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Propagation of Hermite-cosh-Gaussian laser beams in non-degenerate germanium having space charge neutrality. (English) Zbl 1159.78338

Summary: 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 \(R_n < R_d\), where \(R_n\) is the self-focusing length and \(R_d\) is the diffraction length. The behaviour of the \(f\) parameter with the dimensionless distance of propagation \(\eta \) for various \(b\) values is examined by numerical estimates. The results are presented graphically.

MSC:

78A60 Lasers, masers, optical bistability, nonlinear optics
78A40 Waves and radiation in optics and electromagnetic theory
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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