The nonlinear Schrodinger equation with variable coefficients is analyzed by means of projection matrix method. An exact analytical solution is obtained, which clearly shows how the variable fiber dispersion, nonlinear, and loss coefficients affect the propagation of ultrashort optical pulses. The obtained solution is used to analyze the propagation properties of ultrashort pulses in dispersion-decreasing fibers. It is found that the ultrashort pulse can realize stable soliton transmission if the fiber dispersions have some certain profiles related to the fiber loss and nonlinear properties. A small variation in the dispersion has a similar perturbative effect to an amplification or loss. The exponentially dispersion-decreasing fiber is studied exemplificatively to demonstrate the obtained results.
We report on a theoretical analysis of a channel dielectric waveguide consisting of periodically interlaced negative refractive index medium and positive index medium. The dispersion relation for TM modes is obtained. The properties of guided wave modes have been numerically disclosed. It is shown that the waveguide can exhibit negative group velocity dispersion as well as extraordinarily large group velocity dispersion. The Poynting vector within the waveguide can change both sign and magnitude. The distribution of energy flux density of different sections relates to the frequency and the width of the channel waveguide.