Abstract
We formulate moment equations that quantify the soliton self-frequency shift in amplifying fibers. Soliton evolution is quantified in terms of energy, chirp, duration, delay, and central frequency and as a function of fiber properties of gain, dispersion, and nonlinearity and their wavelength-dependence. Results from the moment equations agree closely with results obtained from the nonlinear Schrodinger equation but without heavy computational resources requirements. Moment equations also have the great advantage of explicitly revealing the optimal initial pulse chirp that is required to induce maximum soliton self-frequency shift and energy conversion efficiency. The formulation is a simple and precise tool of utmost interest for the design of wavelength converters and supercontinuum sources based on soliton self-frequency shift.
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