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Definition: a measure for the incident optical power required for achieving significant saturation of an absorber or a gain medium
The saturation power of a laser gain medium is the optical power of an input signal which in the steady state leads to a reduction in the gain to one half of its small-signal value. The saturation intensity is the corresponding optical intensity, i.e., the saturation power per unit area.
Usually it is assumed that the gain is small, i.e., input and output power are similar. For high gain, it is common to refer to the output power.
For a low-gain laser amplifier, saturation intensity and power can be calculated according to
where hν is the photon energy at the signal wavelength, σem and σabs are the emission and absorption cross sections at the emission wavelength, 
is the upper-state lifetime, and A is the mode area.
The quantity σabs is zero for four-level gain media but should not be forgotten for quasi-three-level gain media.
Figure 1: Dependence of laser gain on the optical power, calculated for the steady state. When the power equals the saturation power, the gain is reduced to one half the small-signal gain.
A comparison with the equations for the saturation energy shows that the saturation power can be calculated as the saturation energy divided by the upper-state lifetime.
These quantities can be defined in an analogous way for saturable absorbers.
Importance of the Saturation Power
The saturation power plays an important role in various areas of laser physics and laser or amplifier design. Some examples are:
- It determines the amount of input power of an amplifier required for achieving most of the possible output power.
- The laser intensity in the gain medium of a four-level laser equals the saturation intensity if the pump power is twice the threshold pump power. This is remarkable, because the laser intensity in this situation is thus determined only by a property of the gain medium, not by cavity losses etc.
- For a saturable absorber, as used e.g. in a mode-locked laser, the ratio of continuous-wave intracavity power and saturation power is an important parameter for the initial pulse formation process.
The saturation power should not be confused with the saturated output power, which is usually not precisely defined but means the output power achieved for an input signal power which causes significant amplifier saturation. Obviously, the saturated output power (other than the saturation power) depends on the pump power.
Pump Saturation
A subtle detail is that the saturation characteristics can be modified if the pump intensity of the gain medium is comparable to or higher than the pump saturation power (which is defined as above, but based on photon energy and cross sections at the pump wavelength). In this situation, the rule that the gain is reduced to one half for an intensity equal to the saturation intensity (as defined above) does no longer hold.
For two reasons, however, pump saturation effects are in most cases not very important for lasers and amplifiers:
- In most solid-state bulk lasers, the pump intensity is well below the pump saturation intensity, so that such effects do not occur. (On the other hand, in certain fiber lasers such effects can be very strong.)
- Even if pump saturation is significant at some location within a laser crystal or amplifier, it may overall not be important, as long as the pump absorption within the whole gain medium is quite complete. In such a situation, local pump saturation simply means that some of the pump power is absorbed at another location within the same medium, effectively not changing the overall saturation characteristics.
See also: gain saturation, saturable absorbers, saturation energy, cross sections
Category: physical foundations
