Optical limiting for microsecond pulses

We present a dynamical theory of nonlinear absorption and propagation of laser pulses with duration in the microsecond time domain. The general theory is applied to fullerene C-60 because of its good optical limiting properties, namely, a rather low ground state absorption and a strong triplet-triplet absorption. It is shown that sequential absorption involving strong triplet-triplet transitions is the major mechanism of nonlinear absorption. The intrinsic hierarchy of time scales makes an adiabatic solution of the coupled rate equations valid, which therefore can be reduced to a single dynamical equation for the ground state population. The slow evolution of this population is defined by an effective rate of population transfer to the triplet state and by the pulse duration. The propagation effect plays an important role in the optical power limiting performance. The intensity of the field as well as the population of the triplet state decreases during the pulse propagation, and a weakened nonlinear sequential two-photon absorption is followed by a linear one-photon absorption which gradually becomes the dominating process. The competition between these qualitatively different processes depends on the field intensity, the length of the absorber, and the concentration. The pulse propagation is studied by solving numerically the two-dimensional paraxial field equation together with the effective rate equation for the ground state population.