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Abstract
The multi-channel perfect vortex (PV) array based on metasurface has important applications in optical communication, particle manipulation, quantum optics, and other fields due to its ultra-thin structure and excellent wavefront control ability. However, it is very challenging to utilize a single metasurface to simultaneously achieve independent channel PV arrays at different wavelengths with low crosstalk and low structural complexity. Here, we propose and design a single rectangular structured metasurface based on TiO2, achieving a multi-channel PV beam array with dual-wavelength and dual-polarization multiplexing. Simulation and experimental results show that when two orthogonal linearly polarized beams with wavelengths of 532 nm and 633 nm are incident on the metasurface, clear PV arrays with corresponding topological charge arrangements can be obtained in different diffraction regions of the same observation plane. The metasurface proposed in this article can enhance the channel capacity of a PV beam array through wavelength-polarization-multiplexing, thus having important application potential in spatial information transmission, high-dimensional information storage, and secure information encryption.
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1. Introduction
Vortex beam (OV) is a special type of beam that carries orbital angular momentum (OAM) with a circular distribution of intensity, zero central intensity, and no diffraction effect [1,2]. It is widely used in optical trapping [3,4], nonlinear optics [5,6], and information transmission [7,8] and other fields. In the field of information transmission, due to the difficulty that the diameter of the optical ring of traditional vortex light enlarges with increasing topological charge, the information capacity per unit area cannot meet the growing demands of information transmission. The Perfect Vortex (PV) [9], with its ring diameter independent of the topological charge, can break through the limitation of the number of multiplexed traditional vortex beams in a finite cross-section. Furthermore, in terms of spatial freedom, the use of vortex beam arrays can further enhance information bandwidth. Correspondingly, researchers have proposed different implementation methods for vortex beam arrays, whose core devices mainly include phase type Diffractive Optical Elements(DOE) [10], spatial light modulator [11], Dammann vortex grating [12], etc. However, these devices may have drawbacks such as high system complexity, low integration, and single function, making it difficult to match with existing highly integrated information processing systems.
Metasurface has the characteristics of lightness, planarization, and easy integration. With the characteristics of its ability to flexibly and effectively regulate the amplitude, phase, polarization, and other characteristics of electromagnetic waves in different bands [13–15], it has significant advantages in generating optical vortex and vortex arrays. In 2017, Huang et al. [16] proposed a three-dimensional vortex array thin layer dielectric metasurface capable of generating independently controllable topological charges. In the same year, Zhang et al. [17] proposed a geometric phase-type metasurface capable of generating focused 3D PV beams in a wide wavelength range of 600-1000$nm$. The researchers also proposed different vortex beam and array generation methods based on metasurface multi-channel multiplexing by matching the incident conditions of light with different OV modes. For example, multiplexing the incident wavelength with OAM [18], multiplexing the polarization state with OAM [19], multiplexing the incident angle with OAM [20], etc. In 2018, Jin et al. [18] proposed a wavelength multiplexing type metasurface that can achieve differentiated OV array generation under different wavelengths of incident light. In 2021, Xie et al. [19] proposed a polarization multiplexing type metasurface that achieves the generation of PV beams with topological charges varying with the incident polarization. In the same year, Jin et al. [20] proposed an angle multiplexing metasurface that generates an OV array with a style that can change with the incident angle. However, it is still challenging to generate such independent PV arrays that have arbitrary distribution of topological charge, ring size with arbitrary position, and multiple information channels with low crosstalk, using metasurfaces with low structural complexity in different wavelength channels. This is because a simple structure is difficult to achieve independent phase control under different wavelength incident conditions, and it is also difficult to obtain the phase distribution corresponding to the required array style according to design requirements. Therefore, studying the generation of independent PV arrays with low crosstalk and multiple information channels in different wavelengths based on metasurfaces is of great significance, and can significantly increase the information capacity per unit cross-section.
In this article, we propose a metasurface based on a simple $\text {TiO}_2$ rectangular structure, which achieves independent dual-wavelength-polarization multiplexing multi-channel PV array generation. When two orthogonal linearly polarized lights with a wavelength of 532$nm$ and 633$nm$ are vertically incident on a metasurface, two different styles of PV arrays with independent and low crosstalk can be generated based on the differential control characteristics of the anisotropic metasurface meta-atoms under different incident conditions. In addition, we also obtained a diverse distribution of PV arrays with freely set topological charges, diffraction regions, and PV ring diameters at different wavelengths through simulation. Finally, based on the simulation optimization results, we designed and fabricated a metasurface based on $\text {TiO}_2$. We experimentally observed clear PV array patterns under 532$nm$ $x$-polarized and 633$nm$ $y$-polarized incident beam. The transmission efficiency is 57% and 64%, and the diffraction efficiency is 34% and 38%, respectively. The multi-wavelength PV array generation method based on simple structured metasurfaces designed in this article has the characteristics of low crosstalk, high information channel capacity, and ease of manufacture. It can be applied to larger capacity information transmission and thus has potential application value in future high-capacity signal transmissions such as optical interconnection and optical networks.
2. Theoretical deduction and design method
2.1 PV array generation theory
In this work, we use the characteristics of anisotropic meta-atom with different phase control capabilities for orthogonal linearly polarized light to design a metasurface for generating PV beam arrays.Figure 1(a) is the schematic diagram of the metasurface to generate PV arrays of different distributions of topological charges and wavelength generated by metasurfaces under the incidence of orthogonal linearly polarized light at wavelengths of 532$nm$ and 633$nm$. The meta-atom is composed of a single rectangular nanorod on $\text {SiO}_2$ substrate, as shown in Fig. 1(b), where $P$ is the periods of meta-atom of the metasurface in the $x$ and $y$-directions; $H$ is the height of the rectangular $\text {TiO}_2$ nanorod; $L$ and $W$ are the structural parameters of the rectangular $\text {TiO}_2$ nanorod in the $x$ and $y$- directions, respectively; $P$ and $H$ are fixed constants; and $L$ and $W$ are variables.
Fig. 1. (a) Schematic diagram of a two-dimensional PV array generated by metasurface under incident orthogonal linear polarization conditions at 532 nm and 633 nm. (b) Meta-atom composed of $\text {TiO}_2$ nanorods and $\text {SiO}_2$ substrate.
To achieve PV array generation, we need to obtain the phase distribution map of the PV array generated at two wavelengths according to the design requirements. Firstly, to obtain a single PV beam, we need to superimpose the phases of the spiral phase plate, axicon, and Fourier transform lens to obtain the phase distribution required to generate a PV beam [17]:
In the above equation, $x$, $y$ represents the position coordinates relative to the center origin, $\varphi _{\text {axicon}}$ represents the phase of the axicon, where $d$ represents the period of the axicon, $\varphi _{\text {spiral}}$ represents the spiral phase corresponding to the optical vortex with a topological charge of $l$, $\varphi _{\text {lens}}$ represents the phase distribution of the Fourier transform lens with a focal length of $f$, and $\lambda$ is the wavelength of the incident light. The topological charge and the period of the axicon d of PV can be freely set. Further analysis of the relationship between the shape of the PV beam and its intrinsic parameters is detailed in Supplement 1 Fig. S1. Arranging PV beams with different parameters according to a specified array results in a two-dimensional PV beam with a larger information capacity. To achieve the specified array layout of different PVs, we adopted the commonly used Dammann phase grating, whose phase distribution is represented as: [21]
Here, we simulated array structures with incident light of 532$nm$ $x$-polarization, and 633$nm$ $y$-polarization, respectively. The styles and corresponding phase distributions are shown in Fig. 2:
Fig. 2. (a),(b) The PV array simulation diagram obtained by changing the topological charge of the PV at each diffraction order. Under the conditions of orthogonal linearly polarized incident wavelengths of 532 nm and 633 nm, the focal length of the Fourier lens $f=15$ mm, the period of the Dammann grating fringes $\varLambda _x=6\mu m,\varLambda _y=8\mu m$, and the diffraction order are set to $\left ( 4,\pm 4 \right ) ,\left ( -4,\pm 4 \right )$ (532 nm) and $\left ( \pm 4,0 \right ) ,\left ( 0,\pm 4 \right )$ (633 nm), respectively, while maintaining the axicon period of the PV. (c),(d) The phase distributions that can generate the diffraction results in (a) and (b).
In addition, to further demonstrate the high degree of freedom of the array generation, we also simulated many more complex PV arrays of symbols ‘$\square$ ’, ‘$S$’, ‘$Z$ ’, ‘$U$’ and different kinds of ‘$+$’ with different combinations of ring diameters, topological charges, and wavelengths, as shown in Fig. 3. The modes and diffraction levels of PV to generate symbols in each array are elaborated in detail in Supplement 1 Fig. S2 and the following tables. Based on the simulation results, we have achieved the function of independently setting the topological charge and ring radius of PV at different wavelengths and diffraction levels.
Fig. 3. Under the orthogonal linearly polarized incident conditions of 532 nm and 633 nm, the spacing between the Dammann grating fringes are $\varLambda _x=\varLambda _y=16\mu m$ and the focal length of the lens $f=15$ mm are set. By setting the diffraction order $(m, n)$, topological charge $l$, and axicon period $d$ of each PV, array distributions of different styles can obtained. The specific parameters of PV in the array can be found in Fig. S2 and Tables S1-S8 of Supplement 1.
2.2 Theory and design of metasurface
To achieve the above simulation results under different incident conditions, we need to design the meta-atoms corresponding to each position of the metasurface reasonably, in order to obtain an accurate phase response. When the incident light is perpendicular to the metasurface element, the relationship between the transmitted electric field and the incident electric field is expressed as [22,23]:
In this work, the meta-atoms are composed of $\text {TiO}_2$ rectangular nanopillars and $\text {SiO}_2$ substrate. The height of the rectangular pillar is $H=600nm$ uniformly, the unit periods in both directions are $Px=Py=500nm$ and the structural parameters $L$ and $W$ in the $x$ and $y$-directions are ranged from 50$nm$ to 450$nm$ with a step size of 5$nm$. The Finite Difference Time Domain (FDTD) algorithm is used to establish a library of phase shift and transmission efficiency response to the meta-atom, where $x$ and $y$-directions are set to periodic, and $z$-direction is set to perfectly matched layer (PML). 532$nm$ $x$-polarized light and 633$nm$ $y$-polarized light are incident from the $\text {SiO}_2$ substrate into the rectangular $\text {TiO}_2$ nanorods, and a monitor is placed above the rectangular $\text {TiO}_2$ nanorods to record the phase and transmission of the output light field. The simulation results are shown in Fig. 4, which illustrates the relationship between the phase shift and transmission efficiency with the structural parameters $(L, W)$ of the rectangular pillar with respect to 532$nm$ $x$-polarization and 633$nm$ $y$-polarization, respectively. The figure shows that $\text {TiO}_2$ nanorods can exhibit high transmission efficiency (>65%) for both incident wavelengths in some regions, and their phase modulation range can cover the full range of 0-2$\pi$.
Fig. 4. The library of the electromagnetic response of meta-atoms obtained through FDTD simulation. (a),(c) Normalized phase modulation $\varphi _x$ and transmission efficiency $T_x$ of $x$-polarized incident light with a wavelength of 532 nm. (b),(d) Normalized phase modulation $\varphi _y$ and transmission efficiency $T_y$ of $y$-polarized incident light with a wavelength of 633 nm.
Based on the required phase distribution from our previous works, we can select the size of the rectangular column corresponding to the phase arrangement required to generate the vortex beam array, thereby constructing a metasurface for generating the vortex beam array. Here, to select the most suitable combination of meta-atoms, we have established a scientific evaluation function [24,25]
3. Result and discussion
The metasurface designed in this article is composed of 512 $\times$ 512 meta-atoms. We selected two phase distributions corresponding to the PV array pattern shown in Fig. 2 as the target phase of the metasurface, and selected meta-atoms combinations from the meta-atom library that can simultaneously satisfy two sets of phases under two wavelengths to form the designed metasurface device. In the simulation process, we first use FDTD algorithm to simulate the entire metasurface and obtain the light field distribution at the back surface of the metasurface after modulation of light waves with different wavelengths and polarization states. Then, we use the Fresnel–Kirchhoff diffraction integral to calculate the propagation of light waves in free space and obtain the corresponding receiving plane light field distribution at the specified distance. The diffraction simulation results are shown in Fig. 6(a)–(c), where the average transmission efficiency of $x$-polarized 532 $nm$ light incident is 68.0%, and the average transmission efficiency of $y$-polarized 633 $nm$ light incident is 74.4%. The diffraction efficiency is 40.6% and 54.1%, respectively. The transmission efficiency is defined as the ratio of the total energy of the receiving plane to the power of incident beam on the metasurface, while the diffraction efficiency is defined as the ratio of the power of PV rings to the power of incident beam.
Our work uses the Atomic Layer Deposition (ALD) method [26] to fabricate the designed metasurface, the manufacturing process of metasurfaces is detailed in Fig. S3, and the electron microscopy scanning image of the metasurface is shown in Fig. 5(b). The size of the fabricated metasurface is $256\mu m \times 256\mu m$, with a meta-atom period of 500 $nm$. We built an optical path to test the metasurface, and the experimental optical path is shown in Fig. 5(a). The beams emitted by two lasers with working wavelengths of 633$nm$ and 532$nm$ are transformed into linearly polarized light with orthogonal polarization states through different polarizers. They are combined through a splitter prism and then vertically incident onto the metasurface. A CMOS camera (Hikrobot, MV-CS050-20GC) is placed to capture and record images of the PV beam array.
Fig. 5. (a) Schematic diagram of the experimental optical path used for metasurface validation. (b) Electron microscopy scanning structure imaging of metasurface.
Figure 6(d)–(f) shows the intensity distribution of the PV array captured by the camera when orthogonally polarized lights with wavelengths of 532$nm$ and 633$nm$ are incident on the metasurface, separately and then simultaneously. The obtained PV array distribution is consistent with the simulation results, and one can observe clear images of the required patterns of rings, which shows that the quality of the generated PV beam is good. Figure 6(d) and (e) show the imaging results of green and red light separately, and Fig. 6(f) shows the combination of the two lights simultaneously, where one can observe clear imaging of rings of different colors and low crosstalk between them. These results show that our work can achieve clear imaging of PV arrays and the wavelength multiplexing works perfectly.
Fig. 6. Simulation and Experimental results of PV arrays generated by the designed metasurface under different conditions of incident light. (a),(d) 532 nm $x$-polarized light incident. (b),(e) 633 nm $y$-polarized light incident. (c),(f) Two lights incident simultaneously
However, due to design and fabrication deviations, the modulation phase of the metasurface does not fully match the target phase, and limited by experimental conditions, the laser spot size exceeds the size of the metasurface, with only a portion (~50%) of the light participating in metasurface phase modulation. Therefore, the results captured by the camera have low energy crosstalk in their respective channels, and zero-level bright spots appear in the center. The modulation phase of the metasurface does not fully match the target phase, resulting in low energy crosstalk in their respective channels and zero-order bright spots appearing in the center. The experimental measurements showed that under the incident conditions of 532$nm$ and 633$nm$ beams, the transmission efficiency of the metasurface was ~57% and ~64%, respectively. In order to match the experimental results with the simulation results, we shield the intensity of the spot at the zero-order position and the diffraction is defined as the ratio of the power of the PV rings to the power of remaining light at the PV ring. The calculated diffraction efficiency is ~34% and ~38%. Compared to the simulation results, the reason for the decrease in efficiency may come from fabricated errors of metasurfaces, experimental operation errors, etc. To achieve better results, the above drawbacks should be overcome in future work.
4. Conclusion
In summary, we propose and design a dielectric metasurface based on simple $\text {TiO}_2$ structures, which achieves the generation of a two-dimensional PV beam array with dual-wavelength and polarization multiplexing in the visible light band. Firstly, we simulate a diverse array layout based on the theory of PV array generation. Then, we use FDTD to obtain the mapping relationship between the geometric parameters of anisotropic rectangular meta-atoms and the modulation phase and transmittance. Based on that, we select the phase of one set of PV arrays as the target and establish an evaluation function to select the appropriate meta-atoms to constitute a metasurface. Finally, the metasurface was fabricated using the ALD method, and its functionality was verified through simulation and experiments. The experimental results showed that the designed metasurface can obtain clear and low crosstalk PV array patterns under the simultaneous incidence conditions of 532$nm$ wavelength $x$-polarized light, and 633$nm$ wavelength $y$-polarized light. The measured transmittance is above 50% in all wavelength channels. The metasurface proposed in this article has advantages such as low cross-talk between wavelengths, high information channel capacity, and easy of manufacture, which can achieve larger capacity information transmission. It has great potential in the field of optical communication, high-dimensional information storage, and secure information encryption.
Funding
National Natural Science Foundation of China (61275167); Shenzhen Higher Institution Stability Support Plan (20200812103045003); LingChuang Research Project of China National Nuclear Corporation; Basic Research Project of Shenzhen (JCYJ20170817101827765, JCYJ20180305125430954); Guangdong Basic and Applied Basic Research Foundation (2023A1515010168).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data that support the findings of this study are available from the authors on reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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