Polarization of sky light from a canopy atmosphere

Abstract

Light from the clear sky is produced by the scattering of unpolarized sunlight by molecules of the atmosphere and is partially linearly polarized in the process. Singly scattered light, for instance, is fully polarized in viewing directions perpendicular to the sun direction and less and less so towards the parallel and antiparallel directions, where it is unpolarized. The true, multiple, scattering is much less tractable, but importantly different, changing the polarization pattern's topology by splitting the unpolarized directions into pairs. The underlying cause of this 'symmetry breaking' is that the atmosphere is 'wider' than it is deep. Simplifying as much as possible while retaining this feature leads to the caricature atmosphere analysed here: a flattened sheet atmosphere in the sky, a canopy. The multiple scattering is fully tractable and leads to a simple polarization pattern in the sky: the ellipses and hyperbolas of standard confocal ellipsoidal coordinates. The model realizes physically a mathematical pattern of polarization in terms of a complex function proposed by Berry, Dennis and Lee (2004 New J. Phys.6 162) as the simplest one which captures the topology.