Self-Action of Laser Beams in Semiconductors

We have derived an expression for the nonlinear dielectric constant due to nonparabolicity of the conduction band and energy-dependent scattering processes in semiconductors under the influence of an external laser beam. The self-action phenomenon due to the combined effect is then studied. The role of linear and nonlinear absorption coefficients is incorporated in the analysis of self-action to show that (i) the former leads to a lower threshold value of the incident power of the beam for self-focusing to occur, and (ii) the latter decreases the self-focusing length, the reduction being appreciable at optical frequencies. Some properties of the self-action phenomenon are then described in practical situations. These considerations are applied in detail to a particular sample of $n-\mathrm{I}\mathrm{n}\mathrm{S}\mathrm{b}$, where the absorption threshold is found to be significantly greater than the diffraction threshold and therefore, defocusing is favored. Finally, the possiblity of self-focusing, taking absorption effects into account, is discussed in elemental and group-III-V compound semiconductors—Ge, Si, GaAs, GaSb, GaP, InAs, InSb, InP, and AlSb — for visible He-Ne and infrared $Q$-switched C${\mathrm{O}}_2$ lasers.