Gain saturation and self-focusing considerations in the design of optical amplifiers

We extend the stability analysis of the quasioptical equation given by Bespalov and Talanov and by Suydam to the case of Frantz‐Nodvik pulse propagation. When ${\mathrm{\epsilon \; \approx \; (An}}_0{g}_0{\text{/2 π λ)}}^2\text{≪ 1}$ , we find that the logarithm of the perturbation growth divided by the input intensity depends on the input illuminance and the media gain. This relationship is important in amplifier design. The asymptotic growth may be given in closed form even when $\text{ε ≫ 1}$ . This form is used for design refinements when indicated by an a posteriori estimate.