Saturable absorber

A saturable absorber is a material or device that absorbs strongly at low intensity and becomes more transparent at high intensity, because the light depletes the ground-state population faster than it recovers. In a laser cavity this lowers the loss for intense pulses relative to continuous light, so the laser pulses without an electrically driven modulator. It is characterized by four numbers: the saturation fluence (10–100 μJ/cm² for a typical semiconductor saturable absorber mirror), the modulation depth (the saturable part of the loss, often around 1% in bulk solid-state lasers), the nonsaturable loss, and the recovery time (from about 100 fs to microseconds, depending on the material).

Fast absorber model. When the absorber recovers faster than the pulse changes, absorption follows the instantaneous intensity:

$$\alpha (I)=\frac{{\alpha }_0}{1+I\mathrm{/}{I}_{\text{sat}}}+{\alpha }_{\text{ns}},$$

where ${\alpha }_0$ is the saturable (low-intensity) absorption, $I_{\text{sat}}$ the saturation intensity, and ${\alpha }_{\text{ns}}$ the nonsaturable absorption that remains at high intensity.

Slow absorber model. Most real absorbers recover more slowly than a femtosecond or picosecond pulse, so they respond to the pulse fluence $F$. For a thin absorber with small-signal saturable loss $q_0$ and saturation fluence $F_{\text{sat}}$, the loss seen by the pulse is

$$q(S)=q_0\frac{1-e^{-S}}{S},S=\frac{F}{F_{\text{sat}}}\mathrm{.}$$

Worked example. A 10 nJ intracavity pulse on a SESAM spot of 50 μm radius (area $7.85\times {10}^{-5}$ cm²) has fluence 127 μJ/cm². With $F_{\text{sat}}=50$ μJ/cm², $S=2.5$ and the pulse sees $0.36q_0$: for 1% modulation depth, 0.36% saturable loss instead of 1%.

Materials.

For crystals the saturation fluence is $h\nu \mathrm{/}{\sigma }_{\text{gs}}$, set by the ground-state absorption cross-section. With ${\sigma }_{\text{gs}}\approx 4.3\times {10}^{-18}$ cm² for Cr⁴⁺:YAG at 1064 nm, $h\nu \mathrm{/}{\sigma }_{\text{gs}}\approx 0.04$ J/cm².

SESAMs. The SESAM is the workhorse of mode-locked Nd- and Yb-doped solid-state lasers and many fiber lasers; Ti:sapphire lasers mostly rely on Kerr-lens mode locking instead. A SESAM consists of a semiconductor quantum-well absorber on top of a high-reflectivity DBR mirror, all on a substrate. The design trades modulation depth, saturation fluence, recovery time, and damage threshold against one another; the absorber position in the standing-wave field and a top coating tune the effective saturation fluence. The RSAM adds a resonant cavity to the structure, trading bandwidth for larger modulation depth and lower saturation fluence.

Artificial saturable absorbers. Intensity-dependent nonlinear effects can produce the same loss modulation without an absorbing material:

These rely on the Kerr effect and self-phase modulation, respond in femtoseconds, and are common in fiber lasers, though they often need help to self-start and NPR drifts with fiber birefringence.

Q-switching versus mode locking. A slow absorber, with recovery longer than the cavity round-trip time, lets the gain build up and then releases the stored energy in one pulse, promoting Q-switching; Cr⁴⁺:YAG in passively Q-switched microchip lasers is the standard case. A fast absorber, recovering on the scale of the pulse or the round trip, shapes one circulating pulse and favors mode locking.

Q-switched mode-locking limit. A mode-locked laser with too strong an absorber breaks into Q-switched bursts. The widely used stability criterion is

$$E_p^2>E_{\text{sat,L}}{E}_{\text{sat,A}}\mathrm{\Delta }R,$$

where $E_p$ is the intracavity pulse energy, $\mathrm{\Delta }R$ the modulation depth, $E_{\text{sat,A}}=F_{\text{sat}}{A}_A$ the absorber saturation energy, and $E_{\text{sat,L}}=h\nu A_L\mathrm{/}(2{\sigma }_L)$ the gain saturation energy in a standing-wave cavity. For Nd:YAG (${\sigma }_L=2.8\times {10}^{-19}$ cm²) with a 100 μm gain-mode radius, $E_{\text{sat,L}}=105$ μJ. With the SESAM above, $E_{\text{sat,A}}=3.9$ nJ and $\mathrm{\Delta }R=1\mathrm{\%}$, stable mode locking needs $E_p>64$ nJ, corresponding to $S\approx 16$ on the absorber. Halving both mode radii lowers the limit to 16 nJ. The 10 nJ pulse of the worked example would therefore Q-switch in this cavity; designs that must stay at moderate $S$ reduce $\mathrm{\Delta }R$ or the gain-mode area instead.

How absorbers are characterized. Nonlinear reflectivity (or transmission) is measured as a function of incident fluence with short pulses, and fitted to extract $F_{\text{sat}}$, $\mathrm{\Delta }R$, and the nonsaturable loss. Recovery time comes from a pump-probe measurement: a strong pulse saturates the absorber and a delayed weak pulse samples the recovery.

Pitfalls. At high fluence, two-photon absorption and free-carrier absorption make the reflectivity roll over and eventually damage the device, so the operating point is kept at moderate $S$. A slow component in a SESAM's recovery can support satellite pulses.

Common questions

What does a saturable absorber do in a laser?

It adds a loss that is higher for weak light than for intense light. The cavity then favors a short, intense pulse, which passes with lower loss than the same energy spread out in time, and the laser mode-locks or Q-switches without an active modulator.

What is the difference between a fast and a slow saturable absorber?

A fast absorber recovers within the pulse duration, so its loss follows the pulse intensity and it shortens the pulse directly. A slow absorber recovers after the pulse; it saturates on the leading edge and relies on gain saturation or soliton shaping to form the trailing edge.

References: Siegman, Lasers (University Science Books, 1986); Svelto, Principles of Lasers (5th ed., 2010); Keller et al., "Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435 (1996); Hönninger et al., "Q-switching stability limits of continuous-wave passive mode locking," J. Opt. Soc. Am. B 16, 46 (1999); Haiml, Grange & Keller, "Optical characterization of semiconductor saturable absorbers," Appl. Phys. B 79, 331 (2004).