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Definition: small-signal gain of an optical amplifier per unit pump power or per unit stored energy
The gain efficiency of an amplifier can be defined as the small-signal gain divided by the pump power to achieve this gain in the steady state. For three-level gain media, it is more sensible to use the differential gain efficiency, i.e. the derivative of the small-signal gain with respect to the pump power. The gain efficiency may also sometimes refer to the stored energy instead of the pump power.
For a gain medium with emission and absorption cross sections σem and σabs and photon energy hν at the signal wavelength, and a mode area A (assuming a top-hat profile), the dependence of the gain on the stored energy can be simply calculated as
where the power amplification factor is exp(g). (For a four-level gain medium, σabs = 0.) This shows that the gain efficiency in terms of stored energy is inversely related to the saturation energy: high laser cross sections lead to a high gain efficiency, but also to a low saturation energy.
The pump power required for achieving a certain stored energy in the steady state depends on the upper-state lifetime of the laser transition: the shorter this lifetime, the higher is the rate with which ions needs to be pumped into the upper laser level. For the differential gain efficiency in terms of pump power, this leads to the equation
where ηp is the pump efficiency, including the pump absorption efficiency, the quantum efficiency of the pumping process, and the quantum defect. Psat is the saturation power, which is the saturation energy divided by the upper-state lifetime.
A high gain efficiency can be desirable for an amplifier when a high gain is wanted. However, it can be preferable to have a not too large gain efficiency in cases where a high energy needs to be stored in a gain medium – for example for Q switching of a laser, or if pulses need to be amplified to high energies. The gain efficiency of an amplifier can also depend on the pump wavelength. For example, erbium-doped fiber amplifiers pumped at 980 nm tend to have higher gain efficiencies than those pumped around 1450 nm, even though the latter can have a higher power efficiency.
See also: gain, saturation energy, amplifiers, Spotlight article 2007-05-10
Categories: amplifiers, lasers
