The effect of spherical aberration on singularities and spectral changes of focused beams

The singular transformation and spectral behaviour of spatially fully coherent polychromatic plane beams focused by an aperture lens with spherical aberration ( SA) is studied. The expressions of the light intensity and the spectrum distributions in the focal region of a plane beam focused by a lens with SA are derived. It is shown that, with the SA, one axial singularity will split into two new singularities. At the off-axial positions, new singularities appear and split with increasing SA. The phase at the positions of the singularities is indeterminate and the spectrum is split into two lines with equal height. In addition, the numerical calculation shows that the spectrum is red-shifted at the side of the singularities close to the focus and blue-shifted at the side far away from the focus.