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Abstract
Optical metasurfaces empower complete wavefront manipulation of electromagnetic waves and have been found in extensive applications, whereas most of them work in either transmission or reflection space. Here, we demonstrate that two independent and arbitrary phase profiles in transmission and reflection spaces could be produced by a monolayer all-dielectric metasurface based on the asymmetric photonic spin-orbit interactions, realizing full-space wavefront independent manipulation. Furthermore, the supercell-based non-local approach is employed to suppress crosstalk between adjacent nanopillars in one supercell for broadband and high-efficiency wavefront manipulation in full space. Compared with the conventional unit cell-based local approach, such a method could improve efficiency about 10%. As a proof of concept, two metadevices are designed, in which the maximum diffraction efficiencies are ∼95.53%/∼74.07% within the wavelength range of 1500-1600 nm in reflection/transmission space under circularly polarized light incidence. This configuration may offer an efficient way for 2π-space holographic imaging, augmented reality, virtual reality technologies, three-dimensional imaging, and so forth.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces, the two-dimensional equivalence of metamaterials, can flexibly manipulate the polarization, phase, amplitude, and frequency of electromagnetic waves by the collective contributions of subwavelength nanostructures [1,2]. Many exotic phenomena and extraordinary functionalities have been found, such as the spin Hall effect [3], invisibility cloaking [4], dynamic display [5,6], full-color printing [7], augmented reality [8], generation of vortex beams [9], especially for the asymmetric photonic spin-orbit interactions (APSOIs) [10,11]. By the combination of the geometric phase (GP) and waveguide propagation phase (WPP), independent modulation of the left-handed and right-handed circularly polarized (LCP and RCP) light can be achieved according to the APSOIs, which provides an unprecedented opportunity for the polarization-dependent holography [10], asymmetric transmission [12], multistate switching of photonic angular momentum [13], broadband achromatic lenses [14], edge detection [15], and so forth [16–18]. However, most of these metasurfaces realize functional decoupling by changing polarization, frequency (wavelength), and incident angle of the incident light, which only work in either transmission or reflection space, that is, another space is abandoned [17,19–22]. Therefore, its spatial degrees of freedom need to be further exploited for various applications, such as real 2π-space holographic imaging, full-space multicolor display, among many others.
Previously, the cascaded metallic scheme commonly operating in the gigahertz (GHz) range is employed. However, such a multilayer design increases the fabrication burden and suffers from the large absorption loss that hinders its expansion to other frequencies [23–26]. Based on the wave vector control method, single-layer plasmonic and all-dielectric metasurfaces have shown the capabilities of full-space manipulation, in which the spurious grating orders or evanescent waves reduce the efficiency under the conditions of diffraction angle and critical angle [27–29]. Moreover, the efficiency restriction likewise exists in the single-layer all-dielectric metasurface due to the application of the multipolar interference principle [30]. Another approach, relying on the spatial arrangement of structures (such as segmented and bilayer schemes), has been proposed [31,32]. Nevertheless, this way may reduce pixel utilization or increase the fabrication cost. Recently, the configuration of the supercell, including two/four nanostructures in one period, is designed and applied in giant circular/linear asymmetric transmission [12,33,34], independent amplitude control [35], multiple printing-image [36], and so forth [17,19,28]. It may surmount the abovementioned constraints for full-space control, but the crosstalk between adjacent nanopillars in one supercell is commonly ignored resulting in the abrupt phase and limited working bandwidth of each supercell. Besides, this abrupt phase may hinder the precise full-space wavefront independent manipulation.
Here, a platform of monolayer all-dielectric metasurfaces is proposed to achieve full-space independent wavefront manipulation based on the APSOIs that yield two independent phase profiles in reflection and transmission space. Benefitting from the supercell-based non-local approach, the crosstalk between adjacent nanopillars in one supercell can be efficiently suppressed. To show its high performance, two metadevices are designed to demonstrate the spatial asymmetric photonic spin-Hall effect and full-space arbitrary and independent wavefront manipulation. This broadband and high-efficiency full-space wavefront independent manipulation configuration may be found in many potential applications in 2π-space holographic images, augmented reality or virtual reality technologies, three-dimensional imaging, and so forth.
2. Concept and design
The schematic of the full-space arbitrary and independent wavefront manipulation metadevice with supercells based on the APSOIs is shown in Fig. 1. To achieve full-space independent wavefront manipulation, the supercells should satisfy two conditions: (1) The incident lights with different spin states (LCP and RCP) will be split into transmission and reflection space, respectively; (2) Two independent phase profiles could be obtained by supercells in different spaces. Previous research has demonstrated that the cross-polarized light will be split into full space when there is a phase difference of π between adjacent nanopillars in one supercell according to the principle of constructive and destructive interference [12]. To satisfy condition (2), integer parity design has exposed that the back propagation of light can double the phase retardation fron each nanopillar due to the additional propagation in the nanopillar [28]. Furthermore, the interactions between adjacent nanopillars can be suppressed to reduce the abrupt phases with the supercell-based non-local approach [37]. Therefore, by the combination of the GP(θ) and WPP(β), two independent phase profiles of Φr = 2θ+β and Φt = -2θ may be obtained in reflection and transmission space, respectively. As illustrated in Fig. 1, this multi-functional metadevice can produce a focusing optical vortex beam in reflection space and a focused beam in transmission space under circularly polarized (CP) light illumination from the substrate.
Fig. 1. The schematic of the multi-functional metadevice based on the APSOIs. The wavefront independent manipulation in full space is achieved. It can generate a focusing optical vortex/a focused beam in reflection/transmission space. The LCP-RCP and RCP-LCP indicate that the incident LCP/RCP light is converted to reflected/ transmitted RCP/LCP light, respectively.
To explore the physical mechanism of the multi-functional metadevice (in Fig. 1), we begin with the analyses of the principle of constructive and destructive interference using the unit cell-based local approach (Fig. S1, Supplement 1). For simplicity, each nanopillar is recognized as a local transparent half-wave plate that maximally converts CP incident light into transmitted light with opposite helicity. When a beam with arbitrary polarization Ei normally illuminates on a supercell, the total phase difference of Δφ between two nanopillars (in one supercell) is expressed as [12]
where θ0 = -π/4 and β0 = π/2 are the rotation angle and WPP difference between two adjacent nanopillars, respectively. σ = ±1 is the spin state of CP light incidence, respectively, which offers Δφ = π/0 for LCP/ RCP illumination. Therefore, the incident LCP/RCP light can be split into reflection/transmission space due to destructive/constructive interference. Within this approach, supercells are constructed by individually designing each unit cell, and the crosstalks between adjacent cells are commonly ignored, which leads to the abrupt phase and low efficiency of supercells as shown in Supplement 1 Figs. S1–S3.On the contrary, if the θ0 is set to -π/4 according to Eq. (1) it is possible to split incident CP light in full space by directly designing the supercells, i.e., employing the supercell-based non-local approach. Besides, it has demonstrated that the back propagation of light can double the phase retardation fron each nanopillar due to the additional propagation in the nanopillar based on the unit cell-based local approach [28]. In other words, when the WPP of the transmitted light covers the 0-π range, the corresponding reflected light will carry the phase covering the whole 2π range (Fig. S2, Supplement 1). Benefitting from the supercell-based non-local approach can suppress the crosstalk in one supercell and the abrupt phase. Therefore, it is possible to generate additional WPP (β) only for reflected light [33] The reflected (Er) and transmitted (Et) beams can carry two different phase profiles according to the APSOIs, written as
Without losing the universality, the proposed configuration for full-space wavefront independent manipulation is aimed at a wavelength of 1550 nm (the communication wavelength in the near-infrared range). A supercell, comprising two pairs of twin blue and yellow nanopillars is schematically illustrated in Figs. 2(a)-(b). Each nanopillar is located at the center of the subunit cell with the half period (P = 1300 nm) of a supercell, in which blue and yellow nanopillars have the same height (H = 1000 nm) but different sizes. The materials of the substrate and nanopillars are sapphire (Al2O3) and silicon (Si), respectively, whose refractive indexes are from the Palik’s Handbook [38]. The rotation angle between two adjacent nanopillars is set as -45° (θ0) to split incident CP light in full space according to Eq. (1).
Fig. 2. (a) 3D view and (b) top view of a supercell. The cross-polarized (c) reflected and (e) transmitted amplitudes and (d), (f) corresponding WPP shifts of 12 supercells in the wavelength range of 1500-1600 nm for CP light incidence from the substrate.
According to the supercell-based non-local approach, 12 supercells with a phase interval of ∼π/6 are selected (their geometrical parameters are listed in Supplement 1). Their simulated results calculated by the CST Microwave Studio based on the finite element method (FEM) are shown in Figs. 2(c)-(f). In Fig. 2(c), the supercells show a high average cross-polarization amplitude of ∼0.86 within the wavelength range of 1500-1600 nm for LCP incidence in reflection space. Furthermore, the WPP shift is approximately linear and covers the whole 2π range as illustrated in Fig. 2(d). On the other hand, most of the energy is transmitted, straightforwardly, under RCP illumination in Fig. 2(e). The transmitted cross-polarized amplitude of the 12 supercells exceeds ∼0.9 (in the wavelength range of 1500-1600 nm) on average, while their phase (WPP) shifts maintain nearly unchanged as displayed in Fig. 2(f). These performances are affected by the dimension of supercells, thus the amplitude increases/reduces as H, P, L (L1 and L2), and W (W1 and W2) increase/reduce. This phenomenon may be affected by the red/blue shift of amplitude spectra and interactions of electric and magnetic fields of supercells [22,33]. Moreover, the red/blue shift can be observed in transmitted and reflected phase spectra as the H, L, and W increase/reduce, but the effects of P varying from 1260 to 1340 nm on the phase spectra are small and can be neglected as shown in Supplement 1. The electric field distributions Ex of the designed supercells under CP light incidence are illustrated in Supplement 1. It demonstrates that each supercell can provide Δφ = π/0 for LCP/ RCP illumination leading to destructive/constructive interference to split the incident light with different spin states into different spaces. Then, when we generate one phase profile by the combination of the GP and WPP in reflection space and another phase profile only relying on the GP in transmission space, it is possible to achieve independent and arbitrary wavefront manipulation in full space.
3. Spatial asymmetric photonic spin-Hall effect
Photonic spin-Hall effect (PSHE) depicts the spin-dependent splitting of light caused by spin-orbit interactions that describes the coupling between the spin and orbit degrees of freedom of photons during the transport of light [11,39]. Different from the conventional symmetric/asymmetric PSHE that is commonly implemented in either transmission or reflection space, the schematic of them in full space is shown in Fig. 3(a) (left/right). For spatial symmetric PSHE, the incident LCP/RCP light is diffracted in opposite directions, such as -1st/+1st order in reflection/transmission space, which is caused by the symmetric photonic spin-orbit interactions, imprinted with a geometric phase ±2θ. In Fig. 3(a) (right), the spatial asymmetric photonic spin-Hall effect based on the APSOIs is demonstrated with an efficient metadevice. It can diffract the incident LCP/RCP light to arbitrary directions in full space and the corresponding schematic top view is inserted in Fig. 3(b). This gradient metadevice (using the supercell-based non-local approach) with sizes 24P×P shows different deflection angles for LCP/RCP incidence in reflection/transmission space, in which the deflection angles in two different spaces are set as sin−1[λ/(24 P) + λ/(12 P)] and sin−1[−λ/(24 P)] (λ = 1550 nm is the operating wavelength), respectively. At the bottom of Fig. 3(b), it plots the normalized far-field intensity distributions calculated by the finite integral technique (FIT) in the CST. The deflection angles in reflection and transmission space are about 8.6° (θr) and -2.8° (θt), respectively, which agree well with the theoretical predictions.
Fig. 3. (a) The schematic of the spatial symmetric/asymmetric (left/right) PSHE. (b) Top view of the metadevice and its normalized far-field intensity distributions under the LCP and RCP illumination. (c) The diffraction efficiencies (top) and extinction ratios (bottom) as a function of the wavelength. (d)-(e) The x-components of the electric fields on the xoz plane for LCP and RCP excitation, respectively.
In Fig. 3(c), this metadevice diffracts the incident LCP light to the -3rd order with a high average diffraction efficiency (∼91.1%) and an extinction ratio (∼19.1 dB) in the range of 1500-1600 nm, in which corresponding maximums are ∼95.53% (at 1566 nm wavelength) and ∼24 dB (at 1400nm wavelength), respectively. The diffraction efficiency is defined as the ratio of the energy of the designed diffractive order to the total energy of the reflected/transmitted light [33]. The extinction ratio is defined as ER = 10*log(P1/P2), where P1 and P2 present the power of the designed diffractive order (LCP/RCP) and the power of 0th order (RCP/LCP) in reflection/transmission space, respectively [28]. Besides, it can be observed that the diffraction efficiency and extinction ratio are ∼88.94% and ∼20.5 dB at the wavelength of 1550 nm, respectively. Compared with the metadevice based on the unit cell-based local approach in Supplement 1 Fig. S6, such a supercell-based non-local approach could increase efficiency ∼10% in the wavelength range of 1500-1600 nm.
However, almost all the power is transmitted and deflected to the +1st order by this metadevice under RCP incidence. In the wavelength range of 1500-1600 nm, the diffraction efficiency and extinction ratio exceed ∼72.7% (the maximum is ∼74.07% at 1563 nm) and ∼18.3 dB on average, which are over ∼68.92% and ∼14.86 dB at 1550 nm wavelength, respectively. In fact, the working bandwidth of this device can be expanded to 1400-1700 nm with an average diffraction efficiency of ∼68.25% and an extinction ratio of ∼14.25 dB. It reveals broader working bandwidth than the device with the unit cell-based local approach (Fig. S6, Supplement 1). The x-components of the electric field distributions (in Figs. 4(d)-(e)) further verify that the energy is deflected in reflection and transmission space for LCP and RCP illumination, respectively, that is, the achievement of full-space wavefront independent manipulation.
4. Full-space arbitrary and independent wavefront manipulation
To further demonstrate the arbitrary and independent wavefront manipulation in full space, a multi-functional metadevice that could generate a focusing optical vortex (FOV) beam and a focused beam in reflection and transmission space, respectively, is designed as depicted in Fig. 4(a). Vortex beams, featuring a doughnut intensity distribution and a helically structured wavefront exp(ilφ) (φ is the azimuthal angle), have been extensively applied in information storage [40], optical trapping [41], holography [42,43], and so forth [44]. The phase profile of the FOV in Fig. 4(a) (left) is composed of the superposition of a focusing phase and a vortex phase, which could be expressed as [45]
Fig. 4. (a) 3D view of the metadevice (middle), phase distributions (on the z = 0 plane) of the FOV (left), and focused beam (right). The theoretical ((b), (e)) and simulated ((c), (f)) intensities (on the focal plane) in reflection and transmission space for LCP and RCP incidence, respectively. (d), (g) The normalized sectional intensity curves of theory and simulation calculations along the x-direction.
For LCP light incidence, the FOV with the doughnut-shaped focal spots emerges in reflection space on the z = fr plane, whose theoretical and simulated results, calculated by vectorial angular spectrum theory and the FIT in the CST, show good agreement as displayed in Figs. 4(b)-(c), respectively [48]. Corresponding efficiencies are up to ∼85.63% (in theory) and ∼72.18% (in simulation), in which the efficiency is defined as the ratio of the optical power of the FOV in the region (with a radius of three times full width at half maximum (FWHM)) to the reflected power [45]. Their normalized sectional profiles along the x-direction are shown in Fig. 4(d). The simulated FWHM is ∼2.59 μm, which is nearly consistent with the theoretical calculation (∼2.5 μm). Some disturbances in simulation may originate from interactions between supercells where the amplitude and phase are imperfect as we expected. Moreover, the arrays of the FOV with different topologic charges could be acquired by holography technology for various applications.
When the spin state of the incident light is changed to RCP, it passes through the metadevice and then is focused on the focal plane (z = ft). The theoretical intensity distribution of the focal spot in Fig. 4(e) agrees well with the simulated result in Fig. 4(f). Corresponding focusing efficiencies reach ∼88.2% (theory) and ∼76.35% (simulation), respectively, whose definition is similar to the efficiency of FOV, i.e., the ratio of the focused power in the region (with a radius of three times (FWHM)) to the transmitted power. Their normalized intensities along the x-direction reveal that the simulated FWHM of ∼9.332 μm approximatively approaches the theoretical calculation of ∼9.122 μm and both of them reach the diffraction limit (1.22λ/2NA = 9.09 μm, NA = 0.104 is the numerical aperture) [49]. The slight difference may be caused by the fact that theoretical calculations assume perfect phase distributions and uniform amplitude. These results indicate that this metadevice could achieve arbitrary and independent wavefront manipulation in full space with high performances.
To fabricate the designed metadevices, the potential fabrication roadmap is shown in Fig. S7 [50]. Firstly, electron beam lithography (EBL) can be used to transfer the patterns in a positive electron resist (Pr) on a silicon-on-sapphire (SOS) wafer (silicon thickness: 1000 nm). Then, a chromium (Cr) layer is deposited using electron beam evaporation to reverse the generated pattern with a lift-off process. Finally, it is used as a hard mask for inductively coupled plasmas (ICP) etching and is then removed in the aqueous solution.
5. Conclusion
In summary, we propose a platform of monolayer all-dielectric metasurfaces to achieve full-space independent wavefront manipulation. With the supercell-based non-local approach, the incident circularly polarized light is split into different spaces with high efficiency due to the suppression of crosstalk in one supercell. Furthermore, two independent and arbitrary phase profiles are generated in full space according to the asymmetric photonic spin-orbit interactions. To verify the proposed method, a spatial asymmetric photonic spin-Hall effect metadevice, diffracting incident left-/right-handed circularly polarized light to -3st/+1st order orders in reflection/transmission space with the average efficiency of ∼91.1%/∼72.7% (in the range of 1500-1600nm), is designed. In addition, another metadevice that could generate a focusing optical vortex beam (in reflection space) and a focused beam (in transmission space) is proposed to demonstrate its versatility. It is believed that this work would have extensive applications in display technology, microscopy technology, and computer science.
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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