Multilevel Maxwell–Bloch-equation description of ultrashort laser pulse amplification in inhomogeneously broadened XeCl media

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Abstract
Coherent amplification of short-pulse XeCl lasers is studied theoretically by using multilevel Maxwell—Bloch equations in which the vibrational—rotational structures of a XeCl gain spectrum are included. The model used considers 100 transitions each in the P and R branches for six different vibrational transitions of XeCl(B,v = 0) → XeCl(X,v′ = 0−5). Coherence components between sublevels in the B and X states are also properly calculated. The model can successfully predict coherent effects such as a quantum beat caused by the spectrum overlap of the several vibrational—rotational transitions involved in a short-pulse laser spectrum. During amplification, laser pulses experience some nonlinear effects caused by the complex gain spectrum structure and by the coherent interactions; thus a considerable change in the laser pulse shape and a substantial reduction in the duration of the amplified laser pulse are predicted. The Frantz—Nodvik equation in the rate-equation limit and even single-level Maxwell—Bloch equations are not applicable for short-pulse propagation analyses in inhomogeneously broadened gain media.