Physical mechanism for the geometric phases in optics and angular momentum holonomy (2404.05747v1)

Abstract: Vast literature on the experiments and mathematical formulations on the geometric phases signifies the importance of this subject. Physical mechanism for the origin of the geometric phases in optics was suggested in 1992 by the author in terms of the exchange of the angular momentum. Some of the literature has taken notice of it, however, the real import of the suggested mechanism and the angular momentum holonomy conjecture has remained elusive. The present contribution delineates the prevailing confusions and offers a thorough discussion on the nature of the light waves to resolve the conceptual issues. It is argued that at a fundamental level there exist only two types of geometric phases arising from (i) the geometry of the wave vector space, and (ii) the polarization state space. For the light beams of definite polarization spatial modes (HG or LG modes) the geometric phase has origin in the wave vector space that is different than the spin redirection phase for the polarized light. Angular momentum holonomy is proposed to be equivalent to the geometric phase in general.