We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2 × 2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

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A brief review of effects in information recording systems based on complex compounds of polyvinyl alcohol (PVA) with metals (Au, Cu, Pt, Bi) is presented. As the result of irradiation, the chain reaction process of decomposition causes the aggregation of metal atoms or metal salts molecules to point centers or dendritic crystals. Some features of these processes are outlined.

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