Mode-Locking and Ultrashort Laser Pulses

We now concentrate on the time dependence of laser oscillation in a cavity whose gain curve encompasses a large number of axial modes. Each axial mode amplitude will oscillate with a time dependence of the form exp[ift) (t — x/c) + I0J, with circular frequency 

We now consider what happens when all of the axial modes are forced to oscillate at the same phase, say f Q. For simplicity, we assume that 2k + 1) modes oscillate with identical amplitude Eq, and that the equally spaced mode frequencies run from (o = coq — k Aco to co = coq + k Aco, with Aco = 2nAv = nc/E = 2tc/T The total oscillation amplitude then simplifies into 

This function is periodic, with period T equal to the cavity round-trip time (Fig. 9.16) it corresponds physically to the fact that one light pulse is propagating back and forth inside the cavity at all times. Since part of this pulse is transmitted outside the cavity everytime it strikes the output coupler reflector, the laser output consists of a train of pulses equally spaced in time by T The zeros in E(r) on either side of the primary pulse peaks are separated by the duration 2T/ 2k + 1), which gives an upper bound estimate cf the laser pulse width Tp. For a 1-m optical path length cavity, the round-trip time T is 2Ejc = 6.67 ns. If 9 axial modes are forced to oscillate in phase with equal 

Mode-locking does not occur spontaneously in a simple laser cavity. Either it must be actively driven by a cavity element which introduces cavity losses with a period of exactly T/2 (i.e., one-half the optical round-trip time), or it must be 

Drexhage, in Dye Lasers, Springer-Verlag Topics in Applied Physics, Vol. 1, Dye Lasers, F. P. Schafer (Ed.), Springer-Verlag, Berlin, 1973. 

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