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Physical Review A

Phase conjugation using the surface nonlinearity of a dense potassium vapor

Jeffery J. Maki, William V. Davis, Robert W. Boyd, John E. Sipe

Published Dec 1, 1992• 30 citations
Publisher

Abstract

We observe optical phase conjugation using the surface nonlinearity of a dense atomic potassium vapor. For an atomic number density of 1.5\ifmmode\times\else\texttimes\fi{}${10}^{17}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, phase-conjugate reflectivities of 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ are measured for pump intensities approaching the saturation intensity of 10 W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. We also demonstrate aberration correction using surface phase conjugation. The measured properties of the surface-phase-conjugate signal are in excellent agreement with the predictions of a theory of surface phase conjugation by degenerate four-wave mixing, in which the origin of the nonlinear response is saturated absorption.

DOI
10.1103/physreva.46.7155

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We observe optical phase conjugation using the surface nonlinearity of a dense atomic potassium vapor. For an atomic number density of 1.5\ifmmode\times\else\texttimes\fi{}1017{10}^{17}1017 cm\ensuremath−3{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}cm\ensuremath−3, phase-conjugate reflectivities of 4\ifmmode\times\else\texttimes\fi{}10\ensuremath−5{10}^{\mathrm{\ensuremath{-}}5}10\ensuremath−5 are measured for pump intensities approaching the saturation intensity of 10 W cm\ensuremath−2{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}cm\ensuremath−2. We also demonstrate aberration correction using surface phase conjugation. The measured properties of the surface-phase-conjugate signal are in excellent agreement with the predictions of a theory of surface phase conjugation by degenerate four-wave mixing, in which the origin of the nonlinear response is saturated absorption.
It is often desirable that a phase conjugate mirror be able to correct for polarization distortions in addition to correcting for wavefront aberrations. Such a device is called a vector phase conjugate mirror. It has been predicted within the context of the third-order theory that vector phase conjugation can be achieved by degenerate four-wave mixing using atomic two-photon transitions between S-states.1 We recently developed a theory of the polarization properties of two-photon resonantly enhanced degenerate four-wave mixing which can treat saturation effects due to pump waves.2 Our results show that for the case of linear and parallel pump wave polarizations, vector phase conjugation occurs with high quality and high reflectivity for two-photon transitions for which the nonresonant Stark shift is very small. We have also found that for the case of circular and counterrotating pump wave polarizations, perfect vector phase conjugation occurs for equal pump wave intensities. We have studied experimentally the effects of saturation and Stark shifts for S → S two-photon transitions of atomic sodium. We have found that high fidelity vector phase conjugation can be obtained.
In atomic vapors, the variation of the phase-conjugate reflectivity versus frequency has been a subject of interest these recent years. At low incident intensity for the pump and probe waves, a Lorentzian curve centered at the atomic resonance frequency is observed. At high pump intensity a splitting is observed, and the phase-conjugate reflectivity tends toward zero at the atomic resonance frequency.1 A correct treatment for this complex situation has been derived recently by Bloch and Ducloy.2 However, their theory leads to intricate calculations for which it is difficult to find physical interpretations. A great simplification is obtained by using the dressed-atom approach. The calculations are easier to derive and lead to clear physical interpretations. New results are predicted, some of them have already been observed experimentally.
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 report on a high-reflectivity (up to 670%) wide-bandwidth (up to 230 MHz) phase-conjugate mirror formed using backward-four-wave mixing with continuous-wave pump beams in a 2-mm potassium vapor cell. The reflectivities and bandwidths are significantly larger than have been measured previously, and the bandwidth is ten times greater than is predicted theoretically. The reflectivity-bandwidth product is more than an order of magnitude improvement over those previously achieved with other continuous-wave phase-conjugate systems.
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.