Relaxation oscillation

Relaxation oscillations (engl. Relaxation oscillations ) are a phenomenon in laser technology , which describes the variation of the intensity of a laser beam in response to a disturbance in the laser operation.

mechanism

In stationary laser operation (cw operation) the gain of the laser corresponds to the threshold gain below which no laser oscillation can take place. This effect is known as gain clamping . The time development of the laser intensity inside the resonator depends on the gain and reads ${\displaystyle g}$

${\displaystyle I(t)=e^{{\frac {cl}{L}}(g-g_{t})}}$

with the length of the amplification medium, the length of the laser resonator and the threshold gain, which is determined by the resonator losses. For the exponent is less than zero and exponential damping takes place. In the opposite case, the light field experiences an exponential gain. It should be noted that the gain is generally a function of frequency , so . The same applies to . However, this is not important for the understanding of relaxation vibrations. ${\displaystyle l}$ ${\displaystyle L}$ ${\displaystyle g_{t}}$ ${\displaystyle g<g_{t}}$ ${\displaystyle g}$ ${\displaystyle \nu }$ ${\displaystyle g=g(\nu )}$ ${\displaystyle g_{t}}$

Under certain circumstances it can happen that the gain increases to a value above the threshold value (e.g. in the event of fluctuations in the pump power, when the laser is started up, etc.). In this case, the gain factor exceeds the resonator losses, with the result that the intensity of the light field within the resonator increases exponentially. Increasing field strengths reduce the population inversion of the laser to a greater extent, which leads to a reduction in the gain (see also: gain saturation ). If the gain falls below the threshold value as a result, the light field itself experiences an exponential decay. If the population inversion can build up again to above the threshold value due to the lower laser intensity, the process described continues cyclically. As a rule, the amplitudes of the relaxation oscillations drop exponentially, so that after some time, stationary laser operation is reached again.

Relaxation oscillations can be observed particularly well in ruby lasers . Usual oscillation periods are in the order of magnitude of 21 µs with decay lengths in the range of 2 ms. The intensity of a ruby ​​laser beam often consists of a series of irregular spikes, which can be traced back to relaxation oscillations that are continuously excited by mechanical and thermal fluctuations.

Individual evidence

1. ↑ PW Milonni, JH Eberly: Lasers (= Wiley Series in Pure and Applied Optics . Volume 7) John Wiley & Sons, 1988, ISBN 0-471-62731-3 , p. 296.
2. ↑ Hans Joachim Eichler, Jürgen Eichler: Lasers: designs, beam guidance, applications . 7th edition. Springer, 2010, ISBN 978-3-642-10461-9 , pp. 296 .
3. ↑ PW Milonni, JH Eberly: Lasers (= Wiley Series in Pure and Applied Optics . Volume 7) John Wiley & Sons, 1988, ISBN 0-471-62731-3 , p. 369.
4. ^ PW Milonni, JH Eberly: Lasers (= Wiley Series in Pure and Applied Optics . Volume 7) John Wiley & Sons, 1988, ISBN 0-471-62731-3 , p. 370.