Passive mode-locking

A Nd:YVO₄ crystal beside a flat high reflector, a lens that focuses the mode near the far end, a semiconductor saturable absorber and a 95% output coupler. A second lens collimates the output, a pick-off sends a little of the train through an ND filter to a fast photodiode, and an autocorrelator measures the pulses.

853 mm between the mirrors, a 3 mm Nd:YVO₄ crystal pumped with 15 W, a 50 mm lens 53 mm from the output coupler, and an absorber passing 99% unbleached that recovers in a picosecond. A second 50 mm lens collimates the output. Photodiode bandwidth 1 GHz.

The pulse returns to the coupler once per round trip, so the train repeats at the free spectral range,

with $L$ the optical length (the crystal counts $n$ times its length). Haus’s master equation holds the pulse in shape: each round trip the gain line narrows the pulse’s spectrum and so stretches it, while the absorber, saturating, trims its weak wings. The two balance in a $\mathrm{sech}^2$ pulse. With a weakly saturated absorber of depth $q_0$, a gain $g$ on a line of half-width $\Omega_g$, intracavity pulse energy $W$ and absorber saturation power $P_A$,

The lab solves the saturated case exactly. An intensity autocorrelator cannot see the pulse directly; it reports the width of its autocorrelation, 1.543 times the pulse for $\mathrm{sech}^2$.

1. Read the photodiode: a train of spikes about 5.7 ns apart, 175 MHz. The detector is too slow to resolve each pulse, so each spike has the photodiode’s own shape.
2. Work out c/2L from the mirror spacing plus (n − 1) × 3 mm for the crystal, n = 2.17.
3. Read the autocorrelator: about 16 ps, so the pulses last about 10 ps.
4. Raise the absorber’s transmission to 99.5%, halving its depth: the pulses lengthen to about 14 ps.

• Move the high reflector and the crystal 40 mm to the left: the rate drops to c/2L, about 167 MHz, and the pulses barely change.
• Lower the pump to 4 W: the inspector warns that the pulse is too weak to keep the train steady (Q-switched mode-locking).
• Swap the absorber for Cr:YAG, which recovers in microseconds: the laser Q-switches instead.