Studies On Transmission Of Optical Pulses And Optical Waves In Inhomogeneous Fibers And Waveguides

The transmission of optical pulses in fibers has been an attractive topic of research because of their important applications to optical communication in past decades.Recently,with the progress of optical communication,and the appearance of dispersion management and the comprehensive management of dispersion,nonlinearity and gain/loss,the transmission of optical pulses in inhomogenenous fibers has been obtained the particular attentions.The transmission of optical pulses in inhomogeneous fibers can be described by the generalized nonlinear Schr(o|¨)dinger equation with variable coefficients.Otherwise,because it may provide an effective means for all-optical circuits and control,spatial soliton has also attracted more interest.In the dissertation,based on the generalized nonlinear Schr(o|¨)dinger equation with variable coefficients,the generalized higher-order nonlinear Schr(o|¨)dinger equation with variable coefficients,the nonlinear wave equation governing the transmission of optical waves in the inhomogeneous parabolic-index waveguides,and the nonlinear wave equation describing the transmission of azimuthally polarized nonparaxial optical waves in Kerr media,by analytical and numerical methods,we in detail discuss the transmission of chirped dark(gray) solitons in inhomogeneous fibers, generation,compression and transmission of pulse trains under higher-order effects,nonlinear tunneling of optical similaritons in inhomogeneous waveguides,nonparaxial ring solitary waves in Kerr media.Here,the results obtained and the methods used may be helpful to provide some theoretical analysis for studying the stable transmission of optical pulses in real optical soliton control systems or inhomogeneous fiber systems,and studying all-optical switches and logic.The main contents are as follows: (1) Based on the nonlinear Schr(o|¨)dinger equation with variable coefficients,governing the transmission of picosecond optical pulses in inhomogeneous fibers,and by using direct transformation of variables and functions,the explicit chirped dark(gray) soliton solutions are presented.By employing the exact solutions,we in detail analyze the propagation characteristics of the chirped dark(gray) soliton,including the stability against either the deviation from integrable condition or the initial perturbation,and the interaction between the chirped dark(gray) solitons. Because we use a super-Gaussian pulse as a background wave in our numerical simulation,it is necessary to analyze the propagation of finite-width super-Gaussian background waves and chirped dark(gray) solitons superimposed upon finite-width background waves.The results show that the dark(gray) solitons can be effectively compressed by choosing the appropriate initial chirp.And the chirped dark(gray) pulses are stable against the deviation from integrable condition,as well as the initial perturbation. The super-Gaussian background waves can stably propagate in inhomogeneous fibers,even though chirped dark(gray) solitons are superimposed upon them.When the ratio of the width of the background wave to the initial width of chirped dark(gray) soliton is large enough,the numerical solutions of chirped dark(gray) solitons can be in agreement with the exact solutions.Even if the width of background waves is not enough broad,chirped dark(gray) pulses can also maintain their soliton characteristics.These results can provide some theoretical analysis for experimental verification.(2) A generalized higher-order nonlinear Schr(o|¨)dinger equation with variable coefficients,describing the transmission of subpicosecond and femtosecond optical pulses in inhomogeneous fibers,is considered.Imposing generalized Hirota conditions on the variable 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 it 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 large enough,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.(3) The nonlinear wave equation,governing the transmission of optical waves in the inhomogeneous parabolic-index waveguide,is considered.By using the direct transformation of variables and functions,we present the exact general bright and dark spatial self-similar solutions.As an application, we discuss the nonlinear tunneling of optical similaritons and their interactions.The results show that under integrable condition,the optical waves can similarliy pass through the nonlinear barrier or well.And the interaction between the neighboring waves is elastic collision in certain distance.Under nonintegrable condition,when they pass through the nonlinear barrier,the optical waves can be effectively compressed for the relatively small value of height parameter of nonlinear barrier.However, when the parameter is large enough,the wave splits into some filaments. These results may be helpful to provide some theoretical analysis for studying all-optical switches and logic.(4) Finally,the nonlinear wave equation,which is obtained directly from the Maxwell equations,describing the transmission of azimuthally polarized nonparaxial optical waves in Kerr media,is considered.By numerical method, we present a set of nonparaxial solitary wave solutions.Then using these results as initial approximations,by the conservation law and finite-difference methods,we discuss the propagation of the nonparaxial dark and ring solitary waves.The results show that these methods can effectively simulate the stable propagation of nonparaxial dark solitary waves.But by these methods,the nonparaxial ring solitary waves only stably propagate in finite distance,then they become unstable.