Focusing Gaussian beams by an annular lens with spherical aberration

In this paper, focusing Gaussian beams by an annular lens with spherical abberation is discussed. The expressions for the axial light intensity of Gaussian beams focused by an annular lens with primary spherical aberration have been derived. The numerical calculation shows that, for the annular lens with negative spherical aberration, the axial maximum focused intensity can be made larger than that of aberration-free cases. By choosing suitable values of central obstruction ratio of the annular lens with negative spherical aberration, one can obtain an axial maximum focused intensity much greater than that of aberration-free cases. In addition, the positive spherical aberration can shift the best focal position (z/f)(m) (the position where the axial focused inensity is maximum) far away from the lens so that the positive focal shift can be achieved (i.e. Delta z/f = (z/f)(m) -1 > 0). It is shown that, when the Fresnel number of the outer radius of the annular lens is small (e.g. N-a less than or equal to 1), the effect of the spherical aberration on focusing Gaussian beams can be neglected.