Propagation of Hermite-cosh-Gaussian laser beams in non-degenerate germanium having space charge neutrality

In this paper, we analytically investigate Hermite-cosh-Gaussian (HChG) laser beam propagation in non-degenerate germanium having space charge neutrality for the first three mode indices. The field distribution in the medium is expressed in terms of beam-width parameter f and decentred parameter b. The differential equations for the f parameter are established by a parabolic wave equation approach under paraxial approximation. Analytical solutions are obtained under the condition Rn Rd, where Rn is the self-focusing length and Rd is the diffraction length. The behaviour of the f parameter with the dimensionless distance of propagation for various b values is examined by numerical estimates. The results are presented graphically.