Example 8. Interplay of Diffraction and Gain Saturation

The example is describing the laser beam propagation through an Iodine amplifier that exhibits nonlinear gain saturation. The scheme was taken from the paper published by Ernst E. Fill,Optics Communications, v.49, no.5, 362-366 (1984).

Results of calculations with FRESNEL can be reproduced using iodine.scm and iodine.pls.
The energy density and the intensity temporal profiles right after the input diaphragm are shown in the next figure.

Parameters of Relaying Telescope and Amplifier are set according to the shown optical scheme layout. The Target was installed right at the Amplifier output (distance = 0).
The energy of the beam was selected to have the energy density at the input to the amplifier close to the saturation energy density (Q_s) for Iodine laser active medium. With high gain of the amplifier it corresponds to strong saturation of the signal. More important is that the diaphragm size and its edge softening are chosen to provide transversal spread of the beam spatial components at the amplifier input. The Amplifier was split into 10 sections to take into account the beam transversal evolution and gain saturation along their propagation through the gain medium.
The beam spatial and temporal distributions obtained at the amplifier output are shown in the figure below.

Note that not only the transversal beam distribution is changed due to gain saturation (on the beam edge the energy density is close to 1 J/cm² that is well above Qs), but the pulse shape is also strongly deformed - the amplification of the trailing part of the pulse is much lower. Without gain or at very low input energy level the optical system gives undistorted pulse spatial and temporal profiles. Observed complex beam profile distortion occurs due to combined effect of nonlinear gain and propagation in amplifying medium that occupies Fresnel diffraction zone from N_f=1.15 (input to amplifier) to N_f= inf.