Vol. 9, issue 03, article # 15

Abstract:

The equation is derived for the field in the cross section of a searchlight tubular beam formed with an axicon with a laser source at the input. The equation in the form of a Fourier integral transforms the function of radial coordinate at the axicon input into the function of radial frequency at its output in the Fraunhofer zone. The calculations made with the use of a fast Fourier algorithm permit the real time control over the searchlight beam shape at an arbitrary distance from the source based on data measured in the near zone. In a particular case of a homogeneous plane wave and Gaussian beam at the output, the integral can be calculated explicitly, and the solution may be represented as the degenerate hypergeometric Kummer functions.