optical Kerr medium is used. First, the phase conjugate intensity is calculated for a nonlinear medium thinner than the overlapping region of two pumping beams, where the intensity is relatively low. The results are used to calculate the output angle of the phase conjugate beam against the z-axis and the azimuth angle in the x-y plane. Then, a similar analysis is conducted for a medium sufficiently thick to cover the interaction region of two pumping beams. The differences between the above two cases are described and comparison with plane-wave pumping is made. Finally, the effects of spot size and curvature variation with Gaussian beam pumping on conjugate beam intensity are discussed for the case of a thick medium. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 2, 80(4): 67–75, 1997