Gain Medium

definition:
Medium for laser amplification.

In laser physics, a laser gain medium is a medium that can amplify light power (usually in the form of a beam). In laser, the medium needs to compensate for the loss of the resonant cavity, which is usually referred to as the laser active medium. It can also be applied to fiber amplifiers. Gain refers to the degree of amplification.  
Due to the increase in energy of the amplified beam caused by the gain medium, the medium itself also needs to receive energy, which is achieved through the pumping process. Generally, it is designed to be pumped by current (electric pump) or input light wave (optical pump), and the wavelength of the pump should be smaller than the wavelength of the signal light.  

Types of laser gain media
There are many types of gain media, and the common ones are as follows:

1. Some direct bandgap semiconductors, such as GaAs, AlGaAs, InGaAs, are typically pumped by current in the form of quantum wells (see semiconductor lasers)
2. Laser crystals or glass, such as Nd: YAG (neodymium doped yttrium aluminum garnet, see yttrium aluminum garnet laser), Yb: YAG (ytterbium doped YAG), Yb: glass, Er: YAG (erbium doped YAG), or titanium sapphire, in solid sheet form (see bulk laser) or optical glass fiber (fiber laser, fiber amplifier). These crystals or glasses are doped with some laser active ions (mostly trivalent rare earth element ions, sometimes transition metal ions) and pumped by light waves. Lasers using these media are commonly referred to as doped insulator lasers.  
3. Ceramic gain media are usually doped with rare earth element ions.  
4. Laser dyes, usually liquid solutions, are used in dye lasers.  
5. Gas lasers use gases or gas mixtures, usually pumped by discharge devices (such as CO2 lasers and excimer lasers).  
6. Some special gain media, such as chemical gain media (converting chemical energy into light energy), nuclear pump media, and wigglers in free electron lasers (transferring energy from fast electron beams into the beam).  

Compared to most crystalline materials, ion doped glass has a larger amplification bandwidth, allowing for larger wavelength tuning and the generation of ultra short pulses. The disadvantages are slightly poor temperature characteristics (limiting the output power obtained) and small laser cross-section, resulting in a large pump power threshold (for passive mode-locked lasers) and unstable Q-switching. You can refer to the comparison between laser crystals and glass in the entry for more information.  
The doping concentration of crystals, ceramics, and glass usually needs to be carefully optimized. In the presence of strong pump absorption at short wavelengths, a relatively high doping concentration is required, but this can also cause energy losses related to quenching processes, such as upconversion caused by laser active ion clusters and energy transfer to defects.  

Important physical effects
In most cases, the physical basis of the amplification process is stimulated radiation, which means that the incident photons trigger more photon radiation, causing the excited laser active ions to first transition to a slightly lower energy excited state. The process of a four level gain medium and a three-level gain medium is different.  
The less frequent amplification process is stimulated Raman scattering, which involves converting some high-energy pump photons into low-energy photons and phonons (related to lattice vibrations). If the incident light power is high and the gain medium reaches gain saturation, the gain will decrease. That is to say, with limited pump power,
An amplifier cannot add any amount of power to the incident beam. In laser amplifiers, the number of upper level ions decreases under saturation conditions due to stimulated radiation.  
There is a thermal effect in the gain medium, as a portion of the pump light power is converted into heat. The temperature gradient generated and the accompanying mechanical stress can cause prism effect, resulting in distortion of the amplified light beam. These effects can destroy the beam quality of the laser, reduce efficiency, advantages, and even destroy the gain medium (thermal rupture).  

Related physical properties of laser gain media
In laser applications, the physical properties of many gain media are important. Mainly includes:

1. It is best for the peak gain to occur in the wavelength region where laser transition is required
2. The substrate medium has high transparency in the working wavelength range
3. Good pump light source, efficient pump absorption
4. Appropriate upper level lifetime: It should be long enough for Q-switching applications and short enough for fast power modulation
5. High quantum efficiency is obtained from low quenching effects, excited state absorption, and similar processes, or from favorable effects such as multiphoton transitions or energy transfer
6. Ideal four level behavior, as quasi three level behavior introduces some additional constraints
7. High strength and long lifespan, chemical stability
8. For solid-state gain media: The base medium needs to have good optical quality, which can be cut or polished to high quality (appropriate hardness), allow doping with high concentration of laser active ions without forming clusters, good chemical stability, good thermal conductivity and low thermal optical coefficient (weak thermal prism effect during high-power operation), resistance to mechanical stress, optical isotropy is usually required, but sometimes birefringence (reducing thermal depolarization effect) and polarization related gain may also be needed (see polarization of laser radiation)
9. Low pump power threshold at high gain: the product of radiation cross-section and upper level lifetime is relatively large
10. Low beam quality requirements for pump light sources: high pump absorption is necessary
11. Wavelength tuning: requires a large gain bandwidth
12. Ultra short pulse generation: wide and flat gain spectrum; Appropriate dispersion and nonlinearity
13. Passive mode-locked laser without Q-switching stability: sufficiently large laser cross-section
14. High energy pulse amplification (positive feedback amplifier): The impact of high optical damage threshold and low saturation on gain

Note that in some cases, conflicting requirements may be necessary. For example, very low quantum defects are not compatible with a four level system. The laser cross-section corresponding to a large gain bandwidth is smaller compared to the ideal situation, and thus the quantum defects will not be very small. The disorder in solid-state gain media increases the gain bandwidth, but also reduces thermal conductivity.
A short pump absorption length is advantageous, but it can exacerbate thermal effects.  
The requirements for gain media vary in different situations. Therefore, many gain media are still very important for applications, and it is necessary to choose the appropriate gain media when optimizing the design of lasers.