Influence of saturable-absorber transmission and optical pumping on the reproducibility of passive mode locking

Following the Letokhov model for passive mode locking, which describes the buildup of ultrashort light pulses from noise, the statistical behavior of passive mode locking and the discrimination characteristics of the nonlinear absorber are examined. The probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</tex> of having a second ultrashort pulse of a certain intensity within the resonator round-trip time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2tL</tex> is described. This probability is essentially a function of the initial dye absorption coefficient x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> and a pumping parameter t <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> that is a measure for the excitation rate of the optical pump. Experimental results are reported that confirm these theoretical considerations.