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IEEE Journal of Quantum Electronics

Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing

Solomon M. Saltiel, B. Van Wonterghem, Tracy E. Dutton, J.A. Hutchinson, Peter M. Rentzepis

Published Jan 1, 1988• 8 citations
Publisher

Abstract

The authors present theoretical and experimental data which show that the value of the phase conjugate reflectivity of degenerate four-wave mixing depends on whether the retroreflection or counterpropagating schemes are used. It is also shown that the retroflection method may result in decay constants which are not related to the decay of the gratings formed in the nonlinear medium.>

DOI
10.1109/3.8574

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LARGE-SIGNAL RESULTS FOR DEGENERATE FOUR-WAVE MIXING AND PHASE CONJUGATE RESONATORS

Prc Zheu, Usa Visiting

A calculation procedure and various large-signal and numerical solutions are presented for degenerate four-wave mixing in optical Kerr media, and for phase conjugate resonators using degenerate four-wave mixing. The solutions presented take full account of nonlinear refractive index changes, pump depletion, signal saturation, distributed losses, and possible external mirrors with laser gain. We find that including the nonlinear index change generally causes little change in the reflectivity or power output of degenerate four-wave mixing devices, at least with symmetric pumping. The optimum power output from a phase conjugate resonator with and without a laser gain medium is calculated. The results provide some theoretical guidance for designing phase conjugate resonators. PACS Code 42. 65. Bp; 42. 60. Da

Journal of Tianjin University Science and Technology•Jan 1, 1982•0 citations
The authors present theoretical and experimental data which show that the value of the phase conjugate reflectivity of degenerate four-wave mixing depends on whether the retroreflection or counterpropagating schemes are used. It is also shown that the retroflection method may result in decay constants which are not related to the decay of the gratings formed in the nonlinear medium.>
The phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.
Four wave mixing, a third-order optical parametric process, is the nonlinear optical process in which four waves interact with each other through the third-order optical nonlinearity. In this process, three waves form a nonlinear polarization at the frequency of the fourth wave. An important application of degenerate four wave mixing is the generation of phase conjugate wave or simply the phase conjugation. The phase conjugate wave has the same wavefront as the incident wave; however, it propagates backward. The phase conjugation is equivalent to the time reversal. Straightforward application of the time reversal is the correction of phase aberration. Suppose that, the incident wave propagates in the nonuniform medium, such as a laser amplifier, where the temperature is fluctuated by intense pumping. Then, the incident wave suffers severe phase aberration during the propagation and the transmitted wave is then reflected by the phase conjugate mirror and goes back into the same nonuniform medium.
We present a model to describe degenerate four-wave mixing in critical binary liquid mixtures and we analyze it through an experimental study of phase conjugation in critical microemulsions. The two concentration gratings related to the four-wave-mixing configuration give contributions to the conjugated signal which can be separated from their different formation and relaxation times. The model quantitatively describes the amplitude and the dynamics of the gratings and thus of the conjugate signal when one approaches the critical point. The theoretical predictions fit very well with the experimental data. Close to the critical point a 10% reflectivity has been obtained in this medium using a beam power of 1 W from a cw Ar+{\mathrm{Ar}}^{+}Ar+ laser. The limitations of these reflectivities at higher powers are discussed.
We have derived the polarization dependent coupling constants for transmission and reflection gratings in degenerate four-wave mixing, measured phase-conjugate signals for various polarization conditions, and determined the relative contribution of the two gratings to the signal. The results obtained with cryptocyanine dissolved in methanol as the nonlinear medium show that the signal from transmission grating is 1.53–2.14 times larger than that from a reflection grating depending on the angle between the wave vectors of the forward pump beam and the probe beam.
Current experimental studies of degenerate four-wave mixing in saturable absorbers1,2 have shown that the dependence of the reflectivity on the pump intensity exhibits a double maxima. This phenomenon can arise from the fact that the medium approximates a set of four-level quantum systems. We have carried out a detailed analysis of the nonlinear processes of degenerate four-wave mixing in a four-level system. Because resonant saturable absorbers are being considered for systems applications, e.g., optical phase conjugation and wide FOV filters, the results presented are relevant to various optical phase conjugation devices. There are two distinct regimes which are of interest. The first case is when the intramolecular relaxation is very weak or absent. The second is when the intramolecular relaxation is strong. For the weak case the medium behaves like a set of two distinct dipole radiation sources which can generate interference effects.
A calculation procedure and various large-signal and numerical solutions are presented for degenerate four-wave mixing in optical Kerr media, and for phase conjugate resonators using degenerate four-wave mixing. The solutions presented take full account of nonlinear refractive index changes, pump depletion, signal saturation, distributed losses, and possible external mirrors with laser gain. We find that including the nonlinear index change generally causes little change in the reflectivity or power output of degenerate four-wave mixing devices, at least with symmetric pumping. The optimum power output from a phase conjugate resonator with and without a laser gain medium is calculated. The results provide some theoretical guidance for designing phase conjugate resonators. PACS Code 42. 65. Bp; 42. 60. Da