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Physical Review A

Nonlinear refractive index near points of zero absorption and in the dead zone

Harry Friedmann, A. D. Wilson‐Gordon

Published Nov 1, 1995• 9 citations
Publisher

Abstract

Cross focusing (defocusing), determined by the probe Kerr coefficient, which is defined as the derivative of the probe refractive index with respect to the pump intensity, is studied at points of probe nonabsorption and in the dead zone. Spatial control of the probe can be achieved not only by the probe Kerr coefficient itself but also by its strong variation with pump intensity at points of probe nonabsorption. This strong variation allows the pump beam to be used as a waveguide for the probe.

DOI
10.1103/physreva.52.4070

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The theoretical basis for electromagnetically-induced focusing (EIF), which is caused by spatial variations in the coupling laser strength in an electromagnetically-induced transparency (EIT) experiment, is studied in detail. Using a numerical model it is shown that radial changes in both absorption and refractive index are important in predicting the probe beam's propagation conditions. Detailed calculations of the focusing and defocusing during EIF under various conditions are presented and compared with appropriate experiments. Diffractionlike patterns are predicted for, and observed on, a probe beam after propagation through a smaller EIT aperture. \textcopyright{} 1996 The American Physical Society.

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Cross focusing (defocusing), determined by the probe Kerr coefficient, which is defined as the derivative of the probe refractive index with respect to the pump intensity, is studied at points of probe nonabsorption and in the dead zone. Spatial control of the probe can be achieved not only by the probe Kerr coefficient itself but also by its strong variation with pump intensity at points of probe nonabsorption. This strong variation allows the pump beam to be used as a waveguide for the probe.
We show that under suitable conditions, a weak nondegenerate probe may become spatially confined in a Doppler-broadened medium composed of two-level atoms due to the effect of a strong resonant copropagating pump beam. The induced spatial solitons result from the interplay of diffraction and induced focusing of the probe. Realistic conditions that include effects of probe absorption and pump reshaping on propagation are examined. In order to avoid absorption of the near-resonant probe, which would make the strong induced focusing unobservable, the unique properties of the dead zone are exploited.
We show that under suitable conditions, a weak nondegenerate probe may become spatially confined in a Doppler-broadened medium composed of two-level atoms due to the effect of a strong resonant copropagating pump beam. The induced spatial solitons result from the interplay of diffraction and induced focusing of the probe. Realistic conditions that include effects of probe absorption and pump reshaping on propagation are examined. In order to avoid absorption of the near-resonant probe, which would make the strong induced focusing unobservable, the unique properties of the dead zone are exploited.
In this paper, we theoretically and experimentally investigate the controllable nonlinear focusing of the weak laser beam on the basis of the induced nonlinear effects by another strong pump laser beam. When couple laser beams co-propagate in the Kerr medium, it is possible to change the refractive index by the pump beam, and the locally changing medium in turn modifies the weaker probe beam. Depending on cross-phase modulation theory, we obtain an exact analytical solution to the model under the approximate condition and qualitatively verify it in experiment. The results show that the weaker probe beam can be induced to focus at any position due to induced nonlinear effects from the stronger pump beam under certain conditions.
In this paper, we investigate the novel behavior of induced focusing in nonlinear metamaterials (MMs) through designing probe-pump configuration, where the coupled waves may simultaneously experience negative refractive index or positive refractive index, or one experiences positive refractive index and another experiences negative refractive index both analytically and numerically. It is shown that cross-phase modulation (XPM) in MM not only brings some new features to the behavior of induced focusing, but also makes it possible in the ordinary positive-index materials (OMs), where it is otherwise impossible. First, we reveal that weak probe beam can be focused by strong pump beam even when their centers are completely overlapping each other. Moreover, it is found that the separated distance between coupled waves has an optimal value, which results in the strongest focusing of probe beam. Finally, another most notable property is that a spatial induced focusing is found to occur for different combinations of the signs of refractive index decided by the probe and pump beams, respectively, implying that a spatial XPM in MMs can be used as a more powerful tool for controlling the inducing focusing, when compared with the corresponding case in OMs. Our findings demonstrate that MMs can provide us unique opportunities unattainable in OMs to manipulate the all-optical control of optical focusing behavior through the new physical mechanism of XPM.
The theory of probe beam amplification via degenerate optical wave mixing in a Kerr medium is presented. This theory includes consideration of the self-phase modulation, two-wave mixing, and multiwave mixing terms in the coupled-wave equations. Both analytical solutions, under the assumptions of a nondepleted pump beam and a transparent Kerr medium, and numerical solutions with these assumptions removed are presented. Our solutions show that under certain conditions, phase matching can be satisfied and a high probe beam gain is possible, even for a zero phase shift between the refractive index and the intensity gratings.
The theoretical basis for electromagnetically-induced focusing (EIF), which is caused by spatial variations in the coupling laser strength in an electromagnetically-induced transparency (EIT) experiment, is studied in detail. Using a numerical model it is shown that radial changes in both absorption and refractive index are important in predicting the probe beam's propagation conditions. Detailed calculations of the focusing and defocusing during EIF under various conditions are presented and compared with appropriate experiments. Diffractionlike patterns are predicted for, and observed on, a probe beam after propagation through a smaller EIT aperture. \textcopyright{} 1996 The American Physical Society.