Investigation On Nonlinear Optical Effects Of Weak Light In Coherent Atomic Media

Since the invention of laser, the study of nonlinear optics has attracted extensive attention and acquired very wide applications. The study in this aspect has deepened the understanding of the interaction between light and matter, and extended largely the research domain of traditional optics. By using nonlinear optical effects one can obtain new coherent light sources and find solutions of many problems in optical physics and optical techniques. Furthermore, the microscopic structures and dynamics of matter can be explored deeply by applying nonlinear optical effects and laser techniques. In addition, nonlinear optics have also very important applications in the study of quantum computation and quantum information. The rich and beautiful nonlinear phenomena appeared in processes of the interaction between light and matter are one of the important aspects in nonlinear physics. In a long term, in order to obtain a stronger nonlinear optical effect, the main topic in nonlinear optics has been the off-resonant interaction between strong laser and media, called high-field nonlinear optics.In the early development time of nonlinear optics, it was recognized that a significant nonlinear optical effect could be obtained under a weak input light intensity, if the input light field is resonant with the medium under consideration. However, it has been thought for a long time that it is not realistic to get a strong nonlinear optical effect by using the resonance between light and a medium because the medium has a very strong absorption at resonance. In recent years, a breakthrough occurred by the finding and the deep research of electromagnetically induced transparency (EIT), which can result in strong nonlinear optical effects under weak light condition (i. e. nonlinear optics at weak light level). The so-called EIT is a quantum interference effect induced by an applied control laser field, by which the absorption of a probe field can be largely suppressed. In addition, EIT can results in a significant enhancement of nonlinear optics susceptibilities, the large change of dispersion property, which result in strong nonlinear optical effect and the reduction of probe-field group velocity. Although in the recent decade there have been many nice research works on the study of the light pulse propagation in EIT systems, most of them have been focused on the linear optical properties. The possibility of ultraslow optical solitons in EIT systems has been proposed in recent years, but the studies on the instantaneous optical response property, the generation mechanism of the ultraslow solitons and soliton trains, multi-component temporal and spatial optical solitons, and how to realize highly-efficient four-wave mixing, etc are still lacking or not in depth, and some physical problems and relevant theory deserve to be explored further.In this dissertation, we have explored nonlinear effects of weak light in coherent atomic media deeply, using the multiple-scales method combined with numerical simulations developed in resonant nonlinear optics by our research group recently. We firstly have studied the generation of ultraslow optical solitons and soliton trains by modulational instability in EIT medium; Then we have presented the instantaneous nonlinear optical response properties in EIT medium; The condition of formation and propagation properties of temporal and spatial solitons have been also discussed; Finally we have proposed a scheme to realize a highly efficient four-wave mixing (FWM) by means of EIT properties of multi-level atoms. Our works included the following aspects:1. The exist of ultraslow optical solitons in EIT system has been predicted theoretically. In such resonant system, optical solitons would have great potential application in optical information processing and engineering, because of stable propagation and low power. However, the produce of such optical soliton experimentally and theoretically was unsolved. So we studied the generation of solitons and train of soliton waves by the modulational instability of probe fields in a three-state A-type EIT medium. Starting from original Maxwell-Schr(o|¨)dinger equations (MSE), we obtained nonlinear Schr(o|¨)dinger equation (NLSE) describing the envelope of probe field by by multiple-scales method. The numerical simulation showed that the modulational instability domain of motion equation for the atomic state amplitudes and probe field were determined by the coefficients of NLSE. So the plane wave could be modulated into soliton trains or single solitons. We have compared these numerical results of original MSE with those obtained from NLSE in detail. In addition, we have demonstrated that under experimental parameters, the generations of single soliton or a couple of solitons could be realized by injecting the initial probe field, obtained from the analytic results of asymptotic theory. These results might provide a guidance that would be useful for experimental generation of ultraslow optical solitons.2. Because of the large Kerr nonlinearity enhancement, EIT-based systems have potential applications in optical apparatus of low power, such as optical switching. Therefore, instantaneous optical response properties would deserve to be explored further. We have studied the transient linear and nonlinear optical properties of a atomic system with an EIT configuration. Applying multi-scales method in the equations of density matrix that described response of atoms to probe and signal fields in four-level N-type system, we have calculated the transient linear and nonlinear susceptibilities of probe fields, by taking account of the depletion of ground state. We have also presented the expressions for transient nonlinear susceptibilities stemmed from self-phase modulation and cross-phase modulation. It showed that, in contrast to previous results of the amplitude equation under undepleted ground-state approximation, the contribute of depleted ground state to nonlinear susceptibility was so important that it would not be ignored. We believed that our theory could be generalized to study the instantaneous optical response properties of other multi-level atomic systems.3. There have been several works appeared already that studied single-component optical solitons. However, two-component solitions in EIT-based systems was also of particular interest, which have not been discussed in a single species of atoms. We have investigated the conditions for formation of temporal and spatial two-component solitons, and their propagation properties. Initiated from MSE, the coupled Ginzberg-Landau equations (GLE) were obtained by multiple-scales method. The EIT effect resulted in the imaginary parts of coefficients in these GLE less than the corresponding real parts. Therefore, we could deduce the GLE to coupled nonlinear Schr(o|¨)dinger equations. The formations and propagation properties of single-component, two-component temporal and spatial solitons were discussed, respectively. It was shown that generation of such optical solitons just required very low power. Their robust propagation and collision property have been confirmed by numerical simulation.4. The significant enhancement of Kerr nonlinear susceptibility in EIT-related media motivated many promising applications, of which multi-wave mixing was considerably interesting. We have proposed a scheme to obtain a highly efficient FWM in a coherent six-level tripod system, and generate coherent short-wavelength radiation. We have demonstrated that the absorption of pump field could be suppressed by using a double-dark resonance and multi-photon destructive interference. In addition, a pump wave and an internally generated FWM wave mediated by EIT propagating with matched ultraslow group velocities could result in longer time of interaction, and hence a significant enhancement of FWM conversion efficiency was realized. We have shown both analytically and numerically that the FWM process and an energy transfer from the pump wave to the FWM wave.The research of nonlinear effect related to EIT, not only advances the basic theory of nonlinear optics in coherent medium, but also have a potential application in the nonlinear optical apparatus and optical information processing and transmission at a low light level.