Vortex waves with orbital angular momentum (OAM) are a highly active research topic in various fields. In this paper, we design and investigate cylindrical metagratings (CMs) with an even number of unit cells that can efficiently achieve vortex localization and specific OAM selective conversion. The multifunctional manipulation of vortex waves and the new OAM conservation law have further been confirmed through analytical calculations and numerical simulations. In addition, we qualitatively and quantitatively determine the OAM range for vortex localization and the OAM value of vortex selective conversion and also explore the stability for performance and potential applications of the designed structure. This work holds potential applications in particle manipulation and optical communication.

Hyperbolic shear polaritons (HShPs) emerge with widespread attention as a class of polariton modes with broken symmetry due to shear lattices. We find a mechanism of generating quasi-HShPs(q-HShPs). When utilizing vortex waves as excitation sources of hyperbolic materials without off-diagonal elements, q-HShPs will appear. In addition, these asymmetric q-HShPs can be recovered as symmetric modes away from the source, with a critical transition mode between the left-skewed and right-skewed q-HShPs, via tuning the magnitude of the off-diagonal imaginary component and controlling the topological charge of the vortex source. It is worth mentioning that we explore the influence of parity of topological charges on the field distribution and demonstrate these exotic phenomena from numerical and analytical perspectives. Our results will promote opportunities for both q-HShPs and vortex waves, widening the horizon for various hyperbolic materials based on vortex sources and offering a degree of freedom to control various kinds of polaritons.

Transformation optics (TO) facilitates flexible designs of spatial modulation of optical materials via coordinate transformations, thus, enabling on-demand manipulations of electromagnetic waves. However, the application of TO theory in control of hyperbolic waves remains elusive due to the spatial metric signature transition from (+,+) to (-,+) of a two-dimensional hyperbolic geometry. Here, we proposed a distinct Pythagorean theorem, which leads to establishing an anisotropic Fermat’s principle. It helps to construct anisotropic geometries and is a powerful tool for manipulating hyperbolic waves at the nanoscale and polaritons. Making use of absolute instruments, the excellent collimating and focusing behaviors of naturally in-plane hyperbolic polaritons in van der Waals α–MoO3 layers are demonstrated, which opens up a new way for polaritons manipulation.