RESUMEN
An investigation is made of the formation of a single soliton, or a pair of solitons, from initially nontransform limited pulses in a nonlinear Kerr medium having anomalous dispersion. A qualitative physical explanation is given for the formation of soliton pairs. Approximate solutions for the amplitudes and the velocities of the generated solitons are established and corroborated by numerical solutions of the Zakharov-Shabat eigenvalue problem.
RESUMEN
It is shown that solitons emerging from pulses launched with frequencies at, or close to, the zero-dispersion point in a single-mode optical fiber are ordinary bright solitons corresponding to the nonlinear Schrödinger equation. These solitons are inherently frequency shifted into the anomalous-dispersion regime, where the third-order dispersion acts as a small perturbation. We therefore conclude that an optical-soliton-based communication system should be designed with the carrier frequency in the anomalous-dispersion regime but not too close to the zero-dispersion point, where the formation of an unwanted dispersive-wave component would degrade the system performance.
RESUMEN
A simple approximate analytical expression is derived for the intensity-modulation index in a phase-shift-keying coherent optical transmission system, accounting for both group-velocity dispersion and higher-order dispersion. This provides an analytical generalization of previously presented numerical results obtained in the limits of pure group-velocity dispersion and higher-order dispersion, respectively. The subsequently derived maximum transmission distance for 50% intensity modulation is found to be long at the zero-dispersion wavelength. However, for high modulation frequencies, the maximum transmission distance decreases rapidly when the wavelength deviates from the zero-dispersion wavelength. Comparisons with previously obtained numerical solutions show good agreement.
RESUMEN
The dynamics that result from the combined effects of spatial diffraction, nonlinearity, and a parabolic graded index for wave propagation in optical fibers are presented. An approximate analytical solution of the nonlinear Schrödinger equation in a graded-index fiber is obtained by using a variational approach. Particular emphasis is put on the variation of both the pulse width and the longitudinal phase delay with the distance of propagation along the fiber.
RESUMEN
The classical problem of determining the solitons generated from symmetric real initial conditions in the nonlinear Schrödinger equation is revisited. The corresponding Zakharov-Shabat scattering problem is solved for real and symmetric double-humped rectangular initial pulse forms. It is found that such real symmetric pulses may generate eigenvalues with nonzero real parts corresponding to separating soliton pulse pairs. Moreover, it is found that the classical formula relating the number of eigenvalues to the area of the pulse is not always correct.