The generation of picosecond pulses in passively mode-locked solid-state lasers II Pulse compression and broadening†

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Abstract
This is the second in a series of papers analysing the generation of picosecond pulses in passively mode-locked solid-state lasers. The growth of intensity fluctuations inside the cavity and the corresponding development of a train of output pulses are carefully considered. This paper is particularly concerned with the problem of pulse compression and broadening. The wave-like character of radiation inside n laser easily is first considered ; it is then shown that the radiation intensity function I = I(t, x) can be mathematically represented by a wave growing or decaying with distance. Simple mathematical expressions arc derived for a gradual change of such properties of the wave as its slope and curvature at a given point. The concept of width of a radiation peak is then introduced and its variation on passage through a non-linear medium, such as a saturable absorber, is carefully analysed. Pulse compression in ring and conventional cavities is discussed, including the effect of excited state absorption, both discrete and uniformly distributed components being considered ; the effect of radiation overlapping, typical of conventional cavities, is also analysed. The results of these investigations are then applied to two specific systems, namely Nd : YAG and Nd ; glass lasers. The concept of pulse broadening is then introduced and discussed in some detail, bearing in mind its two main causes : variation in the spectral composition of radiation duo to a natural mode selection process and optical dispersion, the latter becoming significant at very high output levels when the frequency spectrum can be substantially broadened by non-linear effects (self-modulation of phase). Some ‘empirical ’ expressions are then suggested for the pulse broadening at the end of the linear stage of operation and for the combined pulse broadening and compression at the point, of maximum laser output. It is shown that the overall effect is invariable that of net pulse broadening, pulse compression merely counteracting pulse broadening to some extent during the non-linear stage of operation, pulse broadening due to optical dispersion is then briefly discussed, its damaging effect on the generation of very short pulses being emphasized. The paper ends with a discussion of the design parameters required for the generation of picosecond pulses.