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Physical Review Letters

Phase Conjugation of Weak Continuous-Wave Optical Signals

Mary Yvonne Lanzerotti, Robert W. Schirmer, Alexander L. Gaeta, G. S. Agarwal

Published Sep 9, 1996• 6 citations
Publisher

Abstract

We demonstrate phase conjugation and aberration correction of femtowatt signals using nearly degenerate four-wave mixing in an atomic vapor. Our theoretical and experimental results are in qualitative agreement and show that the conditions under which the minimum signal can be phase conjugated are similar to the conditions under which the phase-conjugate mirror can be operated near its quantum-noise limit.

DOI
10.1103/physrevlett.77.2202

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We demonstrate phase conjugation and aberration correction of femtowatt signals using nearly degenerate four-wave mixing in an atomic vapor. Our theoretical and experimental results are in qualitative agreement and show that the conditions under which the minimum signal can be phase conjugated are similar to the conditions under which the phase-conjugate mirror can be operated near its quantum-noise limit.
We present the results of a comprehensive investigation of the quantum-noise properties of a continuous-wave phase-conjugate mirror (PCM) formed using backward-four-wave mixing in potassium vapor. We characterize the quantum-noise properties of the PCM as functions of the vapor density, pump detuning from resonance, and relative frequency detuning of the signal beam from the probe beam. We compare the noise measurements of the PCM with the predicted noise of an ideal quantum-noise-limited PCM and determine the value of the minimum signal that can be used to perform phase conjugation with unity signal-to-noise ratio. For the range of vapor densities studied, we find that the PCM operates nearest the quantum-noise limit and that the value of the minimum signal is lowest under conditions in which the reflectivity is maximized. These results demonstrate that it is possible to perform phase conjugation with signals as weak as 14 fW with near-unity reflectivity. Our measurements are in qualitative agreement with the predictions of a quantum theory of phase conjugation via nearly degenerate four-wave mixing in a two-level system.
Summary form only given. We use a high-reflectivity phase-conjugate mirror (PCM) to demonstrate that optical phase conjugation can be performed on continuous-wave signal beams having power spectral densities as low as 5 x 10/sup -18/ W/Hz (i.e., 19 photons/sec.Hz). Our high-reflectivity (>600%), wide-bandwidth (90 MHz) PCM is formed by performing four-wave mixing in a potassium vapor cell using a frequency-stabilized Ti:sapphire laser that is tuned near the D/sub 2/ line. We have measured the noise spectra of the conjugate beam as functions of pump detuning from resonance, probe-pump detuning, pump-probe angular separation, and the number density of potassium atoms.
We have measured the conjugation fidelity produced by four-wave mixing in sodium vapor using weak probe beams that were aberrated by simulated atmospheric turbulence. Near-diffraction-limited (1.3 times the diffraction limit) return beams were obtained for both moderate (D/r(0) approximately 10) and strong (D/r(0) approximately 25) simulated turbulence, down to probe-beam pulse energies of 200 pJ. We believe this to be the first systematic study of conjugation fidelity as a function of probe energy.
Phase conjugation (PC) of extremely weak signals using a phase-conjugate mirror based on Mandelstam-Brillouin-enhanced four-wave mixing, coupled with an optical quantum amplifier, is considered. PC of a pulse with energy 4*10/sup -17/ J is achieved. PC conditions for amplified superluminescence noise of the optical quantum amplifier are specified and the limiting parameters are estimated. It is shown experimentally that if the signal-to-noise ratio (S/N) is equal to unity, the energy of an input signal for which phase conjugation is possible corresponds to 30 photons per transverse mode.>
We present a brief review of optical phase conjugation by four-wave mixing in atomic vapors. We emphasize the particular properties of vapors for this process. We discuss the case of nearly resonant excitation for two-level atoms, the case of multilevel atoms where the nonlinearity arises from optical pumping and the nearly resonant two-photon excitation. We finally describe the modification of phase-conjugate signals when one goes from the Bragg regime to the Raman-Nath regime and we show how one can achieve a phase-contrast mirror rather than a phase-conjugate mirror in this last case.
A quantum theory of nearly degenerate backward four-wave mixing in a two-level atomic system is developed. The theory is used to calculate the quantum noise produced by a phase-conjugate mirror based on this system. The results indicate that in the case of pure radiative broadening the ideal quantum-noise limit is reached for relatively small pump-wave strengths and for relatively large probe-pump and pump-resonance detunings, so that the phase-conjugate reflectivity is far from its maximum value. Conversely, in the collisionally broadened case, operation closest to the quantum-noise limit occurs near the point of maximum reflectivity.