Lasers

Passive Q-switching

A Cr⁴⁺:YAG crystal absorbs 1064 nm light until enough of it arrives to bleach it. Put one inside a Nd:YAG laser and the cavity stays shut while the pump stores energy in the crystal; the first photons bleach the absorber, the cavity opens, and the stored energy leaves in one pulse a few nanoseconds long. Then the absorber recovers and it starts again.

What you are looking at

A curved high reflector, the Nd:YAG crystal, the Cr:YAG absorber and a 90% output coupler. A 5% pick-off and a neutral density filter send a little of each pulse to a fast photodiode; the power meter catches the rest.

How the bench is set up

Spherical mirror R = 500 mm, a 5 mm Nd:YAG crystal pumped with 10 W into a 0.3 mm spot, a Cr:YAG absorber passing 85% unbleached, a flat 90% output coupler 100 mm from the first mirror. Photodiode bandwidth 1 GHz into 50 Ω.

The theory

With the absorber shut the pump raises the inversion until the closed cavity reaches threshold. Measured against the open cavity’s threshold that inversion is

N_i = \frac{L_{\text{closed}}}{L_{\text{open}}},

the round-trip losses with the absorber unbleached and bleached. The pulse takes the inversion down to $N_f$ , given by Wagner and Lengyel:

N_i - N_f = \ln\frac{N_i}{N_f}.

Each unit of threshold inversion holds $(h\nu/\sigma)\,A/2$ of energy over a mode of area $A$ , so a pulse carries

E = \frac{h\nu}{\sigma}\,\frac{A}{2}\,(N_i - N_f) \times \text{the coupler’s share of the loss}.

None of that depends on the pump. The pump sets only how fast the inversion climbs back from $N_f$ to $N_i$ : in $\tau_2 \ln\frac{P - N_f}{P - N_i}$ , with $\tau_2$ the upper-state lifetime.

What to measure

Pulse energy set by the absorber, not the pump

Read the photodiode: pulses about 13 ns long, about 9.5 kHz apart. Select the crystal and the inspector lists the pulse energy, length, rate and peak power.
Divide the meter’s average power by the repetition rate (and by 0.95 for the pick-off): about 81 µJ a pulse.
Raise the pump to 15 W. The pulses come about 1.7 times as often and carry the same energy.
Lower the absorber’s transmission to 70%: fewer, shorter, stronger pulses. Raise it towards 95% and they weaken and lengthen.

What the model leaves out

The pulse is worked out with the switch already open. That holds when the absorber bleaches well before the gain saturates, which the lab checks; when it doesn’t, the inspector says the laser runs continuously.
Every pulse is identical: there is no jitter, no pulse-to-pulse noise and no transverse structure.

Things to try

Change the output coupler to 80%: fewer, stronger pulses, about 110 µJ each.
Swap the absorber for the semiconductor one. It recovers in a picosecond, too fast to hold the cavity shut, and the mode here is too large for it to saturate, so the laser runs continuously.

References

A. E. Siegman (1986), Lasers, University Science Books.
W. G. Wagner and B. A. Lengyel (1963), Evolution of the giant pulse in a laser, Journal of Applied Physics 34, 2040.
J. J. Degnan (1995), Optimization of passively Q-switched lasers, IEEE Journal of Quantum Electronics 31, 1890.

More experiments, and how the lab works, are in the laser lab’s overview.