Focal shift in the axisymmetric Bessel-modulated Gaussian beam

The focal shift of the axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) is investigated by using two different approaches. The first approach is based on the encircled-power criterion and the second one is the conventional method based on the axial irradiance. In this last case, a third-order equation governing the amount the relative focal shift is derived. Moreover, it is shown from numerical calculation results that the two approaches provide mainly the same results; the focal shift of the axisymmetric QBG beam depend on the Gaussian Fresnel number Nw and the beam parameter μ.