Regenerative amplifier

A regenerative amplifier (regen) is a stable optical cavity containing a gain medium, a thin-film polarizer and a Pockels cell. A seed pulse, usually picked from a mode-locked oscillator, enters through the polarizer; the Pockels cell is then switched to its quarter-wave state so that the pulse is trapped and makes many round trips, gaining energy on each pass through the pumped crystal. When the pulse energy nears saturation, the cell switches again and the pulse leaves through the polarizer. A typical Ti:sapphire regen, pumped by a 15–25 mJ Q-switched green laser at 1 kHz, amplifies 1 nJ seed pulses to about 5 mJ before compression, a gain of about 67 dB, in some 15–25 round trips.

Round trips and gain

If each round trip multiplies the pulse energy by a net factor $g$ (gain times cavity losses), the number of round trips needed to reach a total gain $G$ is

$$N = \frac{\ln G}{\ln g}.$$

For $G = 5\ \text{mJ}/1\ \text{nJ} = 5\times10^6$ and $g = 2.5$ per round trip (net single-pass gain about 1.58), $N \approx 17$. A 1.5 m linear cavity has a round-trip time of

$$t_\text{rt} = \frac{2L}{c} \approx 10\ \text{ns},$$

so the pulse spends about 170 ns inside, and the Pockels cell must switch between states in less than 10 ns to avoid clipping the pulse on entry or exit. This estimate uses small-signal gain throughout; in practice the last few round trips run into gain saturation, which lowers $g$ and adds round trips but also stabilizes the output energy against seed fluctuations. The build-up is monitored with a fast photodiode behind a cavity mirror, which shows a train of pulses growing round trip by round trip; the dump is timed a round trip or so after the peak.

Why a stretcher is needed

A 5 mJ pulse of 100 fs duration with a Gaussian shape has a peak power of about 47 GW, far more than a centimetre-long crystal can carry without self-focusing and a large nonlinear phase (B-integral). Regens for femtosecond pulses therefore operate inside a chirped-pulse amplification system: the seed is stretched to around 200 ps, which brings the intracavity peak power down to about 23 MW, and a pulse compressor after the regen restores the short duration. Grating compressors transmit roughly 60–75%, so the 5 mJ becomes about 3–4 mJ at 25–50 fs.

Typical systems

Ti:sapphire regens dominate for 800 nm femtosecond work; ytterbium crystal and thin-disk regens run at higher average power and repetition rate with durations of a few hundred femtoseconds, and picosecond regens based on Nd-doped crystals seed high-energy multipass amplifiers. At 1 kHz from an 80 MHz oscillator, the pulse picker selects one pulse in 80 000.

Regens and multipass amplifiers

A multipass amplifier sends the pulse through the crystal a fixed number of times along geometrically separate paths, with no switch. A regen reaches higher total gain because the number of passes is limited only by timing, and its output mode is the cavity's TEM₀₀ mode regardless of seed alignment. Its drawbacks are the long material path, which adds dispersion that the compressor must remove, and the Pockels cell's limited contrast.

Pitfalls

Leakage through the polarizer and imperfect Pockels-cell switching produce pre- and post-pulses spaced by the round-trip time, at a level set by the polarizer and Pockels-cell extinction; these matter in high-field experiments and are cleaned with an extra Pockels cell outside the regen. Between pulses, the cavity also amplifies spontaneous emission, which forms a nanosecond pedestal of amplified spontaneous emission if the seed is weak or mistimed. Gain narrowing, the preferential amplification of the spectral centre, reduces the bandwidth over the many passes and lengthens the compressed pulse. At high repetition rates, where the inversion does not fully recover between pulses, the output energy can alternate from pulse to pulse (period doubling); the operating point is chosen to avoid this regime.

Common questions

What is the difference between a regenerative amplifier and cavity dumping?

Both use a fast switch to release energy from a cavity. Cavity dumping extracts a pulse that formed in the laser itself, whereas a regen amplifies an external seed, so the output carries the seed's pulse duration, spectrum and timing. A regen with no seed behaves as a cavity-dumped Q-switched laser.

Why do regenerative amplifiers run at kHz rates?

The gain crystal must store enough energy between pulses to supply millijoules, which requires pump pulses of several to tens of millijoules; pump lasers with that energy run at 1–10 kHz. The Pockels cell high-voltage driver and the thermal load on the crystal also set limits.

How is the seed injected?

The seed enters through the polarizer or through a Faraday isolator arrangement, and the Pockels cell is triggered while the chosen seed pulse is inside the cavity, synchronized to the oscillator's pulse train.

References: Siegman, Lasers (University Science Books, 1986); D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985); Saleh & Teich, Fundamentals of Photonics 3rd ed. (Wiley, 2019).