Identifying and controlling new degrees of freedom in structured light has exploded of late.¹ One such form of structured light is vectorial beams with spatially inhomogeneous polarization structures, already having found many applications in classical and quantum studies.² New degrees of freedom (DoFs) in such fields have inspired new approaches to encoding and decoding information, for example, using the vectorness and nonseparability as a quantum-like property,³ and more recently, exploiting embedded topology.⁴ Having identified a DoF, the challenge is to find a suitable toolkit to control it. Here advances have been slim, with the present toolkit often reverting to modal and phase information and disregarding the DoF altogether. Reporting in Nature Communications, Changyu Zhou and colleagues reveal a hidden parity in vectorial light that can be exploited for immediate control by metasurfaces.⁵ Their approach heralds new spatial control of structured vectorial light and simultaneously introduces the notion of a parity-Hall effect to extend the spin-Hall effect beyond its two spin possibilities, opening an exciting new pathway to exploiting vectorial light in classical and quantum communication with high-bandwidth and deterministic detection.

Vectorial light is formed by the non-separable combination of spatial mode and polarization, giving rise to exotically structured and spatially invariant polarization patterns.⁶ When the spatial mode is orbital angular momentum (OAM), the resulting vector vortex beams are eigenmodes of both free-space and optical fibre and have found tremendous applications in a range of fields. Recently these fields have revealed hidden invariances, for instance, the robustness of nonseparability⁷ and their topology⁸ in noisy channels, but unfortunately there is as yet no toolkit for controlling these DoFs. Changyu Zhou and colleagues introduce the notion of parity in vectorial light. Going beyond the identification of a new DoF, they reveal how it can be controlled with metasurfaces for what they coin the parity-Hall effect, separating vectorial light based on parity by bringing structured matter to bear on the control of structured light (Fig. 1).

Fig. 1

Parity in vectorial light and its control. (a) If a vectorial beam is invariant under the action of the parity operator it is assigned an even parity and an odd parity if it is inverted under the action of the parity operator, shown here for radial and azimuthal vectorial light. (b) Mode parity dispersion can be induced by matching the arrangement of birefringent unit cells with the symmetry of the polarization vectors, so that each parity mode experiences a unique birefringent axis. By spatially varying the birefringence of these unit cells, one can then impart different phases onto incident beams depending on their parity. (c) This results in a vectorial version of the spin-Hall effect, coined the parity-Hall effect, where vectorial modes are separated by parity.

The parity of a vectorial beam is determined by its eigenvalue under the action of the parity operator, which inverts the spatial coordinates across the $x$ axis and in doing so maps $(x,y)$ to $(x,-y)$. As a simple example we can consider two of the possible vectorial optical fields created by superimposing two orbital OAM carrying Laguerre Gaussian beams with topological charges $l=\pm 1$. Depending on the relative phases between the two spatial modes, it is possible for all the polarization vectors to be pointing outwards from the centre (radially polarized) or for the polarization vectors to be oriented along the azimuthal direction (azimuthally polarized). The symmetry of the polarization vector in the radially polarized beam means it is invariant to reflections across any axis and has a parity of 1 (even). The azimuthally polarized beam will be a mirror image of itself under the same transformation and so has a parity of $-1$ (odd). A useful feature of modes with opposite parity is that the polarization vectors of the mode with parity 1 will always be at 90-degree angles to the polarization vectors of the mode with parity $-1$ at every point in space.

Zhou and colleagues have demonstrated the ability to independently control vectorial beams of opposite parity by leveraging the different symmetries of each beam’s spatially varying polarization structure. The orthogonality of the polarization vectors for beams of opposite parity at every point in space allows for the use of birefringence to selectively manipulate each mode at every point across the transverse plane. The plane of the metasurface is broken up into unit cells, each with its own birefringent properties: differently orientated birefringent axes and separate phase delays for each axis. The exact orientation and phase retardance of each unit cell is chosen to match the symmetry of the incident beam’s polarization structure. A beam with an even parity will then only be affected by one of the birefringent axes at every point in space while a beam with odd parity will only be affected by the other birefringent axis. This results in the ability to impart vastly different phases to beams of opposite parity.

To implement this principle physically in the metasurface, the authors made use of the generalized Snell’s law of refraction to determine the desired phase for each parity. The phases were chosen specifically to direct modes of even parity in one direction away from the optical axis and direct modes of odd parity in the opposite direction. The ability of the metasurface to control and redirect incident vectorial beams based on their parity is what leads to the titular parity-Hall effect. The metasurface was constructed using titanium oxide resonators placed on a silica substrate. These resonators have an asymmetric, elliptical design which results in a different interaction with the incident beam depending on the beam’s polarization at that point, resulting in locally tailored birefringence. With these resonators, the authors implement their symmetrically distributed and locally varying form birefringent design for parity dependent control over the incident beam.

The selective control over modes of differing parity opens up a new degree of freedom that can be utilized for encoding information. To demonstrate the effectiveness of the parity degree of freedom for this purpose, the authors pair their parity-Hall metasurface design with a lens phase and compensatory vortex phases and demonstrate their design’s ability to accurately sort and spatially separate modes with 7 distinct topological charges (ranging from $l=0$ to $l=6$) of both even and odd parities leading to the successful demultiplexing of 14 channels. This illustrates the possibility of using such a design to separate modes not only based on their amplitude or OAM, but on the parity of the mode as well. The authors further extend the use of parity to meta-hologram generation, where they combine it with topological charge to achieve an 8-channel vector beam demultiplexed hologram. The 8 channels are achieved by making the hologram generation dependent on the polarization topological charge of the incident beam and on the parity of the vectorial beam as a whole. The authors made use of vectorial combinations with topological charges $l=\pm 2$ and $l=\pm 3$. Each unique combination of topological charge and parity encoded a unique hologram and results in a unique image generated from the metasurface.

This advance shows that there is much to be revealed in vectorial structured light, and offers a new approach to immediate deployment in encryption and communication. The associated physical insight of parity in vectorial light will surely inspire further research in the topic, for instance, on the resilience of parity to noisy channels. Intriguing is the possibility of harnessing more than one DoF, as was shown with parity and OAM. If this could be extended it may yet prove the stimulus to accelerate the real-world deployment of structured light in optical communications.