Gain medium

The gain medium (also called the active medium or laser medium) is the optical material in a laser where light amplification through stimulated emission takes place. It contains atoms, ions, molecules, or carriers (depending on type) that can be pumped into excited states and stimulated to emit coherent photons. The choice of gain medium fundamentally determines a laser's operating wavelength, output power capability, and pulse characteristics.

Physical requirements. A useful gain medium must:

1. Support a population inversion — more atoms in an upper energy level than a lower level. This requires an electronic structure with at least three energy levels (typically four).
2. Have a transition with high oscillator strength at the desired output wavelength — strong enough to provide gain that exceeds cavity losses.
3. Permit efficient pumping — typically optical pumping, electrical injection, or a chemical/gas-discharge process.
4. Have low parasitic losses — minimal background absorption, scattering, and quenching at the lasing wavelength.
5. Be thermally and chemically stable under operating conditions.

Categories of gain media.

Class	Examples	Wavelength range	Notable features
Solid-state	Nd:YAG, Yb:fiber, Ti:sapphire, Er:glass	0.7 – 3 μm	High power, narrow linewidth, long upper-state lifetime
Semiconductor	GaAs, InGaAs, InGaAsP, GaN	0.4 – 2 μm	Direct electrical pumping, compact, modulatable
Gas	HeNe, Ar+, CO₂, excimer	0.2 – 11 μm	Very narrow lines, high power CW
Dye	Rhodamine, Coumarin in solvent	0.4 – 0.9 μm	Broadly tunable, but largely replaced by Ti:sapphire
Fiber	Er, Yb, Tm, Ho in silica or fluoride	0.9 – 3 μm	High efficiency, scalable to kW, fiber-format
Quantum cascade	GaAs/AlGaAs superlattices	3 – 25 μm	Engineered subband transitions, mid-IR
Free-electron	Relativistic electrons in a magnetic wiggler	0.0001 – 10000 μm	Tunable across vast spectrum; large facility

Energy level structure. Most useful gain media are 4-level systems (rarely 3-level):

• 4-level system: pump from ground to upper pump level → fast non-radiative decay to upper laser level → lasing transition → fast non-radiative decay to ground. Population inversion easily achieved.
• 3-level system: pump from ground to upper laser level → lasing transition to ground. Requires pumping more than half of all atoms to achieve inversion (high threshold).
• Quasi-4-level: like 4-level but with the lower laser level slightly above ground (thermally populated at low temperature; useful at elevated temperatures).

Common laser materials:

Material	Level scheme	Pump	Laser wavelength
Nd:YAG	4-level	808 nm diode	1064 nm
Yb:fiber	Quasi-3-level	976 nm diode	1030 – 1080 nm
Er:fiber	3-level	980 nm or 1480 nm	1530 – 1565 nm
Ti:sapphire	4-level	532 nm	700 – 1000 nm (broadly tunable)
HeNe	4-level	Electrical discharge	632.8 nm, 1152 nm
InGaAsP MQW	Direct band-to-band	Electrical injection	1310 or 1550 nm
QCL	Engineered subbands	Electrical injection	3 – 25 μm

Gain bandwidth. The frequency range over which the gain medium provides amplification. Determines:

• Tunability: how wide a wavelength range the laser can be tuned over
• Pulse duration limit: shortest pulse is roughly $\Delta t \approx 1/\Delta\nu$
• Multi-mode lasing: number of longitudinal modes that can simultaneously lase
• Mode partition noise: more modes → more partition noise

Material	Gain bandwidth	Shortest pulse (fundamental)
HeNe	1.5 GHz	$\sim 1$ ns
Argon-ion	5 GHz	$\sim 0.5$ ns
Nd:YAG	120 GHz	$\sim 10$ ps
Yb:fiber	30 nm = 8 THz	100 fs
Er:fiber	35 nm = 4.5 THz	100 fs
Ti:sapphire	300 nm = 100 THz	5 fs
InGaAsP MQW	30 nm = 4 THz	100 fs

Pumping schemes.

• Optical pumping: a high-brightness pump source (lamp, diode laser, or another laser) excites the gain medium. Used for solid-state and fiber lasers.
• Electrical pumping (carrier injection): current through a forward-biased semiconductor p-n junction injects carriers that recombine radiatively. Used for diode lasers.
• Gas discharge: electron impact in a gas discharge excites atoms. Used for HeNe, argon-ion, CO₂.
• Chemical: an exothermic chemical reaction populates upper states. Used for HF, DF, COIL.
• Nuclear: gamma rays from nuclear decay (rarely used outside research).

Upper-state lifetime. The time an atom remains in the upper laser level before spontaneously decaying. Determines:

• Energy storage capacity: longer lifetimes store more pump energy → higher Q-switched pulse energy
• Threshold inversion: longer lifetimes require less continuous pump to maintain inversion
• Modulation bandwidth: longer lifetimes limit how fast the gain can be modulated

Material	Upper-state lifetime
Nd:YAG	230 μs
Yb:YAG	1 ms
Er:glass	10 ms
Cr:LiSAF	67 μs
Ti:sapphire	3.2 μs
InGaAsP semiconductor	1 – 5 ns
GaN semiconductor	$\sim 1$ ns

Semiconductor gain media have orders-of-magnitude shorter lifetimes, enabling fast modulation but limiting energy storage.

Gain saturation. As pump or signal intensity increases, the gain coefficient decreases due to depletion of the inversion. The saturation intensity $I_\text{sat}$ characterizes this:

$$g(I) \;=\; \frac{g_0}{1 + I/I_\text{sat}},$$

where $g_0$ is the small-signal gain. At $I = I_\text{sat}$, the gain is halved. Saturation intensity varies dramatically by material:

Material	$I_\text{sat}$ at line center
Nd:YAG @ 1064 nm	1.7 kW/cm²
Yb:glass	33 kW/cm²
Er:fiber	0.5 – 5 kW/cm² depending on doping
InGaAsP MQW	10 MW/cm²
Ti:sapphire	200 kW/cm²
HeNe	0.5 kW/cm²

Confinement factor. In waveguide gain media (semiconductor lasers, fiber amplifiers), only a fraction of the mode overlaps the active region. The confinement factor $\Gamma$ multiplies the material gain to give the modal gain — the relevant quantity for lasing threshold.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 14 (laser amplifiers); Siegman, Lasers (University Science Books, 1986), Ch. 1 – 7 for the comprehensive treatment; Coldren, Corzine & Mašanović, Diode Lasers and Photonic Integrated Circuits (2nd ed., 2012), Ch. 4 for semiconductor gain media.