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Encyclopedia of Laser Physics and Technology

© Dr. Rüdiger Paschotta

Last update: 2008-04-24

Definition: small mutually coupled oscillations of the laser power and laser gain around their steady-state values

When a laser is disturbed during operation, e.g. by fluctuations of the pump power, its output power does not immediately return to its steady state. Many lasers (e.g. solid-state lasers and most laser diodes) are operating in the so-called class-B regime, with the upper-state lifetime being longer than the cavity damping time. In this regime, changes of pump power lead to so-called relaxation oscillations. These are usually damped, eventually leading back to the steady state. Particularly pronounced oscillatory behavior with relatively low oscillation frequencies (often in the kilohertz regime) occurs in solid-state lasers, whereas semiconductor lasers normally exhibit strongly damped relaxation oscillations with rather high frequencies in the gigahertz region. Other lasers, e.g. many gas lasers, operating in the class-A regime with an upper-state lifetime below the cavity damping time, do not exhibit relaxation oscillations, but only an exponential relaxation to the steady state.

Figure 1: Simulated turn-on dynamics of a Nd:YAG laser, assuming that the pump power is suddenly switched on. Before the steady state is reached, the laser emits a number of spikes and undergoes damped relaxation oscillations.

As Figure 1 shows, class-B lasers can exhibit strong spiking e.g. when the pump power is suddenly turned on. After emission of a few spikes (pulses), the laser power exhibits damped relaxation oscillations. The oscillation frequency is similar to the inverse period of the spikes.

Calculations of relaxation phenomena can be based on the dynamic equations as presented in the article on laser dynamics, which can (for small fluctuations, not for spiking) be linearized around the steady state. In the following, the main results of such an analysis are given. The frequency of the relaxation oscillations is determined by the intracavity power, the resonator losses l, the round-trip time T_R of the resonator, and the saturation energy E_sat and the upper-state lifetime _g of the gain medium:

The cavity damping time corresponds to T_R / l, and the first term in the radicand is larger than the second one in the mentioned class-B regime.

For solid-state lasers (with _g >> T_R), the second term of the radicand is negligible (except for operation close to threshold), so that the equation simplifies to

These equations are valid for both four-level and three-level gain media. Only for four-level gain media, the former equation can be transformed into

where r is the so-called pump parameter, which is the ratio of pump power to threshold pump power.

The damping time of the oscillations is about twice the upper-state lifetime of the gain medium for operation just above the laser threshold, and smaller than that at higher powers. (For four-level lasers, it is inversely proportional to the pump parameter.) Note that a saturable absorber in the laser resonator, which may be used for passive mode locking, can strongly reduce the damping; the oscillations can even become undamped, so that the steady state becomes unstable. This leads to the phenomenon of Q-switching instabilities and Q-switched mode locking.

The characterization of the laser dynamics can deliver useful information on the laser parameters such as the resonator losses or the gain saturation energy, thus also the laser cross sections.

Bibliography

See also: laser dynamics, spiking, Q-switching instabilities

Category: lasers

This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics Consulting GmbH. Contact this distinguished expert in laser technology, nonlinear optics and fiber optics, and find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, or staff training) could become very valuable for your business!