SU(2) Poincaré sphere: A generalized representation for multidimensional structured light

Abstract

Structured light, as a general term for arbitrary states of amplitude, phase, and polarization in optical fields, is highly topical because of a myriad of applications it has fostered. A geometric description to graphically group classes of structured light has obvious benefits, with some notable advances in analogous Poincaré sphere (PS) mapping for both spin and orbital angular momentum (OAM), as well as ray-optical PS approaches for propagation-invariant fields, but all limited in dimensionality they can describe. Here we propose a generalized SU(2) PS for arbitrary dimensional structured light. The states on it represent extended families of beams with multidimensional ray-wave structures, accurately described by SU(2) symmetry groups. We outline how to construct this mapping theoretically, revealing insights into mode transformations involving OAM and geometric phase, and fully verify its efficacy experimentally. The generality of our approach is evident by the reduction to prior PS representations as special cases. We also demonstrate an extension of our approach to explain a more general high-dimensional vector beam. This construction naturally accounts for the salient topology of the classical PSs while bringing to more new degrees of freedom and dimensions for tailoring a larger variety of quantum-to-classical structured beams for a variety of applications.

Creation and control of high-dimensional multi-partite classically entangled light

“…Spatial light mode control in lasers allows one to specify the desired modal amplitude, phase and polarisation 15 . While the spatial modes usually refer to the eigenmodes of the paraxial wave equation, there is also a class of complex spatial wave-packet modes that possess a geometric interpretation with SU(2) symmetry, a general symmetry for describing paraxial structured beams with OAM evolution mapped on a Poincaré-like sphere 69 . This geometric mode has the formation of SU(2) coherent state, with the salient property that the distribution of the wave function is coupled with a classical movement trajectory 64 , 70 .…”

Human psychophysical discrimination of spatially dependant Pancharatnam–Berry phases in optical spin-orbit states

“… 33 may provide high resolution for capturing the full spectrum of spin-coupled OAM sensitivity, the current task appears exceedingly effective at identifying high and low spin-coupled OAM discrimination performers, such that anybody unable to achieve ceiling performance will invariably perform near chance. Although both of these works have examined human perception of structured light that possess correlations between two degrees of freedom, protocols exist for the preparation of more complex spatial modes 60 and higher dimensional non-separable states 61 . An interesting future experiment to consider is the measurement of the classical GHZ state correlations using human detectors as per the polarization-based Bell-state projection measurements outlined in Ref.…”

Structural stability of open vortex beams

“…The connection between the ray and wave picture of light is given by the eikonal equation at the high-frequency limit 20 . Such a theoretical consistency is sometimes referred to as the ray-wave duality, which provides useful ideas and techniques for tailoring new types of structured laser beams, e.g., ray-optical Poincaré spheres for structured beams [21][22][23] , propagation-invariant light with shaped caustics 24 , SU(2) geometric modes generated from cavities 25 and holograms 26 , high-dimensional classically entangled light 27 , and new interpretations of self-accelerating beams 28,29 . Inevitably, vortex beams, as an essential class of structured light, can be analyzed in the framework of ray-wave duality.…”