The theoretical study of the propagation of a bell-shaped light pulse through a saturable absorber having excited-state absorption is presented. Assuming that the pulse-width is longer than the first excited-state lifetime of the absorber, a general expression for the steady-state transmission of the absorber is obtained. It is shown that when the excited-state absorption cross-section is larger than the ground-state absorption cross-section (reverse saturable absorber) the absorber acts as a power limiter. An explicit expression for the change of temporal pulse-width in a single transit through the absorber is obtained, which shows that the pulse-width increases due to the presence of excited-state absorption. An analytical expression is presented for the optimum pulse intensity at which the maximum pulse broadening occurs.
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