In view of large information capacity of holographic metasurface and wide applications of structured light, the polarization-encoded structured light generation is proposed based on holographic metasurface. The polarization-encoded structured light generators consist of rotated L-shaped nanoholes and they work under linearly polarized light illumination. The rotated L-shaped nanoholes simultaneously manipulate the intensity, phase and polarization of light field and generate the structured light composed by multiple perfect vortices with polarization-encoded OAM modes. The generated polarization-encoded structured lights also behave the incident polarization dependence. The polarization multiplexing performance of holographic metasurface is embodied in both incident and output fields and it is also verified by the numerical simulations. The designed method can be expanded to construct any transmission or reflection holographic metasurfaces and the generated structured lights provide more switchable OAM channels. The polarization-encoded structured light and the compact holographic metasurface are benefit to broadening the wide applications of structured lights.
Research Article
Polarization-encoded structured light generation based on holographic metasurface
https://doi.org/10.21203/rs.3.rs-2109550/v1
This work is licensed under a CC BY 4.0 License
Journal Publication
published 06 Feb, 2023
You are reading this latest preprint version
structured light
metasurface
orbital angular momentum
holography
Structured light points to the light field with high customized amplitude, phase and polarization distribution1–3. Vector beam possessing spatial varying polarization state and vortex beam carrying spiral phase are two typical structured lights. Since the vortex beams with different topological charges are orthogonal and they provide the orbital angular momentum (OAM) for the interaction of light and matter4, optical vortices have been applied in many fields including optical communication5, particles trapping6, optical encryption7 and quantum memory8. Because of the special focusing effect, high resolution imaging and polarization sensitivity, vector beams have also been applied in many fields9–11. Till now, several methods have been proposed to generate the structured beams. Spiral phase plate12, forked grating13, interferometer14 and metasurface15,16 are utilized to generate vortex beams. Sub-wavelength grating17, q-plate18, spatial light modulator19 and metasurface20,21 are used to generate vector beams. Certainly, the superposition of vortex fields with different OAM modes can generate vector beam22. With comparison to traditional methods depending on the spatial accumulation effect along an optical path, metasurface realizes the light field manipulation with the help of the interaction of light field and nanometer scatterers23–27, therefore it has advantages of ultra-thin and compact structure, ease to integration and convenience to operate.
Simple metasurface can directly modulate the amplitude, phase or polarization of light field using the local light modulation of naonounits and holographic metasurface makes the light field manipulation ability of metasurface fully exert28,29. Zheng et al. proposed the holographic metasurface consisting of nanorods and realized the generation of wavelength-encrypted characters with circularly polarized light illumination30. Xu et al. designed the holographic metasurface consisting of nanopillars and generated different patterns in near-field and far-field with the control of incident circularly polarized light31. Xiao et al. proposed the multiplexing vectorial metaholograms through varying phase difference of two orthogonal circularly polarized lights and obtained the polarization-encrypted images32. Our team designed the holographic metasurface consisting with rectangular nanoholes and obtained the structured vortex fields with the control of incident circularly polarized light31. These above works exhibit the powerful light control of holographic metasurface and the obtained diversely encrypted images show us the multiplexing function of holographic metasurface. Combining the incident polarization state, the more output polarization states may bring more channels for the applications of light field.
In this paper, we propose polarization-encoded structured light (PESL) generation based on holographic metasurface. The output structured lights are encoded by the different linear polarization states and they can be adjusted with the incident linear polarization state. The proposed polarization-encoded structured light generator (PESLG) consists of L-shaped nanoholes etched on sliver film and the rotated nanoholes under the linearly polarized light illumination simultaneously modify the amplitude, phase and polarization of light field. The PESLs are generated by the designed holographic metasurface, and the obtained vortex fields with different OAM modes are encoded by different linear polarization states and they also change with the incident polarization. The theoretical analysis provides the design idea of holographic metasurface. The numerical simulations verify the feasibility of the designed holographic metasurface for the generation of PESLs. The proposed structured light generator realizes the multiple-parameter control of light field. The combination of the polarization-encoded OAM modes and the polarization-dependent output provides more mode choices for the applications of the structured light. The intensity setting of PESL equivalent to the perfect vortex are benefit to the optical encryption, polarization multiplexing and light coupling. We believe that the proposed PESL will be helpful for expanding the applications of structured light in particle manipulation, optical encryption, optical communication, quantum information processing and other areas.
Here, we design the holographic metasurface in terms of the Fresnel holography technique to generate the structured light field. Suppose the target light field is U0(x0,y0), the diffraction light field at the propagation distance of d away from the target field can be expressed by Fresnel integration of U(x,y)=∫∫U0(x0,y0)K(x-x0,y-y0)dx0dy0, where the point spread function of K(x-x0,y-y0) satisfies K(x-x0,y-y0)= [exp(jkd)/(jλd)]exp{jk[(x-x0)2+(y-y0)2]/(2d)} with k = 2π/λ denoting the wave number of the incident field and λ representing the wavelength33. Since the scatterers of metasurface are distributed discretely, the diffraction field should be discretized, and it can be written as
Where p, q, m and n are integers, δx and δy represent the sampling intervals along the x and y axes of the diffraction field, and δx0 and δy0 represent the sampling intervals along the x0 and y0 axes of the target field. While the diffraction field performs the reverse Fresnel diffraction, the obtained field is UH(x0´,y0´) = U0(x0,y0)/(λd)2 and the discretized form is UH(mδx,nδy) = U0(mδx,nδy)(λd)2. One can see that the diffraction field is the same as the target field except for the constant term. This means that the target field can be reproduced at the defaulted distance, and it is also the working principle of metasurface holography. When the target field is a radially structured light including several concentric vortices encoded by different polarization states, one of polarization mode U0i(mδx0,nδy0) can be expressed as,
Where Ci represents the amplitude of vortex, ri is the radius of vortex, wi denotes the waist radius of vortex, and li is the topological charge. For different polarization mode, these parameters may take the same or different values. The amplitude and phase information of the holographic metasurface can be obtained by inserting Eq. (2) into Eq. (1). For simplification, we set the amplitude threshold to construct the metasurface hologram. Here, the phase distribution of radially structured light is realized with the help of the phase delays introduced through rotating the L-shaped nanoholes. As we know, the phase delay introduced by an anisotropic nanohole equals to twice of the rotation angle of nanohole and it is always carried by the cross circularly polarized light31. Therefore, one spiral phase with the circularly polarized state can be easily generated through rotating the nanoholes.
As we know, one linear polarization state of cosγex+sinγey with the polarization angle of γ can be expressed as the superposition of two orthogonal circularly polarized states, namely, cosγex+sinγey= 20.5[exp(jγ)eR+exp(-jγ)eL]/2, where ex=(1, 0), ey=(0, 1), eR=20.5(1, -j)/2 and eL=20.5(1, j)/2 represent the unit vectors for x-polarization, y-polarization, right- and left-handed circular polarization. Thus, two suits of nanoholes with opposite rotation angles can consist of one metasurface with linear polarization output. Figure 1A shows the sketch map of one structured light generator with x-polarization output. The compound metasurface CM is formed through combining the complementary structures of R1 and R2, whose nanoholes are randomly chosen from two metasurfaces of M1 and M2 corresponding to the right- and left-handed circular polarization. This compound metasurface takes effect under the x-polarized light illumination.
Similarly, for the structured light encoded by two orthogonal linearly polarized states, one can construct the compound PESLG in terms of above principle. Suppose one OAM mode of exp(jl1φ) takes the x-polarization and the other OAM mode of exp(jl2φ) takes the y-polarization, the target field with two orthogonal linearly polarized OAM modes can be written as,
While w1 = w2 and r1 = r2, the above equation can be simplified into exp(-r2/w2)exp(jpφ) [exp(jqφ)ex+exp(-jqφ)ey] with p=(l1 + l2)/2 and q=(l1-l2)/2 and it is the so-called vector vortex beam34. While p = 0, it changes into the pure vector beam. Figure 1B shows the schematic diagram for the generation of PESL by the constructed holographic metasurface. This holographic metasurface is composed of four sets of rotated nanoholes, where two sets of nanoholes take effect under the right-handed circularly polarized light illumination and the other two sets of nanoholes take effect under the left-handed circularly polarized light illumination. The rotation angle θ of nanohole at any position equals to l1ϕ/2 for the first set, -l1ϕ/2 for the second set, l2ϕ/2 + π/4 for the third set and -l2ϕ/2 + π/4 for the fourth one.
In order to ensure the quality of the generated PESL, we should optimize the structure parameters of metasurface. The structure parameters include the thickness of silver film, the length and width of L-shaped nanohole and the separation of two adjacent nanoholes, which are labeled in the magnified nanohole inserted in the lower right corner of Fig. 1A. Here, the working wavelength of λ is set at 632.8nm and the propagation distance of d is set at 15µm. Through the optimization, the separations of nanoholes of δx and δy along two orthogonal directions takes 200nm, which satisfies Nyquist sampling theorem δ2N ≤ λd with the sampling number of N taking 200. Two lengths of la and lb take 120nm and two width of wa and wb take 35nm. The thickness of silver film takes h = 150nm. The optimization process is finished with the help of finite-difference time-domain technique34.
In order to testify the reliability of metasurface PESLG, we construct one holographic metasurface that can generate two orthogonal linearly polarized vortex fields with the same radii of 6µm and the topological charges taking l1 = 1 and l2 = 3. The silver film with the thickness of 150nm is deposited on the glass substrate and the L-shaped nanoholes with the optimized dimensions are fabricated in the silver film. The nanoholes rotate in terms of the phase distributions of holographic metasurface. During the simulation process, the boundary condition of perfect matching layer is used to prevent non-physical scattering at the boundary. The minimum mesh step is set at 2nm, the calculation region is set at 42µm×42µm×20µm, the dielectric constant of silver is taken from the value given by Palik35. The observation plane is set at the propagation distance of 15µm above the silver film.
Figures 2A shows the structure diagram of compound PESLG and the magnified part at the right reflects the relative rotation of four adjacent nanoholes. Figure 2B and 2C give the simulated intensity and phase distributions with the incident polarization along the horizontal direction. Where the results in Fig. 2B are the intensity and phase distributions for the x-component of transmission field, and the results in Fig. 2C are the intensity and phase distributions for the y-component of transmission field. Figure 2D and 2E give the simulated intensity and phase distributions with the incident polarization along the vertical direction. Where the results in Fig. 2D show the intensity and phase distributions for the x-component of transmission field, and the results in Fig. 2E show the intensity and phase distributions for the y-component of transmission field. For convenience observation, the gray patches and curved arrows are drawn near the vortices.
From the results in Fig. 2B, one can see that the intensity distribution takes on the annular shape and the phase uniformly increases 2π along the clockwise direction. It means the x-polarized vortex with the topological charge taking 1 generates. From the results in Fig. 2C, one can see that the intensity distribution also takes on the annular shape and the phase uniformly increases thrice of 2π along the clockwise direction. It means the y-polarized vortex with the topological charge taking 3 generates. Although the annular intensity distributions for two cases are the same, the different phase distributions indicate two channels with x- and y-polarization have no crosstalk.
From the results in Fig. 2D, one can see that the intensity distribution still takes on the annular shape and the phase uniformly increases thrice of 2π along the clockwise direction. It means the x-polarized vortex with the topological charge taking 3 generates.The results in Fig. 2E show that the intensity distribution also takes on the annular shape and the phase uniformly increases 2π along the clockwise direction. It means the y-polarized vortex with the topological charge taking 1 generates. Two regular phase distributions indicate two channels with x- and y-polarization have no crosstalk. Moreover, with comparison to the results in Figs. 2B and 2C, two orthogonal polarization-encoded outputs are just exchanged. This is because the change of incident polarization direction makes the left-handed circularly polarized light add the additional phase of π with respect to the right-handed circularly polarized light, and it leads the linear polarization direction to rotate π/2.
From the above theoretical analysis, we know as the rotation angles of two sets of nanoholes satisfy θ1=-θ2, the output beam is the horizontal linear polarization, and as the rotation angles of two sets of nanoholes satisfy θ1=-θ2 + π/2, the output beam is the vertical linear polarization. Similarly, as the rotation angles of two sets of nanoholes satisfy θ1=-θ2 + π/4, the output linear polarization is along the diagonal direction, and as the rotation angles of two sets of nanoholes satisfy θ1=-θ2-π/4, the output linear polarization is along the anti-diagonal direction. Thus, we can also design the integrated PESLG to modulate the amplitude, phase and polarization of light field based on holographic metasurface. For clearness, we arrange the integrated PESLs at the different quadrants. Meanwhile, in order to fully show the intensity, phase and polarization manipulation of holographic metasurface, we customize four structured lights with the same radii, different topological charges and different polarization states.
Figures 3A and 3B give the target intensity, phase and polarization distributions of four integrated PESLs with the horizontal linearly polarized light illumination. The integrated PESLs have the same radii of 5µm and their topological charge taking 2, -1, 4 and − 3. The green arrows inserted in Fig. 3A denote the polarization states of the integrated PESLs. Figure 3C show the simulated total intensity distribution of the integrated PESG under horizontal linearly polarized light illumination, and Figs. 3D and 3E show the phase distributions of x and y components of the integrated PESLs. The intensity distributions of x and y components of the integrated PESLs are also inserted in the free corners of the phase patterns. The inserted blue arrows denote the incident polarization directions and the red arrows denote the detection polarization directions.
The results in Figs. 3D and 3E show that three vortices appear among the phase distributions of x and y components of the integrated PESLs and the topological charges for the corresponding vortices equal to 2, 4 and − 3, which are consistent with the defaulted ones. The annular intensity distributions with the same radii have different brightness. For the vortex with the polarization along the detection direction, the intensity is the brightest. As the polarization of vortex has one cross angle with the detection direction, the intensity of vortex is lower than the former. And the vortex with the polarization orthogonal to the detection direction does not appear. All these results verify the effectiveness of the designed holographic metasurface for the generation of integrated PESLs.
Figures 3F and 3G show the phase distributions of x and y components of the integrated PESLs with the incident polarization along the vertical direction. Just like the analysis in above section, the rotated incident polarization direction brings the additional phase of π to the left-handed circularly polarized light and it leads the output linear polarization direction to rotate π/2. One can see that as the detection polarization is along the horizontal direction, the output results are the same as the ones of Fig. 3E, and as the detection polarization is along the vertical direction, the output results are the same as the ones of Fig. 3D. It indicates that the integrated PESLs can be adjusted by the incident polarization. The results in Figs. 3H and 3I further verify the polarization multiplexing characteristic of the integrated PESLG, where the incident polarization is along diagonal direction.
Figure 3H shows that three vortices appear as the detection polarization is along the horizontal direction except that the one at the lower right corner is invisible. Three vortices appear in Fig. 3I as the detection polarization is along the vertical direction except the one at the upper left corner is invisible. This is because the rotated incident polarization direction brings the additional phase of π/2 to the left-handed circularly polarized light and it leads the output linear polarization direction to rotate π/4. Just because the polarization directions of four vortices rotate π/4, the intensity of the vortex at the upper left corner is the largest as the detection direction is along the horizontal direction, and the vortex at the lower right corner does not appear. Similarly, as the detection direction is along the vertical direction, the intensity of the vortex at the lower right corner is the largest and the vortex at the upper left corner disappears.
The results also indicate that the output PESLs may be controlled by the incident polarization. The integrated PESLG provides more mode combinations with comparison to the traditional polarization multiplexing metasurface with two channels controlled by left- and right-handed circularly polarized light or the horizontal and vertical linearly polarized light. The output perfect vortices with the changeless intensity rings are convenient for the coupling and detecting for different OAM modes. Therefore, this kind of polarization-controllable structured lights are favorable for the coupling, switching and manipulation of parallel OAM modes. The design of compact holographic metasurface is benefit to the integration and miniaturization.
This paper constructs holographic metasurfaces based on Fresnel diffraction to generate the PESLs. The proposed holographic metasurfaces consisting of L-shaped nanoholes simultaneously modulate the amplitude, phase and polarization of light field. The polarization-encoded vortex beams with different OAM modes are obtained the proposed holographic metasurfaces. The output of PESLs also depend on the incident state of polarization. Therefore, the designed PESLGs possess the dual polarization multiplexing function and their performances of the generated PESLs are verified by the numerical simulations. The compact structure of the designed multifunctional metasurface is benefit to the integration. The more polarization modes generated by the proposed PESLG helps to increase the capacity of information propagation and the level of information encryption. The polarization-encoded perfect vortices bring more convenience for the coupling, switching and sensing of OAM modes. These achievements predict that the generated PESL based on holographic metasurface may be applied in optical encryption, large-capacity optical communication and parallel processing of optical information. The design principle of our proposed holography metasurface has universality and it can be expanded into geometric nanounits with any shapes, any transmission or reflection situation, active control and digital coding metasurface. The more performances of PESLGs like the broadband characteristic, high efficiency and speed coding can be improved.
Funding Declaration: This work was supported by the National Natural Science Foundation of China (10874105) and Shandong Provincial Natural Science Foundation of China (ZR2020KA009).
Author Contribution: Writing-original draft preparation, C.Z.; data curation, P.L., J.X. and Y. Z.; supervision, project administration, funding acquisition, S.T. All authors have read and agreed to the published version of the manuscript.
Data Availability Statement: The data presented in this study are available on request from the corresponding author.
Disclosure: The authors declare no conflicts of interest.
- Rubinsztein-Dunlop, H., Forbes, A., Berry, M. V., Dennis, M. R., Andrews, D. L. et al. Roadmap on structured light. Journal of Optics 19, 013001 (2016).
- Forbes, A., de Oliveira, M. & Dennis, M. R. Structured light. Nature Photonics 15, 253–262 (2021).
- Dorrah, A. H. & Capasso, F. Tunable structured light with flat optics. Science 376, e6860 (2022).
- Shen, Y., Wang, X., Xie, Z., Min, C., Fu, X. et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. Light: Science & Applications 8, 90 (2019).
- Ren, Y., Li, L., Wang, Z., Kamali, S. M., Arbabi, E. et al. Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications. Scientific Reports 6, 33306 (2016).
- Padgett, M. & Bowman, R. Tweezers with a twist. Nature Photonics 5, 343–348 (2011).
- Liu, H., Yang, B., Guo, Q., Shi, J., Guan, C. et al. Single-pixel computational ghost imaging with helicity-dependent metasurface hologram. Science 3, e1701477 (2017).
- Nicolas, A., Veissier, L., Giner, L., Giacobino, E., Maxein, D. et al. A quantum memory for orbital angular momentum photonic qubits. Nature Photonics 8, 234–238 (2014).
- Quabis, S., Dorn, R., Eberler, M., Glöckl, O. & Leuchs, G. Focusing light to a tighter spot. Optics Communications 179, 1–7 (2000).
- Lou, K., Qian, S., Ren, Z., Tu, C., Li, Y. et al. Femtosecond laser processing by using patterned vector optical fields. Scientific Reports 3, 2281 (2013).
- Gao, X.-Z., Pan, Y., Zhao, M.-D., Zhang, G.-L., Zhang, Y. et al. Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model. Optics Express 26, 1597–1614 (2018).
- Turnbull, G. A., Robertson, D. A., Smith, G. M., Allen, L. & Padgett, M. J. The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate. Optics Communications 127, 183–188 (1996).
- Padgett, M., Courtial, J. & Allen, L. Light’s orbital angular momentum. Physics Today 57, 35–40 (2004).
- Vyas, S. & Senthilkumaran, P. Interferometric optical vortex array generator. Applied Optics 46, 2893–2898 (2007).
- Wang, H., Liu, L., Zhou, C.-D., Xu, J., Zhang, M. et al. Vortex beam generation with variable topological charge based on a spiral slit. Nanophotonics 8, 317–324 (2019).
- Zhou, C.-D., Mou, Z., Bao, R., Li, Z. & Teng, S. Compound plasmonic vortex generation based on spiral nanoslits. Frontiers of Physics 16, 33503 (2020).
- Niv, A., Biener, G., Kleiner, V. & Hasman, E. Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam–Berry phase optical elements. Optics Letters 29, 238–240 (2004).
- Machavariani, G., Lumer, Y., Moshe, I., Meir, A. & Jackel, S. Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams. Optics Communications 281, 732–738 (2008).
- Liu, S., Qi, S., Zhang, Y., Li, P., Wu, D. et al. Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude. Photonics Research 6, 228–233 (2018).
- Lv, H., Lu, X., Han, Y., Mou, Z., Zhou, C. et al. Metasurface cylindrical vector light generators based on nanometer holes. New Journal of Physics 21, 123047 (2019).
- Zhou, C.-D., Mou, Z., Lu, P. & Teng, S. Compound vector light generator based on a metasurface. Photonics 8, 243 (2021).
- Liu, D., Zhou, C.-D., Lu, P., Xu, J., Yue, Z. et al. Generation of vector beams with different polarization singularities based on metasurfaces. New Journal of Physics 24, 043022 (2022).
- Chen, S., Li, Z., Zhang, Y., Cheng, H. & Tian, J. Phase Manipulation of electromagnetic waves with metasurfaces and its applications in nanophotonics. Advanced Optical Materials 6, 1800104 (2018).
- Li P., Zhang Q., Li Y., Wang H., Liu L., Teng S. Plasmonic lens based on rectangular holes. Plasmonics 13, 1929–1933 (2018).
- Zhang Q., Li P., Li Y., Ren X., Teng S. A universal plasmonic polarization state analyzer. Plasmonics13, 1129–1134 (2018).
- Zhou, C.-D., Mou, Z., Lu, P. & Teng, S. Optical singularity built on tiny holes. Annalen der Physik 533, 2100147 (2021).
- Deng, Y., Cai, Z., Ding, Y., Bozhevolnyi, S. I. & Ding, F. Recent progress in metasurface-enabled optical waveplates. Nanophotonics 11, 2219–2244 (2022).
- Jiang, Q., Jin, G. & Cao, L. When metasurface meets hologram: principle and advances. Advances in Optics and Photonics 11, 518–576 (2019).
- Li, Z., Yu, S. & Zheng, G. Advances in exploiting the degrees of freedom in nanostructured metasurface design: from 1 to 3 to more. Nanophotonics 9, 3699–3731 (2020).
- Shan, X., Li, Z., Dai, Q., Li, J., Fu, R. et al. Metasurfaces with single-sized antennas for reconstructing full-color holographic images without cross talk. Optics Letters 46, 5417–5420 (2021).
- Liu, M., Zhu, W., Huo, P., Feng, L., Song, M. et al. Multifunctional metasurfaces enabled by simultaneous and independent control of phase and amplitude for orthogonal polarization states. Light: Science & Applications 10, 107 (2021).
- Wan, W., Yang, W., Feng, H., Liu, Y., Gong, Q. et al. Multiplexing vectorial holographic images with arbitrary metaholograms. Advanced Optical Materials 9, 2100626 (2021).
- Mou, Z., Zhou, C.-D., Lu, P., Yue, Q., Wang, S. et al. Structured vortices generated by metasurface holography. Photon. Res. 9, 2125–2131 (2021).
- Teng, S., Zhang, Q., Wang, H., Liu, L. & Lv H. Conversion between polarization states based on metasurface. Photonics Research 7, 246–250 (2019).
- Palik, E. D. Handbook of optical constants of solids. Vol. 3 (Academic press, 1998).
No competing interests reported.