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Applied Physics Letters

High-reflectivity, wide-bandwidth optical phase conjugation via four-wave mixing in potassium vapor

Mary Yvonne Lanzerotti, Robert W. Schirmer, Alexander L. Gaeta

Published Aug 26, 1996• 24 citations
Publisher

Abstract

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.

DOI
10.1063/1.117410

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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.
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 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. Previously, we have used four-wave mixing via coherent population trapping to achieve optical phase conjugation (OPC) with high gain, using two dye lasers and a sodium vapor cell. The /spl Lambda/ transition used involved the two hyperfine ground states and one excited state, so that two different optical frequencies were needed to satisfy the two-photon resonant condition between the probe and one of the pump beams. Later, we demonstrated in rubidium that a single hyperfine transition with Zeeman sublevels is enough to achieve OPC with equally high gain, thus eliminating the need for high-frequency sideband generation. However, in order to guarantee that the diffraction from the grating is primarily dispersive, the backward pump beam had to be detuned by about 60 MHz from the probe and the forward pump. One of the key disadvantages of such a nondegenerate scheme is that applications such as phase-conjugate mirrors are hard to implement. Here, we report the observation of optical phase conjugation in rubidium with equally high gain, but all the frequencies are degenerate.
Phase conjugation is an nonlinear effect that results from the four-wave-mixing process. This peculiar effect, in analogy to a mirror, reflects an incident beam in a way that the reflection constitutes the time-reversal of the original beam. By combining the phase conjugate mirror with ordinary mirrors, a special resonator, called phase conjugate resonator (PCR), is constructed. The phase conjugate resonator has been used in a wide range of applications, including phase aberration correction, image transmission, holography, and phase sensing using interferometers. Here, we explore theoretically the properties of phase conjugate mirror by investigating its action upon a variety of quantum states. In addition, we analyze the input-output relations of a phase conjugate resonator. Experimental results are reported that faithfully verify PCR's enhanced stability as compared to normal resonators. Furthermore, we observe a linewidth narrowing effect that is only present in the phase conjugate resonator.
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 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, 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.
The work reported here demonstrates for the first time degenerate four wave mixing (DFWM) phase conjugation in cesium (Cs) atomic vapor. The strong, spectrally narrow transition of cesium at 852 nm gives conjugate reflectivities up to 154% with low pump beam powers. Temperature tuning of the DFWM response over a 30 GHz bandwidth is also demonstrated. An improved experimental design to determine the DFWM angular response shows a field-of-view of 20 mrad at the half response points. Self-focusing effects are observed to be similar to those in sodium vapor with an onset of increased conjugate divergence for reflectivities greater than about 25%.