Propagation of rectangular and Gaussian pulses in a self-focusing optical fiber.

Using analytical expressions for the impulse response of a self-focusing optical fiber, the pulse responses to rectangular and Gaussian input pulses are calculated in two cases where (1) all the possible propagating modes and (2) only the modes with no azimuthal variations are equally excited. The refractive index distribution of the fiber is described by the second- and the fourth-order terms of the radial distance. The effects of the index profile and of the width of the input pulse on the shape and the rms width of the output pulse are clarified. The pulse response of the fiber with the optimized alpha-type index profile is also examined.