Pulse distortion in single-mode fibers

A theory is presented of the propagation of Gaussian pulses in single-mode optical fibers by expanding the propagation constant in a Taylor series that includes the third derivative with respect to frequency. The light source is assumed to have a Gaussian spectral distribution whose width relative to the width of the Gaussian signal pulse is arbitrary. Formulas are derived for the spectrum of the ensemble average of the optical pulse, from which the shape of the average pulse itself is obtained by the fast Fourier transform. Also derived is an expression for the rms pulse width. The theory is applicable at all wavelengths including the vicinity of the zero first-order dispersion point.