Analysis of Temporal Pulse Development in Passively Mode-Locked Lasers

Pulse-shortening and pulse broadening effects in passively mode-locked lasers are analysed. A steady-state pulse duration limit is calculated and compared with round-trip simulations. The numerical calculations apply to a picosecond N d : glass laser. Methods of short-pulse generation are discussed. PACS: 42.55R, 42.60D, 42.65 In passively mode-locked pulsed lasers the statistical spontaneous emission bursts have a duration approximately equal to the inverse of the fluorescence linewidth. In the linear laser phase (constant dye absorption) the finite spectral gain profile of the active medium narrows the spectral width and broadens the duration of the circulating spikes. In the nonlinear laser phase (nonlinear dye transmission, mode-locking region) the most intense spike is preferentially amplified and strong background discrimination is achieved. Pulse shortening occurs in the saturable absorber cell. (For reviews on mode-locking see [1-7].) The natural mode selection in the active medium acts against the shortening. Intensity dependent loss mechanisms like two-photon absorption in N d : glass rods [8] broaden the pulse duration at high laser intensities [9]. In this paper we analyse the pulse shortening and pulse broadening effects in passively mode-locked lasers. Intensity-dependent stationary pulse durations are found by equating pulse shortening and pulse broadening per round-trip in the laser oscillator. In the mode-locking region the transient temporal development of a picosecond pulse with constant background level is simulated and the approach to the stationary situation is studied. The theory presented applies to all passively modelocked lasers, either pulsed or continuously working [10]. The numerical calculations in this paper apply to a passively mode-locked N d : glass laser. The calculations reveal conditions for optimum shortpulse generation in the oscillator. Preliminary measurements with a Pockels cell intensity limiter in the resonator led to pulse shortening in agreement with the theory. 1. Stationary Pulse Durations The changes of pulse duration per round-trip in the oscillator are analysed. Pulses are broadened by the finite spectral width of the gain and by intensity dependent nonlinear losses. Here pulse broadening by two-photon absorption in N d : glass rods is discussed. Pulse shortening occurs in the nonlinear transmission region of the saturable absorber. The pulse duration ratio f$ = AtL0/AtLb where AtL0 is the pulse duration after n +1 round-trips and AtLi the pulse duration after n round-trips, is given by ^ = ^GAIN^TPA^DYE • (1) j 8 G A I N is the ratio of pulse broadening by the finite spectral width of the gain profile. / J X P A represents the ratio of pulse broadening by two-photon absorption in the active medium. / J D Y E is the pulse shortening ratio of the saturable dye. The spectral gain profile of the active medium approximately has the form [9] 0 ( v v o ) = G(v)/G(v o) (2) i i i 1111 1 — i — i i 11111 ® Table 1. Parameters used in calculations