Focal shift in vector beams

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Abstract
We examine the three-dimensional intensity distribution of vector Bessel–Gauss beams with general polarization near the focus of a nonaperturing thin lens. Recently reported linearly and azimuthally polarized Bessel–Gauss beams are members of this family. We define the width and focal plane of such a vector beam using an encircled-energy criterion and calculate numerically that, as for scalar beams, the true focus occurs not at the geometric focus of the lens but rather somewhat closer to the lens. This focal shift depends on the mode number and system parameters and is largest for a narrow beam, long lens focal length, and large wavelength.