Effects of initial frequency chirp on the linear propagation characteristics of the exponential optical pulse

In this paper, the linear propagation characteristics of the exponential opticalpulse with initial linear and nonlinear frequency chirp are numerically studied in asingle mode fibre for be₂<0. It can be found that the temporal full width athalf maximum and time-bandwidth product of exponential pulse monotonically increasewith the increase of propagation distance and decrease with the increase of linearchirp C for C<0.5, go through an initial decreasing stage near zeta=1, thenincrease with the increase of propagation distance and linear chirp C forCgeq0.5. The broadening of pulses with negative chirp is faster than that withpositive chirp. The exponential pulse with linear chirp gradually evolves into anear-Gaussian pulse. The effect of nonlinear chirp on waveform of the pulse is muchgreater than that of linear chirp. The temporal waveform breaking of exponentialpulse with nonlinear chirp is first observed in linear propagation. Furthermore, theexpressions of the spectral width and time-bandwidth product of the exponentialoptical pulse with the frequency chirp are given by use of the numerical analysismethod.