By Irl N. Duling III
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Turn off the gain dispersion and the nonlinear effects and look for a selfconsistent pulse solution circulating in the loop. 27, a minimum width pulse occurs symmetrically in the negatively dispersive fiber. The position of the minimum width is arbitrary at this point. Define a(t) of the master equation as the pulse shape at the fiber cross-section where the pulse is of minimum width. Now turn on the various effects in the master equation separately. The gain dispersion is still approximated by an inverted parabola in the frequency domain.
When the gain medium shortens the pulse, there must be a mechanism that lengthens it, so as to balance the net pulse shortening action. This is now the dispersion. Positive /? and negative GVD broaden the pulse, just as negative [3 and positive GVD do. The existence of solutions does not guarantee stability of the solutions. One very simple stability criterion is the requirement that the gain be less than the loss before and after passage of the pulse. One may evaluate g and £ from the master equation.
8. The spectral width as function of dispersion, with the SPM coefficient as parameter. Short pulse generation 17 pulse if the chirp is large. This is the well known phenomenon of pulse shortening that occurs when a highly chirped pulse passes through a filter. The filter cuts off the wings that have large frequency deviation. When the gain medium shortens the pulse, there must be a mechanism that lengthens it, so as to balance the net pulse shortening action. This is now the dispersion. Positive /?