Focal shift in vector Mathieu-Gauss beams

The three dimensional distribution of focused vector Mathieu-Gauss beams (vMG) is studied in the vicinity of the geometrical focus of an unapertured thin lens. We adopt two different intensity based criteria for defining the actual focus. Our analysis confirms the existence of a focal shift towards the lens for this type of beams. The dependence of the focal shift on the different parameters of the beams is discussed in detail. Beams with different states of polarization are studied as well, and it is shown that the focal shift is independent of the polarization.