Lubomir M. Kovachev, Daniela A. Georgieva. A class of localized solutions of the linear and nonlinear wave equations

Natural Sciences / Physics / Optics

Submitted on: Jun 02, 2012, 10:38:09

Description: Following the tradition from nano and picosecond optics, the basic theoretical studies continue to investigate the processes of propagation of femtosecond and attosecond laser pulses with the corresponding envelope equation for narrow-band laser pulses, working in paraxial approximation. We point, that this approximation is not valid for large band pulses. In air due to small dispersion the wave equation as well as the 3D+1 amplitude equation more accurate describe the pulse dynamics. New exact localized solutions of the linear wave and amplitude equations are presented. The solutions discover non-paraxial semi-spherical diffraction of single-cycle and half-cycle laser pulses and a new class of spherically symmetric solution of the wave equation. The propagation of large band optical pulses in nonlinear vacuum is also investigated in the frame of a system of nonlinear wave vector equations. Exact vector soliton solution with own angular momentum is obtained.

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