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Abstract
In this paper, all-metallic reflective metasurfaces comprising S-shape streamline structures are proposed to achieve the photonic spin-Hall effect with average cross-polarization conversion efficiency exceeding ∼84% in the range of 8-14 µm. By comparing with all-metallic nanobricks, it is demonstrated that the electric field coupling could be enhanced by constructing a similar split ring resonator between adjacent unit elements to further improve its efficiency and bandwidth. As a proof of concept, the photonic spin Hall effect and spin-to-orbit angular momentum conversion could be observed by two metadevices with the maximum diffraction efficiency of ∼95.7%. Such an all-metallic configuration may provide a platform for various high-efficiency electromagnetic components, catenary optics, and practical applications.
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1. Introduction
Photonic spin-Hall effect (PSHE) depicts the spin-dependent splitting of light caused by spin-orbit interactions [1,2]. The mutual interactions between photonic spin angular momentum (SAM) and orbital angular momentum (OAM) could produce two kinds of geometric phases, i.e., the Rytov–Vladimirskii–Berry (RVB) phase and Pancharatnam-Berry (PB) phase [3–5]. The former is related to the evolution of the propagation direction of light, inducing a spin-Hall shift in real coordinate space [6]. Nevertheless, this subwavelength shift is difficult to distinguish, and thus the promising methodologies of the quantum weak measurement technology and multiple reflection technology are proposed to detect it [1,7]. Limited by its weak spin-orbit interaction based on the RVB phase, experimental observation of the PSHE is still a great challenge, especially for multi-wavelength beams [6]. In contrast, the latter yields a spin-Hall shift in momentum space leading to the strong polarization-dependent shift in real space [8,9]. It offers great potential to straightforwardly observe the PSHE and has been extensively applied in spin-photonic devices, such as the transverse and longitudinal spin-dependent splitting [10,11].
Metasurfaces as two-dimensional equivalents of metamaterials have shown exotic electromagnetic properties for manipulation of phase, amplitude, and polarization [12–14]. Among them, the PB-based metasurfaces could not only enhance spin-orbit interactions but also construct a bridge between phase delay (β) and the orientation angle (α) of each antenna, ie. β = 2σα; σ = ±1 represents the left-handed circular polarization (LCP) and right-handed circular polarization (RCP) [15]. Moreover, benefiting from its simple physical mechanism, numerous PB-based metasurfaces are designed for wide-angle metalenses [16,17], beam deflectors [18], holograms [19], optical communication [20], perfect absorbers [21], beam generators and detectors [22], among many others [23]. Since the PB phase only responds to the cross-polarization components for circularly polarized light illumination, it commonly requires higher conversion efficiency for various applications. Although multilayered and all-dielectric designs are proposed to surmount the theoretically predicted upper limit of conversion efficiency (25%) of single-layer plasmonic metasurfaces, these schemes increase the fabrication burden [15,24–29]. Furthermore, the metal-insulator-metal (MIM) configuration suffers from the substantial absorption originating from the Fabry-Perot effect, which makes the power efficiency hard to exceed 80% [30,31]. An alternative method is utilizing all-metallic metasurfaces to implement broadband and high-efficiency wavefront manipulation, whereas it is insufficient for applications in infrared imaging, cloaking, and remote sensing that commonly require the working bandwidth covering the whole long-wave infrared atmospheric window (8-14 µm) [32].
In this work, we present the all-metallic metasurface composed of the S-shape streamline (SS) structures to achieve broadband and high-efficiency PSHE. Benefiting from the enhancement of the electric field coupling effect by constructing a similar split ring resonator between adjacent units, the all-metallic SS structure possesses broader bandwidth (8-14 µm) and higher average conversion efficiency (∼84%) compared with nanobricks. To observe the PSHE and spin-to-orbit angular momentum conversion (SOC), two metadevices with the maximum diffraction efficiency of ∼95.7% are proposed to show their high performance for wavefront manipulation based on the PB phase. Hence, we believe this scheme could provide an effective platform for achieving various high-efficiency and broadband polarization-dependent optical manipulation.
2. Design and methods
2.1 Structure design
To achieve broadband and high-efficiency PSHE, an all-metallic SS structure is proposed as depicted in Fig. 1(a). Gold (Au) is utilized as the material since it can provide high reflectance and low absorption within the broadband spectrum range in Fig. 1(b) [33,34]. The frequency-dependent permittivity of Au could be described by the Drude model [35]:
Fig. 1. (a) Schematic of the SS structure. α is the rotation angle in the xy plane. (b) The reflectance and absorption distribution are calculated by Fresnel’s formulas. (c) Experimental and fitted complex permittivity of Au. (d) 2D schematic view of the SS structure (Λ= 8 µm, w = 1.75 µm, and h = 3 µm). (e) The reflectance of cross-polarization and co-polarization. (f) The phase shift and cross-polarization for reflectance with π/4 interval for LCP incidence at 10.6 µm.
Since the PB phase stems from the spin-orbit conversion instead of phase accumulation along the light propagation path or impedance transitions, it is determined by element structure with different rotation angles [36]. Each anisotropic metallic structure can be treated as a local wave plate. Therefore, when the LCP/RCP light (EiL/R) impinges on the metasurface from the + z-direction, the reflected light Er can be described as [24,37]:
Without loss of generality, this structure is elaborated aiming at a wavelength of 10.6 µm (the working wavelength of the CO2 laser). The simulated results are obtained by using the finite element method (FEM) in CST Microwave Studio. The average cross-polarized reflectance under LCP light incidence as a function of wavelength is shown in Fig. 1(e), in which it exceeds ∼84% from 8 to 14 µm and reaches the maximum of ∼94% at 10 µm. Simultaneously, the unwanted average co-polarized reflectance approximates ∼7.7% over the broadband range. Under these circumstances, each element could be regarded as a reflective half-wave plate, and the incident CP light is almost fully converted into its opposite polarization. According to the principle of the PB phase, the phase shifts in the reflected light can completely cover the 0-2π range by manipulating the local orientation α of the SS structure from 0 to π. An incremental rotation angle of π/4 is employed to expose the physical mechanism, which confirms that the phase shift is consistent with the theoretical PB phase shift as shown in Fig. 1(f) (Corresponding positions and values of the SS structure with different rotation angles are shown in Supplement 1). The approximately linear phase distribution and high reflectance provide the prerequisites for polarization-dependent components design.
2.2 Comparison with other all-metallic structures
To further explore the mechanism of broadband and high-efficiency polarization conversion of the SS structure, all-metallic nanobricks and S-shape ring (SR) elements are designed as a comparison in Fig. 2. Note that all the structures are optimized to obtain the maximum efficiency and bandwidth with the same lattice constant (Λ) but diverse sizes. The polarization conversion rate (PCR) is employed to describe its high performance, which is defined as [38]
where the Rcross and Rco are reflectance of cross-polarization and co-polarization for LCP incidence, respectively. As shown in Fig. 2(a), the average PCR of the SS structure exceeds ∼91.57% in the range of 8 -14 µm, which reaches ∼98.53% from 9-13 µm. Although the SR element and nanobricks likewise reveal high average PCR of ∼97.5% and ∼96.8% (9-13 µm) in Fig. 2(b) and Fig. 2(c), respectively, these performances are lower than the SS structure.Fig. 2. The PCR of (a) SS structure, (b) SR structure (it consists of flipped upside down of the right half part of half ring, in which the inner radius and the outside radius are 1.7 and 3.2 µm, respectively, as shown in Supplement 1), and (c) nanobricks (L = 7.2 and W = 1.6 µm) in Ref. [32]. All the elements possess the same lattice constant Λ= 8 µm and height H = 3 µm. (d)-(f) The extracted normalized electric field(red line) and fitted catenary curve (blue line) between two adjacent patches for different structures at 10.6 µm. The insets are corresponding instantaneous distributions of the electric field Ex. (g)-(i) Corresponding instantaneous electric field distributions for three elements in the xoy plane with periodic boundary conditions in the CST under LCP incidence from the + z direction. The O represents the coordinate origin.
In order to obtain a clearer visualization of this effect, Figs. 2(d)-(f) illustrate the instantaneous electric field distributions Ex in the yoz plane for three different units. When the electromagnetic wave goes through the all-metallic structures, the low loss air waveguide is produced to generate high polarization conversion efficiency. Its physical mechanism is modeled by the catenary theory, in which the effective impedance of the metal array is described by the catenary function [32]. The normalized electric field profiles in Figs. 2(d)-(f) between the adjacent elements can be described by the generalized catenary model [2,39]:
where a, b and c are the variables in the function. The retrieved parameters and coefficients of determination (R-square) of each fitting curve are listed in Table 1. Such field distributions (the insets) in Figs. 2(d)-(f) could be attributed to the near-field interaction between adjacent elements, which can be regarded as the low loss air waveguide to generate high polarization conversion efficiency in a broad range [40]. However, the efficiency of the conventional MIM configuration is hard to reach 80% limited by the substantial ohmic loss induced by the Fabry-Perot effect [24]. In addition, the all-dielectric scheme commonly using high aspect ratio nanostructures that are recognized as the truncated waveguide may induce lower transmissive conversion efficiency due to the large refractive index of the substrate of meta-atom leading to large reflection [41]. Since the Fabry-Perot effect and truncated waveguide effect may induce large resonance, it may destroy the working bandwidth as shown in Supplement 1. Therefore, the proposed all-metallic scheme may surmount the limitations in efficiency and working bandwidth. To further explore this interaction, the instantaneous electric field distributions in the xoy plane for three different elements are shown in Figs. 2(g)-(i). By constructing a similar split ring resonator between adjacent elements (in Figs. 2(g) and 2(h)) to enhance the coupling of this catenary optical field, the bandwidth of S-shape structures is broader than nanobricks in Fig. 2(i). Notably, this split ring resonator has been applied to enhance terahertz (THz) electromagnetically induced transparency (EIT) resonance [42]. Besides, the performances of the SS structure are better than the SR structure, which may benefit from the strong anisotropy of the element. When the period of the SS structure is larger than the wavelength of the incident light, it may be used to generate the continuous phase for the diffraction-free Bessel beam with high performance based on catenary optics [2]. Since the catenary possesses a linear phase gradient, it is advantages to the majority of the phase-based metadevices [43] (see Supplement 1).
Table 1. Retrieved parameters and R-square of each fitting.
3. PSHE metadevice
The PSHE metadevice is implemented by a periodical arrangement of the SS element with an incremental rotation angle of π/24. Therefore, the opposite deflection angle in the reflected mode will be produced for LCP and RCP light incidence to achieve spin-dependent splitting. According to the generalized Snell’s law, the deflection angle is calculated by θ = sin−1(λ/(24 Λ)) (λ is the wavelength of the incident light). The top view of the PSHE metadevice in the xoy plane and corresponding +1st-order diffraction efficiency under LCP illumination are illustrated in Fig. 3(a) (The most of incident power is deflected to −1st-order for RCP). Here, the diffraction efficiency is defined as the ratio of the reflected power toward a specific angle to the total reflected power [44]. Evidently, the average diffraction efficiency of the metadevice outnumbers ∼80% from 8.52 to 12.76 µm (the maximum diffraction efficiency is ∼95.7% at 9.23 µm). Correspondingly, its 0th order noise is well suppressed (close to 0 in a broadband range).
Fig. 3. (a) Elements arrangement and its diffraction efficiencies. (b) The normalized far-field intensity results under the incidence of LCP and RCP at the wavelengths of 9.23, 10.6, and 12.76 µm. (c)-(d) The x-components of the electric fields on the xoz plane for LCP and RCP excitation at 10.6 µm.
To explore its high performance, the normalized far-field distributions of the PSHE metadevice excited by LCP and RCP at three different wavelengths are shown in Fig. 3(b). The deflection angles are 2.75°, 3.16°, and 3.81° at 9.23 µm, 10.6 µm, and 12.76 µm under LCP incidence, respectively, which also can be increased/reduced by arranging unit elements with gradient slopes in the phase spectra. Because of the spin symmetry, deflection angles possess opposite signs for RCP illumination. The electric field distributions in Figs. 3(c) and 3(d) further prove that the energy is refracted in two symmetric angular directions for LCP and RCP incidence, which indicates the implementation of a transverse spin-split of light trajectory, ie strong PSHE. Therefore, this all-metallic configuration could provide a constructive platform to design broadband and high-efficiency PSHE metadevices.
4. SOC metadevice
For the further demonstration of broadband and high-efficiency functionalities, the SOC metadevice that could produce the optical vortex (in the reflected mode) is designed as shown in Fig. 4(a). Because of its dispersion function, the incident beams with different wavelengths are converged in the different z-planes, that is, the focal length is shorter/longer as the wavelength of incident light is higher/lower. Vortex beams, featuring a doughnut intensity distribution and a helically structured wavefront exp(ilφ) (φ is the azimuthal angle and l is the topological charge) around the propagation z-axis, have attracted extensive attention in optical communications [45], quantum information processing [46], optical micromanipulation [47], and vector light fields modulation [48]. To straightforwardly detect the topological charge of vortices, the on-axis focusing phase gradient in Fig. 4(b) and only the center region (with the radius of 0.75 times the radius of the SOC metadevice) carrying OAM in Fig. 4(c) are superposed to compose the SOC metadevice. The final phase distribution after superposition in Fig. 4(d) is expressed as:
Fig. 4. (a) The schematic illustration of the SOC metadevice under LCP excitation at 9.3 µm and 10.6 µm. The phase distributions of (b) focusing, (c) spiral phase plate, and (d) the vortex beam generator on the z = 0 plane. (e)-(f) Theoretical and simulated intensity distributions with l = 3 on the z = 70 µm plane at 10.6 um, and (g)-(h) the z = 80 µm plane at 9.3 um.
In Figs. 4(e)-(h), the simulated intensity distributions of the electric field in the xoy plane at 9.3 µm and 10.6 µm show good agreement with the theoretical results, respectively. Some disturbances are produced in simulation, which may stem from that the amplitude and phase are imperfect as we expected. Note that theoretical results are calculated by vectorial angular spectrum theory and the simulation of the SOC metadevice is employed by FIT in the CST [36]. Benefiting from the interference effect, the value and sign of the topological charge of the OAM can be diametrically identified by the number and twisting direction of the petals [49]. Furthermore, multi-channel vortices with arbitrary topologic charges could be generated by employing holography technology to meet different needs for practical applications.
In addition, the abovementioned all-metallic metadevices are easy to fabricate as follows. First, magnetron sputtering can be used to deposit the chromium (Cr) layer on the cleaned glass substrate. Next, the photoresist is spin-coated on the sample and patterned by laser direct writing. Then, the photoresist pattern is transferred to the Cr layer and glass by the ion beam etching and reactive ion etching, respectively. Eventually, after removing the Cr layer, magnetron sputtering is employed to deposit the Au layer with thickness over the skin depth of Au. Thus the metadevices are obtained and can be regarded as all-metallic ones.
5. Conclusion
In summary, we propose a platform of all-metallic metasurfaces that can achieve broadband and high efficiency photonic spin-Hall effect in the reflection mode. Since the electric field coupling effect could be enhanced by constructing a similar split ring resonator between adjacent units, the all-metallic S-shape streamline element shows higher conversion efficiency of ∼84% in a broad range of 8-14 µm compared with all-metallic nanobricks. Furthermore, two metadevices are designed to characterize its high performances in the infrared band. The proposed flexibility and good ductility metasurface can be easily scaled to any other spectra and used in various practical domains, such as beam steering, holographic display, portable chiroptical spectrometers, and modern communication systems.
Funding
National Natural Science Foundation of China (61575032).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data produced by numerical simulations in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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