Laser mode locking using saturable absorbers

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Abstract
A theoretical model for mode locking induced by saturable absorbers is presented, employing an unidirectional ring laser cavity. Both the gain and loss media are assumed to be homogeneously broadened two-level systems, on-resonance with the radiation field. The loss of the cavity is treated as discrete and is supposed to occur at an equivalent mirror. Laser coupled equations are then derived, employing the density matrix formalism together with Maxwell's equations, using the rotating wave and slowly varying envelope approximations. Time-invariant solutions of the coupled equations are deduced exactly and mode-locking regions are predicted by a perturbation method. It is found that a suitable absorber can produce mode locking if the laser parameters are appropriately chosen. Generation of the steady-state pulses (SSP) by the finite-difference method shows that relatively short intense pulses can be obtained from a mode-locked laser. In addition, the theoretical model is extended to account for the possibility that the absorbing medium may be less easily saturated than the gain medium and/or the phase coherence times of the two media are very different. It is pointed out that our model can be a good approximation to a real laser system under certain circumstances. It can also be used as a guide in the search for a suitable absorber for particular laser systems.

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