Most lasers are operated with a pump parameter between 3 and 10, i.e. significantly but not very far above threshold. This is because extreme values often have some disadvantages:
- For small pump parameters (close to 1), the power conversion efficiency is reduced, the output power depends sensitively on the pump power, and the relaxation oscillations are weakly damped.
- For very large pump parameters, diffraction-limited beam quality is often difficult to achieve (at least in bulk lasers), since e.g. small tails of the pump intensity profile can excite higher-order modes. Also, the power efficiency may be degraded due to the strong influence of parasitic resonator losses.
Extreme values of pump parameters are nevertheless required in some cases:
- Some single-frequency lasers have to be operated with small pump parameters because for stronger pumping additional resonator modes would start to oscillate.
- High-power fiber lasers are often operated far above threshold simply because the threshold power is very low, even with strong output coupling.
- Passively mode-locked lasers often have to be operated far above threshold in order to suppress Q-switching instabilities.
Particularly in the context of four-level lasers, it can be convenient to use the pump parameter <$r$> in equations, as it is most easy to evaluate in an experiment, and thus often well known. In four-level lasers, the intracavity optical intensity in the gain medium (in the steady state, assuming a flat-top mode profile) is (<$r - 1$>) times the saturation intensity. Also, there is a simple equation for the frequency of relaxation oscillations, containing the parameter <$r$>. However, such equations then often do not hold for (quasi-)three-level gain media.
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