Abstract
Structured lights, particularly those with tunable and controllable geometries, are highly topical due to a myriad of their applications from imaging to communications. Ray-wave duality (RWD) is an exotic physical effect in structured light that the behavior of light can be described by both the geometric ray-like trajectory and a coherent wave-packet, thus providing versatile degrees of freedom (DoFs) to tailor more general structures. However, the generation of RWD geometric modes requires a solid-state laser cavity with strict mechanical control to fulfill the ray oscillation condition, which limits the flexiblility of applications. Here we overcome this confinement to generate on-demand RWD geometric modes by digital holographic method in free space without a cavity. We put forward a theory of generalized ray-wave duality, describing all previous geometric modes as well as new classes of RWD geometric modes that cannot be generated from laser cavities, which are verified by our free-of-cavity creation method. Our work not only breaks the conventional cavity limit on RWD but also enriches the family of geometric modes. More importantly, it offers a new way of digitally tailoring RWD geometric modes on-demand, replacing the prior mechanical control, and opening up new possibilities for applications of ray-wave structured light.
Highlights
Light can be modelled as both ray and wave representations, with the ray a fundamental concept in geometric optics and used routinely in lens design, while waves apply to wave optics to describe the phenomena such as interference and diffraction
The multi-path and vector geometric mode can be obtained based on the periodic oscillating ray trajectory in the laser cavity [18–20], while the emitting planar geometric mode can be transformed into structured vortex beam carrying orbital angular momentum (OAM) and coupled with the classical trajectory located on a hyperboloidal ruled surface [21,22]
Hereinafter, we demonstrate the experimental result of generalized ray-wave duality (RWD) geometric modes, including Lissajous and trochoidal parametric-surface modes, multi-axis HLG, planar-to-vortex multi-path geometric modes and RWD geometric modes that break the bottleneck of cavity
Summary
Light can be modelled as both ray and wave representations, with the ray a fundamental concept in geometric optics and used routinely in lens design, while waves apply to wave optics to describe the phenomena such as interference and diffraction. The multi-path and vector geometric mode can be obtained based on the periodic oscillating ray trajectory in the laser cavity [18–20], while the emitting planar geometric mode can be transformed into structured vortex beam carrying orbital angular momentum (OAM) and coupled with the classical trajectory located on a hyperboloidal ruled surface [21,22]. RWD geometric modes with higher complexity can be realized with more controllable parameters in SU(2) coherent state, such as the 3D coherent wave-packets located on the Lissajous curve and trochoidal parametric surfaces [25–27]. These exotic RWD geometric modes largely enrich the family of structured lights with more DoFs [20]. Once multi-parameters of RWD geometric modes being freely modulated, such RWD geometric modes with salient quantum-classical coupled properties would surely broaden the related applications such as optical manipulation [28,29], quantum entanglement [30–33], particle trapping [34–36], communications [33,37], and security encryption [38,39]
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