An exact solution to the Helmholtz equation for a quasi-Gaussian beam in the form of a superposition of two sources and sinks with complex coordinates
An exact solution to the Helmholtz equation is proposed. The solution describes a quasi-Gaussian beam with an arbitrary width and has the form of a superposition of sources and sinks with complex coordinates. It is shown that such a beam always lacks a component that propagates against the principal propagation direction. In addition, when the diameter of the beam exceeds the wavelength, the beam becomes directional in the broad sense: the radiation condition is satisfied with respect to the beam waist plane. For the beam under study, expressions for the angular spectrum and the spherical harmonic expansion coefficients are derived.
Keywordsquasi-Gaussian beams exact solutions to the Helmholtz equation
Unable to display preview. Download preview PDF.
- 2.N. S. Bakhvalov, Ya. M. Zhileikin, and E. A. Zabolotskaya, Nonlinear Theory of Sound Beams (Nauka, Moscow, 1982; AIP, New York, 1987).Google Scholar
- 7.A. M. Tagirdzhanov, A. S. Blagovestchenskii, and A. P. Kiselev, in Proceedings of Symposium on Progress in Electromagnetics Research (Moscow, 2009), pp. 1527–1529.Google Scholar
- 12.A. P. Poddubnyak, Sov. Phys. Acoust. 30, 51 (1984).Google Scholar