Laser applications and other topics in quantum electronics

Certain particular solutions of the quasi-optics equation

A. A. Pikulev

Federal State Unitary Enterprise "Russian Federal Nuclear Center — All-Russian Research Institute of Experimental Physics", Sarov, Nizhnii Novgorod region

Abstract: The dependences of the refractive index on the coordinates, for which nontrivial symmetry groups of the two-dimensional quasi-optics equation exist, are considered. All cases where the Lie-symmetry algebra is two-dimensional are investigated. In such cases, the quasi-optics equation reduces to an ordinary differential equation. Several particular solutions of this equation are obtained. It is shown that all the particular solutions can be divided into three types: plain waves, source functions, and Gaussian beams. The distribution of the amplitude then obeys Gauss's law only for three cases: a transversely homogeneous medium, an optical wedge, and a distributed lens.

PACS: 42.25.Bs, 42.25.Gy

Received: 20.09.1998

 English version: Quantum Electronics, 1999, 29:9, 822–827

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