Evolution of Geometric Phase of light since 1956: A Catalog Review

Abstract: The geometric phase of light is a fascinating phenomenon in optics and arises whenever there is a change in the polarization state of light. It is a fundamentally well-established concept and has recently found extensive applications, particularly in the development of geometric phase elements that enable efficient manipulation of light. In this tutorial review, we discuss the evolution of the geometric phase of polarization on the Poincaré sphere, from its inception by Shivaramakrishnan Pancharatnam in 1956 to its recent advances and applications. This review article aims to focus on core papers related to the geometric phase of polarization rather than providing an exhaustive literature survey. In this review, first, we introduced the basic parameters and corresponding parameter spheres involved in the geometric phase of light. Then, we provide an in-depth analysis of geometric phase in polarization modes, spatial modes, vector modes, and electromagnetic fields. A brief discussion of applications of the geometric phase is also provided. The intriguing explanation given in this review can awaken new ideas related to the geometric phase of light and can open new directions in fundamental and applied optics. Finally, the tutorial is structured as a comprehensive catalog of the geometric phase of light.