By Irl N. Duling III
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Extra resources for Compact Sources of Ultrashort Pulses
32) with the constraints ^ ( f ) 0 (1-33) If the gain medium relaxes slowly compared with one round-trip time JTR, as is the case for solid state lasers, g can be considered fixed at the level determined by the saturation formula S=^ V (1-35) where W is the energy in the pulse, and Pg is the saturation power of the gain. One may use this equation to obtain the pulse energy by noting that, roughly, the loss £ is equal to the gain g. 35) with this result and obtain two equations for the pulse width and the chirp parameter.
This is the state an experimenter would want to realize for the generation of chirp-free pulses. 99) Next we introduce the third order dispersion as a perturbation and suppose that its most important effect is to introduce an additional chirp of time dependent phase >(/), and a time shift ST. 100) gives a phase that is a superposition of t and tanh(//r); the phase is antisymmetric, as opposed to the symmetric phase versus time produced by second order dispersion. The equation does not give a value for ST; 6T simply changes the chirp.
First of all, in modelocked systems with very short pulses in which the optical Kerr effect is strong and compensated by negative dispersion as described above, the saturable absorber action and the gain bandwidth limitation can be considered as perturbations on the soliton of the nonlinear Schrodinger equation. Since this perturbation theory has been worked on extensively, useful analytic approaches are made available. Second, the breakthrough in modelocking techniques that led to the recent renaissance of modelocking and to new records of short pulse generation was initiated by Mollenauer and Stolen's 'soliton' laser which requires an understanding of soliton behavior.