Two sides of the Poincaré sphere in optics: polarization and beam structure.

8 November 2017, 2.15 PM - 8 November 2017, 3.15 PM

Miguel A Alonso (University of Rochester)


This presentation will consist of two parts, each on an area of optics in which the geometric construction known as the Poincaré sphere can be employed: polarization and beam intensity structure. The first part relates to optical systems that employ spatially varying birefringent elements. In particular, a glass window with induced stress birefringence is shown to be useful for several applications. When inserted into the pupil plane of an imaging system, this element induces a point spread function (PSF) that codifies the polarization information, so that the imaging system becomes a single-shot imaging polarimeter (when applied to sparse objects for which the PSFs can be resolved). Applications in microscopy are also discussed. The second part of the talk will present a generalization of the use of the Poincaré sphere to characterize high-order cavity modes, including Hermite-, Laguerre-, and Ince-Gaussians amongst many others. A ray-optical description is provided, in which any beam of this type is represented by a closed loop on the surface of the Poincaré sphere. It is shown that the caustic structure of the modes is related to the abstract representation over the Poincaré sphere through simple geometry. Other types of beams, such as Bessel, Airy, and Mathieu beams can be considered as limiting situations of the cases discussed here.

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