Anomalous Behavior of Spectra near Phase Singularities of Focused Waves

It is shown that remarkable spectral changes take place in the neighborhood of phase singularities near the focus of a converging, spatially fully coherent polychromatic wave diffracted at an aperture. In particular, when the spectrum of the wave in the aperture consists of a single line with a narrow Gaussian profile, the spectrum near a phase singularity (i.e., near points of zero intensity of some particular spectral component) changes drastically along a closed loop around the singularity. The spectrum is redshifted at some points, blueshifted at others, and is split into two lines elsewhere.