This is a collection of problems composed by some participants the workshop “Differential Geometry, Billiards, and Geometric Optics” that took place at CIRM on October 4–8, 2021.

In the last fifteen years several manifestations of geometric phase in optics have been discovered. The most studied manifestations are spin redirection phase and Pancharatnam phase. A new phase on the transformations of optical beam modes has begun to be studied. This article reviews the principles of these phases and discusses the applications that have been proposed and reported in the liter...

The customary defocussed and Foucault modes of Lorentz microscopyare usually described in terms of geometric optics. Wohlleben has shown that geometric optics has a restricted range of validity, however; a more fundamental approach is provided by wave optics. The defocussed and Foucault modes may be discussed in terms of wave optics, and for the defocussed mode it can be shown explicitly that t...

Toward Arbitrary Spin-Orbit Flat Optics via Structured Geometric Phase Gratings In article number 2200800, Peng Chen, Zhi-Han Zhu, Yan-Qing Lu, and colleagues demonstrate a new type of flat-optics elements, termed structured geometric phase gratings, capable complex-amplitude control with polarization switchable behavior. Such an advanced spin-orbit device, compared the present unlocks paraxial...