LAUSR

We present an analytical treatment of ultra-short pulses propagating in an optical fiber in the strong nonlinearity regime, in which the interaction between self-phase modulation (SPM) and group-velocity dispersion (GVD) substantially broadens the input spectrum. Supported by excellent agreement with the simulation results, these analytical solutions provide a convenient and reasonable accurate estimation of the peak position of the outermost spectral lobes as well as the full width at half maximum of the broadened spectrum. We show that our unified solutions are valid for either Gaussian pulse or hyperbolic secant pulse propagating inside an optical fiber with positive or negative GVD. Our findings shed light on the optimization of SPM-enabled spectral broadening in various applications.