Study of symmetry and retracing properties of geometric phase gratings and lenses

• The analysis of different symmetry and retracing properties of geometric-phase (GP) diffraction gratings and GP lenses, compared to standard scalar phase gratings and lenses. • The experimental verification of these properties using simple optical arrangements that include polarization control of the light beam. • The realization of optical systems where GP gratings and lenses are used in a transmission configuration, and others where a mirror is added to analyze their performance on the counter-propagated beam. The purpose of this paper is to analyze the different symmetry and retracing behavior of geometric-phase (GP) diffraction gratings and GP lenses compared to standard scalar phase gratings and lenses. This different behavior is explained by simple flipping transformations of the encoded phase function. Experimental results are included that evidence these properties with simple optical arrangements. These include experiments where the gratings are used in a transmission configuration, and others where a mirror is added to analyze a counter-propagated beam. These properties might be interesting and even crucial when using GP gratings and lenses in optical systems that rely on the precise control of light in forward and backwards propagation.