Numerical treatment of focal shift of focused axially symmetric laser beams

Abstract

Focal shift is a well known phenomenon at present [1]-[3]. It occurs when a converging wave is diffracted at an small aperture with Fresnel number Np = a2 /Xf ^ 1, where / is the radius of the spherical wave in the aperture with radius a, and is the wavelength. Under this condition the focal shift phenomenon appears, i.e. the maximum intensity is no longer at the geometrical focus, but occurs at a point which is located closer to the aperture with the focusing lens. It was first observed dealing with microwaves diffraction about fifty years ago [1] But the publications of Erkkila and Rogers, Li and Wold in 1981 have initiated active investigations of this phenomenon in optics only. It has been recognized that for the unapertured focused beams with a small effective Presnel number Nv, = w1 /f (w is the radius of the beam) the same effect exists. Now many papers on the focal shift of maximum intensity for different beams are published. But there are beams with an off-axis focus and the standard treatment of the focal shift is complicated [2]. In this paper, using the mode-expansion method for modeling the complex optical beam propagation [4], the numerical analysis and experimental investigation of the focal shift defined here as the shift (from the geometrical focus) of the position of the minimal radii (for different beam radii definitions) are presented. The influence of the beam propagation ratio M^ [4] and the effective Fresnel number N^o- = w^/Xf on the focal shift is analyzed for different focused beams. The distinction of the investigated focal shift phenomenon with the so called diffraction shift of intensity maximum for aberrated beams [5] is also discussed.