Studies On Steering Of Optical Beams In Nonlocal Media And Properties Of Ultrashort Pulse Trains In Fibers

One of important purposes, which can be achieved by nonlinear optics, is that one optical beam can be steered by the other one or autoregulation of optical beam, optical spatial soliton is an efficient path to make it come true. All-optical devices, such as all-optical switching, all-optical logic element and optical interconnection device, are primary elements of future all-optical networks. In recent two decades, optical spatial soliton has been an attractive topic of research due to its potential applicability in all-optical control technique. In particular, in recent years, studies on optical spatial soliton are focused on properties of both its propagation in nonlocal nonlinear media and steering in media with optical lattices. The former holds important scientific sense because it involves quest for the propagation properties and the laws of optical spatial soliton. More important, the latter has important practical significance due to its potential application in all-optical control and all-optical information processing and its relation with dynamic properties of optical spatial soliton including switching effect and direction steering.Further, with the development of optical communication technique, there is an argent task to develop all-optical communications systems with high rates and high capacity. As a result, propagation of ultrashort pulse trains in fibers has been paid special attention. In theory, propagation of ultrashort pulse trains in fibers can be described by high-order nonlinear Schrodinger equation.The main contents are as follows:(1) Based on nonlocal nonlinear Schrodinger equation, an approximative analytic solution is presented to describe fundamental soliton in nonlocal medium with exponential response nonlinearity by employing variational approach. By comparing it with the exact solution under special condition and exact numerical solution, it is shown that this approximative analytic solution can well describe the behavior of fundamental soliton in a wide range of parameters, particularly, for a small energy flow. These results are very useful for investigating the properties of the fundamental mode in the media with nonlocal nonlinearity which is exponential response, for instance, properties of fundamental mode in nematic liquid crystal in the case when it exhibits such sort of nonlinearity under proper conditions can be more readily revealed with the aid of the approximative analytic solution than numerical method. In addition, based on nonlinear Schrodinger equation, an approximative analytic solution is presented to describe fundamental soliton in local medium with optical lattices by employing variational approach.(2) Based on (1+1) D and (1+2) D Snyder-Mitchell equations, we have presented corresponding explicit, analytic solution describing the propagation of an optical beam with initial phase-front curvature in strongly nonlocal media. Based on the solution, the propagation and the interaction of the optical beams with the initial phase-front curvature have been discussed in detail. The results have shown that, unlike the propagation of a beam without initial phase-front curvature, the initial phase-front curvature has a significant effect on the propagation of the beam, which results in pulsating behavior, the positive phase-front curvature makes the diffraction initially overcome the refraction and the beam initially expands, whereas the reverse occurs for the negative phase-front curvature. And their interaction can generate a periodic interference pattern, the pattern can vary with the alteration of the initial phase-front curvature, studies have shown that there exists the dependence of the space between nearest adjacent two fringes on the initial phase-front curvature and the initial separation between the centers of two beams. Also, by employing numerical method, we have shown that these properties are still valid to the nonlocal nonlinear Schrodinger equation provided that the characteristic length is much broader than the width of the optical beam. These properties can be used to determine the phase-front curvature by measuring the spacing between fringes. It is very useful for further understanding the properties of optical beams in strongly nonlocal media and may be applied to precision measurements.(3) Based on weakly nonlocal nonlinear Schrodinger equation, we investigate the soliton steering in weakly nonlocal nonlinear media with harmonic modulation of the refractive index by employing numerical method. These results have shown that the weak nonlocality originated from the nonlocal nonlinear response of medium induces a transverse modulation of the refractive index, which leads to the occurrence of interplay between the weak nonlocality-induced transverse modulation and the harmonic modulation. When nonlocal degree is small, the dynamics of soliton is governed by the harmonic modulation because the weak nonlocality-induced transverse modulation is much less than the harmonic modulation, whereas the reverse occurs for the large nonlocal degree. Further study revealed that there exists two key physical quantities: critical nonlocal degree and critical initial angle. When the beam is launched into the medium, the beam is trapped in the central lattice when nonlocal degree (initial angle) is smaller than its critical value, or else, the reverse occurs, i.e, the beam travels along the transverse direction. Thus, one can control the soliton steering in weakly nonlocal medium by employing the competition between the weak nonlocality parameter and the lattice depth. These results are of great importance for us to achieve more effective control of soliton, and can provide theoretical guidance for application studies on all-optical control and all-optical switching.(4) A generalized higher-order nonlinear Schrodinger equation with constant coefficients, describing the transmission of subpicosecond and femtosecond optical pulses in homogeneous fibers, is considered. Imposing generalized Hirota conditions on the coefficients, we obtain exact solutions for a soliton sitting on top of a continuous-wave (CW) background by means of the Darboux transform. In the general form, the same solution provides for an exact description of the development of the modulational instability of a CW state, initiated by an infinitesimal periodic perturbation and leading to formation of a periodic array of solitons with a residual CW background. To obtain a more practically relevant solution for a soliton array without the CW component, we subtract CW background from the exact solution, and use the result as an initial approximation, to generate solutions in direct simulations. As a result, if only the energy of pulse trains is medium, we can obtain robust pulse trains, which are stable against arbitrary perturbations, as well as against violations of the Hirota conditions. It is useful for raising the signal bit-rate and increasing the capacity in optical communications .