Angular-multiplexed multichannel optical vortex arrays generators based on geometric metasurface

Summary

Recently, metasurface-based multichannel optical vortex arrays have attracted considerable interests due to its promising applications in high-dimensional information storage and high-secure information encryption. In addition to the well-known wavelength and polarization multiplexing technologies, the diffraction angle of light is an alternative typical physical dimension for multichannel optical vortex arrays. In this paper, based on angular multiplexing, we propose and demonstrate multichannel optical vortex arrays by using ultrathin geometric metasurface. For a circularly polarized incident light, the desired optical vortex arrays are successfully constructed in different diffraction regions. Moreover, the diffraction angle of the optical vortex array can be regulated by changing the illumination angle of incident light. Capitalizing on this advantage, the angular-multiplexed recombination of optical vortex array is further investigated. The combination of the diffraction angle of light and optical vortex array may have significant potential in applications of optical display, free-space optical communication, and optical manipulation.

Graphical Abstract

Highlights

• •Ultra-thin angular-multiplexed multichannel vortex array generators are demonstrated
• •Geometric phase is employed to realize the desired phase profiles
• •Generation of various multichannel vortex arrays and recombination of vortex array

Optics; Optical Materials; Geometrical Optics; Metamaterials

Introduction

In 1992, Allen at al. recognized that lights in paraxial regime with spiral phase front manifesting as an azimuthal phase term exp(ilϕ) would carry an orbital angular momentum (OAM) of lħ per photon (Allen et al., 1992), where ϕ is the azimuthal angle and l is topological charge. The striking optical properties of vortex light (OAM light) have attracted great attentions in many areas, such as super-resolution imaging (Tamburini et al., 2006), optical micromanipulation (Dholakia et al., 2008), and detection of rotating objects (Lavery et al., 2013). Especially, the unbounded orthogonal modes of l have provided a new degree of freedom for information encoding to improve the capacity and security of the free-space optical communication systems (Gibson et al., 2004). In order to realize multi-channel communication by vortex beams, vortex light array has been proposed and investigated. Several methods have been put forward to generate the optical vortex array, such as phase diffractive optical elements (Khonina et al., 2001), spatial light modulators (Gibson et al., 2004), and Dammann vortex grating (Lei et al., 2015). However, the bulky size of such elements cannot fulfill the requirement of miniaturization, integration, and multifunction of the modern optical system.

Recently, metasurface (Huang et al., 2012; Ni et al., 2013a; Pu et al., 2015a, 2015b; Yu et al., 2011), a two-dimensional artificial metamaterial, has been taken as a candidate of conventional bulky optical element. One of the important advantages of the metasurface is its great capability of amplitude, polarization, wavelength, and phase manipulation of electromagnetic waves by properly adjusting the geometry and the orientation of the subwavelength scale structures at the ultrathin interface. Flat lenses (Aieta et al., 2012; Yu and Capasso, 2014), meta-holograms (Guo et al., 2019; Huang et al., 2013; Li et al., 2016; Ni et al., 2013b; Zhang et al., 2017), beam splitters (Li et al., 2015; Lin et al., 2013), and multifunctional devices (Chen et al., 2020; Ma et al., 2019; Wen et al., 2016; Zhang et al., 2020a) were realized in an ultrathin and compact way. More recently, metasurface-based optical vortex arrays have been studied (Jin et al., 2017; Liu et al., 2016; Zhang et al., 2020b). To further improve the capacity and security of device, the multichannel vortex arrays based on metasurface were also extensively investigated (Huang et al., 2017; Jiang et al., 2018; Jin et al., 2018; Liu et al., 2016; Ren et al., 2016, 2019). For instance, Huang et al. investigated the generation of three-dimensional volumetric vortex arrays based on ultrathin geometric metasurface (Huang et al., 2017). Along the longitudinal propagation direction, a sequence of coaxial two-dimensional vortex arrays was reconstructed through the metasurface, leading to space multiplexing. On the other hand, the wavelength selectivity of metasurface provides another possibility for the generation of multichannel vortex arrays. Jin et al. reported a wavelength-multiplexed metasurface that could produce different three-dimensional optical vortex arrays by changing the wavelength of the incident light (2018; Jin et al.). In fact, polarization and OAM of light can also be regarded as the multiplexing method to modulate vortex arrays. Jiang et al. demonstrated a spin-dependent two-channel vortex beam generator based on metasurface (Jiang et al., 2018). Ren et al. achieved an OAM-conserving meta-hologram, wherein various holographic images composed by optical vortex arrays appeared when light with corresponding OAM illuminates the designed metasurface (Ren et al., 2019). The flexible electromagnetic control of metasurface has provided versatile multiplexing methods for producing the multichannel optical vortex arrays. In addition to the above proposed multiplexing methods, the diffraction angle of light can also be used to modulate vortex arrays effectively. However, to the best of our knowledge, there have been no reports on the generation of multichannel optical vortex arrays with angular-multiplexed metasurfaces.

In this paper, based on the angular multiplexing, the multichannel optical vortex arrays generators are investigated and experimentally demonstrated by using the ultrathin geometric metasurface. The metasurface consists of an array of elliptical nanoholes with spatially varying orientation. When a circularly polarized light is incident on the nanoholes, it generates the desired phase profile for the excited opposite handedness component. By a proper design of metasurface, various vortex arrays diffract at different angles on the transmission side. The pattern and topological charge of the vortex array in each channel can be independently determined. Particularly, the diffraction angle of the vortex array is related to the illumination angle, which means that one can recombine a new vortex array by regulating the illumination angle of incident light, leading to a remarkable enhancement of the optical information security. The multiplexing approach proposed in our work provides an effective way to increase the storage capacity and encryption security of subwavelength optical devices.

Results and discussions

The angular-multiplexed multichannel vortex arrays mean that a sequence of vortex arrays with various topological charges diffracted in the azimuthal direction, as depicted in Figure 1. The implementation of the function depends on the ultrathin geometric metasurface. The metasurface used in our design is composed of elliptical nanohole arrays in a thin metallic film with desired orientation angle φ with respect to the positive x direction. Under the illumination of circularly polarized light, the elliptical nanohole array provides the desired phase profile to the scattered light of the opposite handedness. The relationship between the phase shift and orientation angle of elliptical nanoholes is Φ = ±2φ, namely Pancharatnam-Berry or geometric phase shift, where the signs “+/−” correspond to the left-handed circular polarization (LCP)/ right-handed circular polarization (RCP) incident light. By controlling the orientation angle of elliptical nanoholes from 0 to π, phase shift covering 0 to 2π can be achieved. In our design, each elliptical nanohole is placed at the center of the hexagonal lattice with a lattice constant of 250 nm. The subwavelength size of the unit cell guarantees that the light emitted by the metasurface would not diffract to the higher diffraction orders apart from the zeroth order. The phase profiles of elliptical nanoholes are simulated by the commercial electromagnetic simulation software of CST Microwave Studio. Figure 2A illustrates the phase profile as a function of the orientation angle of the unit cell at a wavelength of 632.8 nm with LCP incidence. Taking the off-axis illumination into consideration, the phase shifts of the unit cell at the different illumination angles are investigated. It can be seen that the phase change covers full 0 to 2π range when the illumination angle of circularly polarized light changes from 0° to 50°. In general, with the change of rotation angle, the generated amplitude of the scattered opposite helicity light maintains nearly consistent because of the unifying size and shape of the elliptical nanohole, as depicted in Figure 2B. The amplitude profiles under the circumstance of different illumination angles are also simulated. It is shown that the nearly equal transmission amplitude is achieved when the angle of incidence changes from 0° to 50°. The conversion efficiency of the elliptical nanoholes can also be obtained in the simulation, which is about 31%. By elaborately encoding the orientation angle and the arrangement of elliptical nanoholes, the desired function can be achieved.

Figure 1.

Schematic of multichannel optical vortex arrays based on ultrathin geometric metasurface

The lights with different colors represent different diffraction angles. θ_in represents the angle of incidence; θ_xj (i = 1, 2, 3 …) represents the diffraction angle.

Figure 2.

Phase and amplitude profiles of the unit cell

(A) The phase change as a function of the orientation angle of the unit cell with different illumination angles at a wavelength of 632.8 nm.

(B) The amplitude shift as a function of rotation angle of the unit cell with different illumination angles. The period of the unit cell is 250 nm. The long axis and short axis length of the nanohole in the simulation are 200 nm and 110 nm, respectively. The thickness of the gold film is 70 nm. The lines with different colors and symbols represent the simulation results at different incident angles.

To achieve angular multiplexing, we employ the principle of superimposition of holograms (Pu et al., 2015b), which can incorporate the information from all angles in a 2D plane. Various vortex arrays with different additional phase shifts are linearly superimposed. The integrated complex field can be expressed as follows:

$$E_{tot}\left(x,y,\lambda ,l,k_x,k_y\right)=\sum _{j=1}^N{E}_j\left(x\text{'},y\text{'},\lambda ,l,\lambda \right)e^{-i\left(k_{xj}x+k_{yj}y\right)}\text{.}$$ (Equation 1)

where $E_{tot}$ is the complex amplitude of the synthetic multichannel vortex arrays, N represents the total number of vortex array, k_xj = k₀sinθ_xj and k_yj = k₀sinθ_yj are the wave vectors, which determine the diffraction angle of single channel vortex array in the x and y direction, respectively, θ_xj and θ_yj are the diffraction angles relative to the x and y axis, respectively. E_j is the individual complex field of a vortex array without any inclination, which can be written as follows:

$${\mathit{E}}_{\mathit{j}}(x^{\prime },y^{\prime },\lambda ,l,\lambda )=\sum _m\sum _n{A}_{mn}{e}^{i{l}_{mn}}{e}^{-i\left(\frac{2\pi }{\lambda }\right(\sqrt{{(x^{\prime }-x_m^{\prime })}^2+{(y^{\prime }-y_n^{\prime })}^2+f^2}-f\left)\right)}$$ (Equation 2)

where x^’ and y^’ are the local coordinates, and m and n represent the diffraction orders in the x^’ and y^’ directions, respectively, for each single vortex beam in the vortex array. A_mn is the amplitude distribution of single vortex light with a topological charge of l_mn. In order to capture the vortex array at a certain plane, the phase profile of $\frac{2\pi }{\lambda }(\sqrt{{(x^{\prime }-x_m^{\prime })}^2+{(y^{\prime }-y_n^{\prime })}^2+f^2}-f)$ is superimposed onto the vortex beam, where f is the focal length of transmitted light, and (x^'_m y^'_n) represents the focus location of a vortex beam at (m, n) diffraction order. According to the Equations (1) and (2), the diffraction angle and the topological charge of the vortex array can be determined independently.

The light field acquired from Equation (1) can be performed by phase-only modulated metasurface. The phase profile imparted to the metasurface can be written as follows:

$$\text{Φ}(x,y,\lambda ,l,k_x,k_y)=\arg \left(E_{tot}(x,y,\lambda ,l,k_x,k_y)\right)\text{.}$$ (Equation 3)

More remarkably, the diffraction angle of vortex arrays is also related to the angle of incidence, that is, we can regulate the vortex array to the desired diffraction angle by changing the illumination angle of the incident light. Meanwhile, this process allows us to recombine the arrangement form of the vortex array.

To validate the capability of the angular multiplexing, several multichannel vortex arrays generators based on geometric metasurfaces are designed and fabricated. We first perform two angular-multiplexed multichannel vortex arrays generators operating at a wavelength of 632.8 nm. Here, for experimental simplicity and sufficient separation between the two vortex arrays, the channel number of the two samples in design is uniformly set as N = 3, and the diffraction angle of the three light arrays is set as θ_x1 = −40°,θ_y1 = 0°, θ_x2 = 0°,θ_y2 = 0°, and θ_x1 = 40°,θ_y1 = 0°, respectively. In principle, the diffraction angle and number of vortex array are unconstrained. However, considering the size of vortex array, the finite angle range of free space, and the light cross talk, the diffraction angle and channel number of vortex array are limited in the actual design process (detailed discussion shown in Section S1, Supplementary Information). In the numerical simulations, the reconstructed light intensity profile for the first multichannel vortex arrays generator is shown in Figure 3A, where the vortex arrays diffracted in three channels are designed as 1 × 3, 4 × 4, and 4 × 1 vortex array, respectively. The topological charge of all the vortex beams for this generator is uniformly defined as l = 1. For the second multichannel vortex array generator, the light intensity distributions of the vortex arrays at different channels are shown in Figure 3C, where the form of three vortex arrays is defined as 2 × 2 vortex array, rhombus vortex array, and 1 × 3 vortex array, respectively. In order to illustrate the flexibility of the design, the topological charge in the vortex array produced by the second multichannel vortex arrays generator is spatially variant. Then, we resort to Equation (1) to superimpose the lights diffracted at different angles. The corresponding phase profiles obtained by Equation (2) are illustrated in Figures 3B and 3D. Note that the center of the focus plane of vortex array is placed at a distance of 50 μm from the metasurface center.

Figure 3.

Intensity and phase profiles of the multichannel vortex arrays generator

(A) Simulated light intensity distribution of the first multichannel vortex arrays generator. The diffraction angle of the left, middle, and right images θ_x1 = −40^∘, θ_x2 = 0^∘, and θ_x3 = 40^∘, respectively. The topological charge of three channels vortex array is uniformly defined as l = 1. The focal length of vortex array is set as f = 50 μm.

(B) The phase profile of the first multichannel vortex arrays generator.

(C) The theoretical light intensity distribution of the second multichannel vortex arrays generator.

(D) The phase profile of the second multichannel vortex arrays generator.

A scanning electron microscopy (SEM) image of the fabricated metasurface is displayed in Figure 4A. The elliptical nanoholes are milled by using the focused ion beam in a 70-nm-thick gold film on the glass substrate. The effective area of each metasurface is a circle with a radius of 15 μm. Since the scattered lights are diffracted into different angles, it is difficult to capture all vortex arrays on the same plane. As mentioned above, the diffraction angle of the light array is related to the illumination angle of incident light, and the change of the illumination angle will alter the direction of emitted light without affecting the reconstruction of the vortex beam. Therefore, by changing the illumination angle of incident light during the test, three diffraction vortex arrays will be captured separately at the desired diffraction angle. To simplify the measurement, we make the detection plane coaxial with the metasurface to capture the transmission light with 0° diffraction angle, as depicted in Figure 4B.

Figure 4.

SEM image and experimental setup of the fabricated metasurface

(A) Schematic of SEM image of the first angular-multiplexed multichannel vortex arrays generator. The major axis and minor axis of the elliptical nanohole are 200 nm and 110 nm, respectively.

(B) Schematic of experimental setup.

Figure 5A presents the experimental results of the first multichannel vortex arrays generator. The switching among different vortex array channels is achieved by tuning the illumination angle of the incident light. When the illumination angle is set as θ_in = 40^∘, the 1 × 3 vortex array appears at the 0° diffraction angle at the position of z = 50 μm (left image in Figure 5A). The light array changes to a 4 × 4 vortex array as the light is normally incident on the metasurface (middle image in Figure 5A). A 4 × 1 vortex array is reconstructed when the illumination angle of light is adjusted as θ_in = −40^∘ (right image in Figure 5A). The measured results of the second multichannel vortex arrays generator are depicted in Figure 5B. When the illumination angle of light is set as θ_in = 40^∘, θ_in = 0^∘, and θ_in = −40^∘, respectively, a 2 × 2 vortex array (left image in Figure 5B), rhombus vortex array (middle image in Figure 5B) , and 1 × 3 vortex array (right image in Figure 5B) successively appear in the imaging area. The topological charge in each vortex array is variant, which agrees well with the theoretical results. The maximum field angle of the generated vortex array for the two generators is about 31°, which is less than the diffraction angle difference of the two adjacent vortex arrays (the difference is 40°). Therefore, there is no cross talk between the reconstructed vortex arrays. Although the generators are designed at the wavelength of 632.8 nm, it also can work at other wavelengths owing to the dispersion-less phase property of the geometric metasurface. We verified the broadband property of the designed generators by measuring the diffraction intensity profiles at different wavelengths from 532 nm to 670 nm, as shown in Figures S3 and S4 (Supplementary Information). Subsequently, the conversion efficiency defined as the ratio of the vortex arrays beam to the overall transmitted power is measured, which is about 18% at wavelength of 632.8 nm in the experiment. Compared with the numerical result, the reduction may originate from the light reflection, experimental errors, and imperfect fabrication. The conversion efficiency can be further improved by using the dielectric metasurface (Zhang et al., 2020b) or changing to the multilayer reflective type metasurface (Zheng et al., 2015).

Figure 5.

Schematic of measured results of the two fabricated generators

(A) Measured results of the first multichannel vortex arrays generator for different illumination angles.

(B) Measured results of the second multichannel vortex arrays generator for different illumination angles.

The experiment results of the fabricated multichannel vortex arrays generators indicate that the diffraction angle of multichannel vortex arrays can be manipulated by changing the illumination angle of incident light, which means that one can recombine the arrangement form of the diffracted vortex array by regulating the illumination angle. We further investigate the recombination of the vortex array by employing angular multiplexing based on geometric metasurface. As depicted in Figure 6A, the desired vortex array is reconstructed at a certain diffraction angle only when two beams with different illumination angles are incident on the metasurface simultaneously. The purpose of the design is to generate a number of “8” consisting of vortex beams (right image in Figure 6B) with topological charge of 1 along the 0° diffraction angle. The implementation of this type of vortex array requires the combination of two kinds of vortex arrays, namely, one is the letter “E” (left image in Figure 6B) and the other is the number “1” (middle image in Figure 6B). The initial diffraction angle of two kinds of vortex arrays is θ_x1 = −40^∘ and θ_x2 = 40^∘, respectively. Thus, when the circularly polarized light is normally incident on the device, there is no vortex array reconstructed at the 0° diffraction angle. While when the incident angle of light is only set as θ_in = 40^∘ or θ_in = −40^∘, the letter “E” or number “1” appears alone at the 0° diffraction angle. The complete vortex array can be reconstructed at 0° diffraction angle under the condition that two incident light beams with different illumination angles irradiate the sample at the same time. The phase profile of the generator is shown in Figure 6C. The performance of the fabricated metasurface is measured by modifying the experimental setup shown in Figure 4B. In order to realize the simultaneous illumination of two incident light beams, a beam splitter is adapted to divide the He-Ne laser into two incident light beams. The detective system is coaxial with the fabricated metasurface to receive the transmission light propagated at the 0° diffraction angle. The illumination angle of two incident lights is adjusted to 40° and −40°, respectively. When the illuminate light at 40° is blocked, the image of number “1” is detected at the plane 50 μm away from the metasurface, as depicted in middle image in Figure 6D. While the detected vortex array profile changes to the letters of “E” as the incident light with the angle of −40° is blocked (left image in Figure 6D). The complete vortex array appears when two light beams strike the sample simultaneously, as illustrated in right image in Figure 6D. The measured light intensity images agree well with the theoretical results. The measured broadband effect of this designed metasurface is depicted in Figure S5 (Supplementary Information). The flexible angle control of the angle-multiplexed metasurface enables us to recombine the form of vortex array at will. Such a method can improve information diversification and safety to a certain extent. In addition, we can employ polarization as another degree of freedom to modulate the generated vortex array to further increase the multiplexing capacity and safety.

Figure 6.

Schematic of the recombination of vortex array and the characterization results

(A) Schematicof angular-multiplexed recombination of vortex array.

(B) Theoretical results of vortex array recombination generator. The light intensity images at left, middle, and right are the letter “E” diffracted to an angle of −40°, the number “1” diffracted to an angle of 40°, and recombined complete vortex array, respectively. The topological charge of each vortex beam is 1.

(C) The phase profile of vortex array recombination generator.

(D) The corresponding experimental results.

Conclusion

In summary, we demonstrate the manipulation of angular-multiplexed multichannel vortex arrays based on ultra-thin geometric metasurfaces. Under the illumination of circularly polarized light, the metasurface emits various vortex arrays with different diffraction angles. And the topological charge of vortex array is spatially variant. Furthermore, the diffraction angle of the reconstructed multichannel vortex arrays can be adjusted by changing the illumination angle of the incident light. Capitalizing on this advantage, a metasurface that can recombine a new vortex array is realized. The experimental results agree well with the theoretical results. Our approach provides an effective way to increase the information capacity and safety and offers a new avenue for many applications such as optical communication, optical display, and optical trapping.

Limitations of the study

Restricted by the limited measuring space and the microscopic detection system is fixed, we cannot detect all multichannel vortex arrays at the same plane. The diffracted multichannel vortex arrays are separately detected by changing the illumination angle.

Methods

All methods can be found in the accompanying Transparent Methods supplemental file.

Published: February 19, 2021