Gain medium

The gain medium, also called the active or laser medium, is the material in a laser that amplifies light by stimulated emission. Its atoms, ions, molecules or charge carriers are pumped into excited states until more of them sit in the upper level of a transition than in the lower one, a population inversion, and light at the transition's wavelength then gains more photons by stimulated emission than it loses to absorption. Examples are Nd:YAG crystals, erbium- and ytterbium-doped fibers, semiconductor quantum wells and the helium-neon gas discharge. The gain medium sets the laser's wavelength, the bandwidth it can be tuned over or mode-locked across, and how much energy it can store for pulses.

What a gain medium needs

1. A transition that can be inverted: an energy-level structure in which pumping can put more population in the upper laser level than in the lower one, which needs at least three levels.
2. Enough gain: a transition strong enough, and a density of active centers high enough, for the gain to exceed the losses of the optical cavity.
3. A practical way to pump it: optical pumping, electrical injection, a gas discharge or a chemical reaction.
4. Low parasitic loss: little background absorption, scattering or quenching at the laser wavelength.
5. Thermal and chemical stability, since part of the pump power always ends up as heat in the medium.

Types of gain media

The lasers built on each, with their wavelengths and uses, are surveyed in Types of Lasers.

Three-level and four-level gain media

• Four-level: the pump lifts the population to a level above the upper laser level, from which it relaxes quickly; the lower laser level lies well above the ground state and empties quickly. The lower level stays nearly empty, so inversion begins with the first excited ions and the threshold is low. Nd:YAG is the standard example.
• Three-level: the lower laser level is the ground state, so more than half of all the ions must be excited before there is any gain. Ruby, the first laser, works this way, and its threshold is high.
• Quasi-three-level: the lower laser level lies so close to the ground state that it is partly populated by heat at room temperature. Erbium at 1.55 µm and ytterbium at 1.03 µm work this way: they need a substantial pump intensity before they become transparent, and cooling the medium lowers the threshold.

Gain bandwidth

The gain bandwidth is the range of frequencies the medium amplifies. It sets how far the laser can be tuned, how many longitudinal modes can lase at once, and the shortest pulse it can produce, since a Gaussian pulse of duration $\mathrm{\Delta }t$ needs a bandwidth of at least $0.44\mathrm{/}\mathrm{\Delta }t$.

Ti:sapphire oscillators have produced pulses of about 5 fs directly (Ell et al., 2001), and the mode-locked lasers of ultrafast optics use the broadband solid-state and fiber media of this table.

Upper-state lifetime

The upper-state lifetime is the time the excited population survives before it decays spontaneously. A long lifetime lets the medium store pump energy for a Q-switched pulse and lowers the pump power needed to hold the inversion; a short one lets the gain follow fast modulation.

Semiconductor gain media store energy for only nanoseconds, which allows direct modulation at gigahertz rates (see modulation bandwidth) but rules out Q-switched pulses of high energy.

Gain saturation

As the intensity in the medium grows, stimulated emission depletes the inversion and the gain falls. For a homogeneously broadened medium,

$$g(I)=\frac{g_0}{1+I\mathrm{/}{I}_{\text{sat}}},I_{\text{sat}}=\frac{h\nu }{\sigma \tau },$$

where $g_0$ is the small-signal gain, $\sigma$ the emission cross-section and $\tau$ the upper-state lifetime; at $I=I_{\text{sat}}$ the gain is halved (gain saturation). For Nd:YAG, with $\sigma =2.8\times {10}^{-19}$ cm² and $\tau$ = 230 µs, $I_{\text{sat}}$ = 2.9 kW/cm². Ti:sapphire has a similar cross-section but a lifetime 72 times shorter, and saturates at an intensity roughly ninety times higher, about 260 kW/cm².

Waveguide gain media

In semiconductor lasers and fiber amplifiers only part of the guided mode overlaps the active region. The confinement factor $\mathrm{\Gamma }$ multiplies the material gain to give the modal gain, the quantity that has to reach the cavity loss at threshold.

Common questions

What is a gain medium in a laser?

The material that amplifies light by stimulated emission once it has been pumped into population inversion. Together with the pump and the optical cavity it is one of the three parts of every laser, and it sets the laser's wavelength.

What are examples of gain media?

Crystals and glasses doped with rare-earth or transition-metal ions (Nd:YAG, Yb:YAG, Ti:sapphire, erbium- and ytterbium-doped fiber), semiconductors (InGaAsP and GaN quantum wells), gases (helium-neon, CO₂, argon ion, excimers), dyes in solution, and the engineered layers of quantum cascade lasers.

What is the difference between a three-level and a four-level gain medium?

In a four-level medium the lower laser level is empty, so gain starts as soon as a few ions are excited. In a three-level medium the lower level is the ground state, so more than half of all the ions must be excited first, which raises the threshold.

Why does the upper-state lifetime matter?

It sets how much pump energy the medium can store. Nd:YAG, at 230 µs, can be Q-switched to high pulse energy; a semiconductor, at a few nanoseconds, cannot store energy but can be modulated directly at gigahertz rates.

References: Siegman, Lasers (University Science Books, 1986), ch. 1 to 7; Koechner, Solid-State Laser Engineering (6th ed., Springer, 2006), for the Nd:YAG and Yb:YAG parameters; P. F. Moulton, "Spectroscopic and laser characteristics of Ti:Al₂O₃," J. Opt. Soc. Am. B 3, 125 (1986); S. A. Payne et al., "Laser performance of LiSrAlF₆:Cr³⁺," J. Appl. Phys. 66, 1051 (1989); R. Ell et al., "Generation of 5-fs pulses and octave-spanning spectra directly from a Ti:sapphire laser," Opt. Lett. 26, 373 (2001); Coldren, Corzine and Mašanović, Diode Lasers and Photonic Integrated Circuits (2nd ed., Wiley, 2012), ch. 4.