A closed form method for the measurement of attenuation in nonlinearly dispersive media

A closed form solution of the equation describing the spectrum of a Gaussian pulse propagating in a medium with nonlinear frequency dependence of attenuation is presented. This solution suggests that in general the spectrum remains Gaussian, subject only to center frequency downshift and bandwidth reduction. The possibility of experimentally determining the two nonlinear material parameters from the measurement of the center frequency downshift and the reduced bandwidth is proposed.