Structuring total angular momentum of light along the propagation direction with polarization-controlled meta-optics

Abstract

Recent advances in wavefront shaping have enabled complex classes of Structured Light which carry spin and orbital angular momentum, offering new tools for light-matter interaction, communications, and imaging. Controlling both components of angular momentum along the propagation direction can potentially extend such applications to 3D. However, beams of this kind have previously been realized using bench-top setups, requiring multiple interaction with light of a fixed input polarization, thus impeding their widespread applications. Here, we introduce two classes of metasurfaces that lift these constraints, namely: i) polarization-switchable plates that couple any pair of orthogonal polarizations to two vortices in which the magnitude and/or sense of vorticity vary locally with propagation, and ii) versatile plates that can structure both components of angular momentum, spin and orbital, independently, along the optical path while operating on incident light of any polarization. Compact and integrated devices of this type can advance light-matter interaction and imaging and may enable applications that are not accessible via other wavefront shaping tools.

Fig. 1. Concept of polarization-switchable and versatile TAM plates.

a Conventional J-plates can impart two independent, propagation-invariant, azimuthaly varying phase profiles e^iℓϕ and $e^{i{\ell }^{\prime }\varphi }$ on the two eigen-polarization states, $∣{\lambda }^{+}⟩$ and $∣{\lambda }^{-}⟩$, while reversing their polarization handedness at the output. b A schematic of the proposed polarization-controlled TAM plate which can switch between two distinct spatially varying vortices, ${\mathrm{\Psi }}^{{\ell }_1\to {\ell }_2}$ and ${\mathrm{\Psi }}^{{\ell }_1^{\prime }\to {\ell }_2^{\prime }}$, in response to the input eigen polarizations $∣{\lambda }^{+}⟩$ and $∣{\lambda }^{-}⟩$. c A versatile TAM plate can control the polarization (Λ) and orbital angular momentum along the optical path. Light of any arbitrary polarization incident on the device will encounter variable polarization transformations as if interacting with different polarizing elements (as shown by the red arrows). d Design principle: the spatially varying vortex, ${\mathrm{\Psi }}^{{\ell }_1\to {\ell }_2}$, is constructed from two series of OAM modes, denoted as ψ^ℓ, each composed of 2N + 1 Bessel functions carrying the same ℓ value and equally separated in a comb-like arrangement in k_z-space. The inset depicts five co-propagating OAM modes within ${\psi }^{{\ell }_1}$ and their envelope (longitudinal profile). By engineering the complex weights of these modes, the longitudinal intensity profile of the resulting envelope, ${\psi }^{{\ell }_1}$, can follow the user-defined function F^ℓ along the z-direction. e ${\mathrm{\Psi }}^{{\ell }_1\to {\ell }_2}$ is realized by superimposing ${\psi }^{{\ell }_1}$ and ${\psi }^{{\ell }_2}$, whose respective profiles F^ℓ were judiciously engineered to cause destructive (constructive) interference at precise locations along z, leading to desired topological charge transition ℓ₁ → ℓ₂ with propagation. f The target propagation-dependent polarization response of the versatile TAM plate takes the form of a 2 × 2 Jones matrix, ${\tilde{F}}^{\ell }$. In general, this can be a polarizer or waveplate-like response. Here, we depict a response that mimics a polarizer or waveplate rotating its fast axis along the optical path.

Fig. 2. Fabricated devices and experimental setup.

a Optical microscope images of sample fabricated TAM plate devices exhibiting a flower petal-like structure. b Scanning electron microscope (SEM) images verifying the smooth sidewall profile of the individual nanofins. The checkerboard-like pattern observed in the nanofin orientations signifies the underlying dual-matrix holography (DMH) implementation; each element of the target dual-matrix hologram is realized on the metasurface by four nanofins. c Experimental setup (top view) used to characterize the devices: a quarter-waveplate (QWP) and half-waveplate (HWP) control the polarization of the beam incident on the metasurface (MS). The output response is filtered and imaged using a 4-f system (f = 5 cm) onto a charge-coupled device (CCD) camera. An interferometric setup, comprising beam splitters (BS) and mirrors (M), is deployed to interfere each vortex beam with a tilted Gaussian beam to characterize its z-dependent topological charge value.

Fig. 3. Polarization-switchable TAM plate with elliptical eigen polarizations.

a Measured output transverse intensity profiles generated by the device in response to $∣{\lambda }^{+}⟩$ and $∣{\lambda }^{-}⟩$ polarizations, in addition to an equal weight of the two. The device responds to $∣{\lambda }^{+}⟩$ polarization by generating a vortex beam changing its charge from ℓ = 1 to ℓ = −3 as it propagates along the z-direction, whereas for the orthogonal polarization, $∣{\lambda }^{-}⟩$, a different vortex evolving from ℓ = 2 to ℓ = −1 is produced. The insets depict the topological phase dislocations obtained from an interferomteric measurement with a tilted Gaussian beam. At each z-plane, a mixture of the two OAM states can be generated by changing the weights assigned to the eigen polarizations incident on the device. b Measured longitudinal intensity profile at the output of the device under the two orthogonal incident polarizations, $∣{\lambda }^{+}⟩$ and $∣{\lambda }^{-}⟩$, confirming the generation of two distinct vortices with spatially evolving topological charges. c, d Simulated data corresponding to the measurements in a, b. e, f Measured and designed eigen polarizations at the input (e) and output (f) of the device. The chirality of incident light is inverted upon interacting with the device. Spatial dynamics of these beams can be found in Supplementary Movies 1 and 2.

Fig. 4. Versatile TAM plate for independent SAM and OAM control along the direction of propagation.

a Optical microscope images of the device. b Measured longitudinal intensity profile at the output in response to incident x-polarization. The polarization response here is chosen to mimic a quarter-waveplate (QWP) with rotating fast axis, as shown by the red arrows. c Measured and simulated transverse intensity profiles of the generated vortex, Ψ^3→2, in response to x-polarization, exhibiting a transition in the topological charge from ℓ = 3 to ℓ = 2. The state of polarization, obtained from Stokes polarimetry, is shown across the spatial extent of the beam, exhibiting a variation in the ellipticity at different propagation distances, as expected from a z-dependent quarter-waveplate-like device. d, e Simulated density maps depicting the OAM density (d) and SAM density (e) along the direction of propagation. f OAM values plotted as a function of propagation distance, obtained by integrating the OAM density in (d) at each transverse plane. The integration is performed twice considering two different aperture sizes: 100 μm (marked by the dashed lines in (d)) and 500 μm. We refer to these integrated values as local and global OAM, respectively. g Local and global SAM obtained by integrating the SAM densities in (e) using the same limits of integration as (f). In both cases, while the OAM/SAM can vary locally their global quantities are always conserved with propagation.

Fig. 5. Versatile TAM plate for independent polarization and OAM control along the direction of propagation.

a Optical microscope images of the device. b Measured longitudinal intensity profile at the output in response to incident x-polarization. The polarization response here is chosen to mimic a half-waveplate (HWP) with rotating fast axis, as shown by the red arrows. c Measured and simulated transverse intensity profiles of the generated vortex Ψ^1→2 in response to x-polarization, exhibiting a transition in the topological charge from ℓ = 1 to ℓ = 2. The state of polarization, obtained from Stokes polarimetry, is shown across the spatial extent of the beam, exhibiting a rotation in the plane of linear polarization at different propagation distances. d Output response of the same device under y-polarization, depicting the evolution of the linear polarization from $\widehat{y}$ to $\widehat{x}$ along the direction of propagation and verifying that the TAM plates can impart its intended response on any incident polarization. The Stokes polarimetry and the evolution of the polarization state on the Poincaré sphere are depicted in Supplementary Fig. 6.