Variational analysis of optimal pulse widths in dispersive nonlinear fibers

Summary form only given. For the transmission of a transform-limited pulse over a distance z in a nonlinear dispersive fiber, the rms pulsewidth /spl sigma/(z) grows linearly with z/L/sub d/ when L/sub d//spl Lt/L/sub n/ (linear limit) and linearly with z//spl radic/L/sub d/L/sub n/ when L/sub d/>L/sub n/ (strong nonlinearity), where L/sub d/ and L/sub n/ are the dispersion and nonlinear lengths, respectively. For a given z in the linear limit, there is an optimum input rms width /spl sigma//sub o/ to minimize /spl alpha/(z). In this case /spl sigma//sub o,opt/ is a function of z and the corresponding minimum output /spl sigma//sub min/ then grows as the square-root rather than linearly with z. The purpose of this paper is to show that there is still an optimum o, in the nonlinear case, but that /spl sigma//sub o,opt/ and /spl sigma//sub min/ grow linearly with /spl radic/|/spl beta//sub 2/|/L/sub n/ z, where /spl beta//sub 2/ is the second order dispersion coefficient. The /spl radic/z dependence of /spl sigma//sub min/ in the linear case is nonrealizable since as z becomes large, /spl sigma//sub o,opt/ increases and hence L/sub d/=2/spl sigma//sub o//sup 2//|/spl beta//sub 2/| also increases. Thus, regardless of how small the input power, ultimately the nonlinear length will become smaller than the dispersion length, and nonlinearities will prevail.