Spectral anomalies near phase singularities in reflection at Brewster's angle and colored castastrophes

The anomalous behavior of a polychromatic beam reflected from the interface of two homogeneous dielectric media at the neighborhood of Brewster's angle is investigated theoretically and examined experimentally. An explicit expression is derived for the spectrum at an arbitrary observation point for a given incident spectrum. By introducing a modifier function it is shown that the spectrum at each point sensitively depends on the observation angle just in the immediate neighborhood of Brewster's angle and wavelength. Finally, the obtained results are applied to account for the horizontal parts of the supernumerary rainbows.