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Acta Physica Sinica

Nonlinear focusing of weak beam by another high power laser

Lin Feng, Chao Tan, Yuan Zhou, Xiquan Fu

Published Jan 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.62.144208

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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.
We have shown previously that two strong laser beams (with the same frequency) counterpropagating in a Kerr nonlinear medium with linear dispersion become un stable when their intensities exceed a certain threshold.1 We demonstrate here that the system exhibits large (theoretically unlimited) amplification of a probe beam when the two pumping beams have their intensities slightly below the threshold. This is in contrast to the conventional phase conjugation due to four-wave mixing in a nondispersive Kerr nonlinear medium. The mechanism of amplification in our system can be explained in terms of positive distributed feedback from the Kerr nonlinear index grating formed by two strong pumping laser beams in the presence of dispersion giving rise to a light-induced distributed-feedback resonator. This feedback is attributed to the fact that the weak beams with both signal frequency, ω + δ, and conjugate frequency, ω − δ, propagate with phase speed different (due to dispersion) from that of a pumping wave with frequency ω, which triggers the exponentially increasing energy exchange between weak and strong beams at the nonlinear index grating (this energy exchange is prohibited in nondispersive media). When the probe frequency approaches a frequency of one of the longitudinal modes of the light-induced distributed resonator, and the pumping intensity approaches the threshold of instability, the resonant amplification increases infinitely; for presently available laser intensity stabilities, amplification as large as 104 is feasible.
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.
In a highly nonlinear thin film, the presence of the diffracted beams from the pump-probe-beam-induced refractive-index grating modifies considerably the energy coupling between the pump and the probe beams. Using coupled amplitude and phase equations, the roles of various factors such as phases and phase shifts, phase modulations, pump-beam intensity, intensity ratio, interaction length, and losses in the medium in the multiwave-mixing processes are clearly identified. We also present experimental results on the dependence of the probe gain on the pump-probe-beam ratio, the pump intensity, and on the interaction length, using a nematic liquid-crystal film as the nonlinear medium.