THE MAJORANA REPRESENTATION OF POLARIZATION, AND THE BERRY PHASE OF LIGHT

A natural geometric representation of the polarization of light with f ixed propagation direction is a dot on a sphere in an abstract space: the Poincare sphere. If the direction of propagation is also included as a variable, a different description, given here, is natural. It is taken from quantum mechanics (from the Majorana picture of a spin syst em), spin one in the case of light. It characterizes polarized light b y two dots on a unit sphere in the real space of directions (i.e. by t wo unit vectors). The direction of propagation is their bisector (or i ts reverse). Projecting the two dots onto the plane perpendicular to t his direction gives the two foci of the polarization ellipse (which li es in this plane and has a unit semimajor axis). As an application of this picture the geometric Berry phase for light is calculated. The re sult accords with the quantum spin-1 formula of Bouchiat and Gibbons, and with the prescription for finding the geometric phase for light gi ven by Bhandari.