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Journal of the Optical Society of America A

Reduction of Rayleigh scattering in nonlinear optical phase conjugations by photo-induced density redistribution in atomic vapors

Mitsuhiro Yokota, Pochi Yeh

Published Oct 1, 1998• 1 citation
Publisher

Abstract

We investigate the reduction of Rayleigh scattering in four-wave mixing due to photo-induced spatial redistribution of atoms in atomic vapors. The Rayleigh scattering from the pump beams in optical phase conjugation is a major source of noise, which affects the fidelity of the phase-conjugated image. In the blue-shifted operation, the atoms are driven toward the low-intensity regions of the standing-wave pattern, leading to a reduction of Rayleigh scattering. We also investigate the effect of saturation on the differential scattering cross section.

DOI
10.1364/josaa.15.002678

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We investigate the reduction of Rayleigh scattering in four-wave mixing due to photo-induced spatial redistribution of atoms in atomic vapors. The Rayleigh scattering from the pump beams in optical phase conjugation is a major source of noise, which affects the fidelity of the phase-conjugated image. In the blue-shifted operation, the atoms are driven toward the low-intensity regions of the standing-wave pattern, leading to a reduction of Rayleigh scattering. We also investigate the effect of saturation on the differential scattering cross section.
Investigates the noise due to Rayleigh scattering and its reduction via the spatial redistribution of atoms due to the standing wave pattern of the pump beams. For operation near the resonance, the interaction of the induced atomic dipole with the optical field leads to a periodic potential for the atoms due to the interference standing wave pattern. An assumption of the Boltzmann distribution yields a periodic distribution of the number density of atoms. In the paper, we investigate the effect of detuning and saturation on the noise due to Rayleigh scattering and address the issue of signal to noise ratio in nonlinear optical phase conjugation. We also investigate the minimum incident intensity needed to achieve a signal to noise ratio of one (S/N=1).
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.
A model is formulated to investigate quantitatively how near-resonant degenerate four-wave mixing (DFWM) in a vapor of homogeneously broadened two-state atoms is affected by radiation scattered from the pump beams. The spectral intensity distribution of the scattered radiation in the interaction volume is obtained by solving the equation of radiative transfer and a detailed treatment of the modification this fluctuating field causes on the optical dipole induced by the coherent laser fields is presented. For a broad parameter regime, this modification can be expressed via a single quantity that incorporates the energy of the fluctuating field together with bandwidths and frequency offsets from the atomic resonance. Numerical solutions are given which show that the scattered field causes the DFWM reflectivity to be depressed by a signficant amount, depending most strongly on a characteristic transverse length of the interaction volume. Approximate analytic expressions for the reflectivity are also given which assist in physically understanding the underlying mechanisms.
Spatial discrete control of the light field has long been regarded as a fascinating and prominent area in optics. Here, we propose two distinct approaches to spatially manipulate the four-wave mixing (FWM) signal by introducing a one-dimensional standing wave into its nonlinear generation and linear propagation dynamics. The FWM is generated by two pump fields and one reference field in an atomic vapor. First, we encode the standing-wave pattern into one pump field and successfully transfer its periodic distribution to the FWM signal. The spatially distributed pump field can modulate the third-order nonlinearity in a discrete manner and induce an equivalent nonlinear amplitude grating, which discretely diffracts the generated FWM signal within a rather wide frequency tuning range. In addition, we also established a linear refractive index grating with the assistance of electromagnetically induced transparency (EIT) by employing the same standing wave to modulate the Gaussian FWM signal in a cascaded atomic configuration. Owing to the instantaneously adjustable EIT condition, we have both theoretically and experimentally demonstrated the sensitive inversion on the bright and dark fringes of the discretized FWM signal by inverting the sign of the two-photon detuning. This work opens opportunities for engineering nonlinear optical effects through optically induced reconfigurable gratings.
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.
We develop a semiclassical theory of the polarization properties of phase conjugation by two-photon resonant degenerate four-wave mixing. The theory includes the effects of saturation by the pump waves. We solve the density-matrix equations of motion in steady state for a nonlinear medium consisting of stationary atoms with a ground and excited state connected by two-photon transitions. As an illustration of the general results, we consider an S0{S}_{0}S0​\ensuremath{\rightarrow}S0{S}_{0}S0​ two-photon transition, which is known to lead to perfect polarization conjugation in the limit of third-order theory. We show that the fidelity of the polarization-conjugation process is degraded for excessively large pump intensities. The degradation can occur both due to transfer of population to the excited state and due to nonresonant Stark shifts. Theoretical results are compared to those of a recent experiment [Malcuit, Gauthier, and Boyd, Opt. Lett. 13, 663 (1988)].