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The absorptance A of the SOC consists of two parts:
The non-saturable part Ans of the absorption can be caused by macroscopic crystal defects with very short relaxation time.
The non-saturable absorption decreases with increasing relaxation time of the excited carriers in the absorber material.
In case of absorbers with a short relaxation time of ~ 1 ps the non-saturable part of the absorption can be Ans ~ 0.2.A0.
The total absorption is the sum of both parts A1 = As + Ans.
The saturation of the absorption can be described with the following formula:
The pulse fluence F depends on the beam radius r for a Gaussian pulse as follows:
Both the fluence and the saturation depend on the beam radius r. To get the effective absorption A for the pulse an averaging over the whole illuminated area on the absorber is needed.
The figure shows the saturation behaviour according to the formulas above for A1 and the averaged absorption A with a
certain value of non-saturable absorption Ans = 0.2 A0.
The absorption values As and Ans are normalized on a value A0 = As + Ans.
The averaging results in a lower saturation simulating an additional virtual non-saturable absorption.
Typical values of a saturable absorber mirror for mode-locking a solid state laser are:
A = 0.02 and Fsat = 70 µJ/cm2.
For mode-locking a fiber laser with more gain the absorption of teh SAm must be also larger:
A ~ 0.3, Fsat ~ 50 µJ/cm2.
The pule energy results from an integration of the radial dependent fluence as
With the laser repetition rate f the average laser output power Pav can be calculated as Pav = E.T.f
• Wavelength dependency
The absorption increases with increasing photon energy, starting at the gap energy of the semiconductor material.
In case of a quantum well structure the absorption increases as a step-like dependency on the photon energy due to the one-dimensional quantisation of free carriers.
Consequently, the reflectance versus wavelength curve of a SOC shows under non-saturated conditions a decreasing reflectance for shorter wavelengths.