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Abstract
Geometric metasurfaces, governed by PB phase, have shown their strong polarization sensitivity and can generate opposite phase delay when the handedness of incident circularly-polarized (CP) light is opposite. Here, we show this interesting characteristic can be employed to generate asymmetric forward and backward propagation with the same incident left- or right-handed CP light, which is hard to achieve with conventional optical elements and devices. Specifically, with the modified holographic design algorithm to consider both forward and backward CP light, an asymmetric meta-hologram is designed, which can project two different holographic images in the forward and backward directions, respectively. We demonstrate this concept by fabricating an asymmetric hologram with a single-size nanostructured metasurface, and the experimentally obtained holographic images in both directions have shown their advantages of high fidelity, broadband response and low crosstalk. The proposed asymmetric metasurface can play an important role in data storages, anti-counterfeitings, optical communications, displays and many other related fields.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurface [1–5] is an array of artificial structures which can flexibly and effectively control the phase [6–9], amplitude [10–15] and polarization [16–21] of incident electromagnetic wave at the subwavelength scale. Benefiting from the unprecedented ability of light manipulation, metasurfaces have broad applications in designing metalenses [22–28], nanoprints [29–36], meta-holograms [37–42] and so on. As a type of two-dimensional materials, metasurfaces exhibit symmetrical transmission characteristics, i.e., the diffraction results are the same in the forward and backward directions with the same incident condition. Therefore, it is difficult to manipulate the light waves asymmetrically, which would limit the advanced application of metasurfaces in the fields of data storages, anti-counterfeitings, optical communications, displays, etc.
The multi-layer design [43–47] is an effective way for metasurfaces to achieve asymmetric transmission. For example, Frese et al. designed a double-layer plasmonic metasurface to realize nonreciprocal wavefront modulation for asymmetric transmission [48]. The holographic image is designed to appear in a specific linearly cross-polarized channel, while disappears in the direction of back propagation. Chen et al. used a three-layer plasmonic metasurface to achieve efficient asymmetric electromagnetic wave transmission and full control of the transmission phase, which can be used to generate directional double-sided images [49]. Yao et al. proposed a dual-layered metasurface to achieve asymmetric focusing in the terahertz region [50]. However, the inherent ohmic loss of metals they used will reduce the transmission efficiency. In addition, the multilayer metasurfaces not only are difficult in both design and manufacturing, but also produce crosstalk between adjacent layers, which would limit its practical applications. Another common approach to implement asymmetric transmission is to use metasurfaces based on segmented nanostructures. Ansari et al. proposed a direction-multiplexed metasurface which consists of two types of different functional zones [51]. However, segmented design approach would decrease the information density of metasurfaces. Recently, the combination of propagation phase and geometric phase is a new path to realize asymmetric transmission for circularly-polarized (CP) incident light. Naveed et al. designed an all-dielectric single-layer metasurface which is composed of the hydrogenated amorphous silicon (α-Si:H) nanoresonators [52]. This metasurface enables asymmetric wavefront generation for backward and forward incident CP light in visible band. However, the nanostructures with varied sizes possess different phase modulations when the operating wavelength changes, which finally results in dispersion and limits the application in a broad band. In summary, current approaches for asymmetric transmission cannot balance the simplicity and functionality, which would hinder the development of asymmetric photonic devices towards being simple, thin and cheap.
In this paper, we propose a transmission-type dielectric metasurface that consists of silicon nanobricks with varied orientations to break the symmetry of spatial transmission and realize bidirectional holography, merely with a single-size nanostructured design approach. The design and experimental results show that it can independently generate two independent holographic images when the left-handed circularly polarized (LCP) light is incident from the forward or backward direction of the metasurface. The proposed metasurface for asymmetric holography can not only provide a new way for information multiplexing, but also provide a new solution for data storages, anti-counterfeitings, optical communications, displays and other fields.
2. Working principles of asymmetric meta-holography
The schematic diagram of asymmetric metasurface hologram is shown in Fig. 1. When LCP light is incident from the forward direction of the metasurface, the letter ‘U’ appears in the Fresnel range, while the letter ‘H’ appears for the backward incidence. The transmission-type dielectric metasurface consists of silicon nanobricks located on a planar dielectric substrate. All the nanobricks we designed have the same sizes, but different orientation angles α (-90°∼90°). And we can control the orientation angles cell-by-cell to steer the geometric phase, which is also called as the Pancharatnam-Berry (PB) phase [53,54] and is exactly twice of the orientation angle ( = 2α). In contrast, switching the illumination from the forward to backward directions is equivalent to performing a mirror operation with respect to the axis along the Y-axis direction of the nanobrick. As a consequence, a phase delay of -2α is generated. Therefore, the phase delays of the light incident from the forward and backward directions are always opposite, no matter the orientation angles. Enable by this characteristic, we propose a modified Gerchberg-Saxton (GS) algorithm [55,56] to calculate the phase distribution of the meta-hologram to enable bidirectional holography.
Fig. 1. Schematic illustration of the asymmetric meta-hologram. (a) Illuminating the metasurface sample from the forward direction (nanostructures on the top) with LCP incident light, the holographic image ‘U’ is designed to appear within the Fresnel range. (b) By flipping the hologram, the holographic image ‘H’ is designed to appear within the Fresnel range.
The flow chart of the modified GS algorithm is shown in Fig. 2, and its detailed steps are as follows. First, the phase distribution of hologram is set as a random phase $\phi _0^n({x,y} )$, then Fresnel transform (S-FFT) is applied to obtain the complex amplitude $g_{11}^n({x^{\prime},\; y^{\prime}} )$ of object1 and $g_{12}^n({x^{\prime},\; y^{\prime}} )$ of object2. If the amplitude errors ${\big |}{{{|{{A_{{t_1}}}({x^{\prime},\; y^{\prime}} )} |}^2} - {{|{A_1^n({x^{\prime},y^{\prime}} )} |}^2}} {\big |}$ and ${\big |}{{{|{{A_{{t_2}}}({x^{\prime},\; y^{\prime}} )} |}^2} - {{|{A_2^n({x^{\prime},y^{\prime}} )} |}^2}} {\big |}$ are less than ε or the iteration time reaches maximum cycle number N, the loop exits and the desired phase distribution $\Psi ({x,\; y} )\; $is obtained. If not, the inverse Fresnel transform (S-IFFT) of $g_{11}^n({x^{\prime},y^{\prime}} )$ is carried out to obtain a new distribution function${\; }g_{01}^n({x,y\; } )$. The phase $\phi _1^n({x,\; y} )$ of $g_{01}^n({x,y\; } )\; $is changed into its negative -$\phi _1^n({x,\; y} )$ to perform the S-FFT. The above iteration process is repeated until the amplitude errors are less than the set ε or iteration number n reaches the maximum number of iterations N, and finally the phase $\Psi ({x,\; y} )$ is obtained.
Fig. 2. Flowchart of the modified GS algorithm. ‘S-FFT’ and ‘S-IFFT’ represent Fresnel transform and inverse Fresnel transform, respectively.
The applicability of the algorithm is based on the fact that opposite phase delay can be generated when LCP light is incident from the forward and backward directions respectively, enable by PB phase. It should be noted that this unique characteristic cannot be obtained by conventional holograms since the generated phase delay is independent of propagation directions, i.e., the algorithm cannot be applicable for conventional hologram to realize asymmetric transmission. Therefore, this interesting characteristic of PB-phase-assisted metasurface can be employed here to realize asymmetric hologram.
3. Unit-cell and meta-hologram design
To enable geometric phase, we can control the anisotropy of the nanobrick by adjusting the electromagnetic response of the nanobrick along the long and short axes. When LCP light with Jones vector $\left[ {\begin{array}{c} 1\\ i \end{array}} \right]$ passes through a nanostructure, the Jones vector of the output light field can be written as
In these equations, ${t_l}$ and ${t_s}$ are the transmission coefficients of the nanobrick along the long and short axes, respectively. $\delta $ is the phase delay for two orthogonal axes. ${|p |^2}\; $and ${|q |^2}$ represent the co-polarized conversion efficiency and cross-polarized conversion efficiency, respectively. The orientation angle α is defined as the angle between x-axis and the long axis of the nanobrick (shown in Fig. 1).
Obviously, to obtain a high polarization conversion efficiency, p should be small enough and q should be large enough, and the ideal design lies that each nanobrick can work as a half-waveplate (p = 0 and q = 1). Figure 3(a) shows the schematic diagram of a nanobrick unit-cell. In order to optimize the geometric parameters of the unit-cell structure (period CS, length L, width W), we used the commercial software CST STUDIO SUITE for numerical simulations. Since changing the sizes of the nanobrick will affect the transmittance and phase delay along the long and short axes, in order to achieve optimal experimental results, we give priority to the highest polarization conversion efficiency at the designed wavelength of λ = 663 nm. The height of the α-Si is fixed at 380 nm, we sweep L and W from 60 nm to 300 nm in steps of 10 nm while the period CS is fixed at 340 nm. The wavelength of the incident light is swept from 545 nm to 700 nm. We finally select the optimized parameters of a unit-cell structure (length L = 160 nm, width W = 60 nm and period CS = 340 nm). With these structural parameters, we simulate the transmission coefficients along the long and short axes and the phase delay between the two orthogonal axes of nanobrick when the wavelength varies from 550 nm to 700 nm, as shown in Fig. 3(b). According to Eq. (2), we calculate the cross-polarization conversion efficiency curve versus wavelength, which is plotted in Fig. 3(c). It can be seen that the cross-polarization efficiency can reach 17.3% at λ = 663 nm.
Fig. 3. Illustration of the unit-cell structure and the numerical simulation results. (a) Schematic diagram of one nanobrick unit-cell. Each nanobrick is optimally designed with period CS = 340 nm, length L = 160 nm, width W = 60 nm, height H = 380 nm and α is the orientation angle of the nanobrick. The operation wavelength is 663 nm. (b) Simulated transmission coefficients and phase difference of the nanobrick when the incident light is linearly polarized (LP) along the long and short axes of the nanobrick, respectively. (c) Simulated cross-polarization efficiency at the LCP light incidence.
In our design, the target images for forward and backward transmission are a letter ‘U’ and a letter ‘H’, respectively. And the reconstruction distances of both two holographic images are set as 955 μm. Then, the phase distributions for reconstructing letters ‘U’ and ‘H’ are calculated by the proposed modified GS algorithm, and the results are shown in Fig. 4(a) and Fig. 4(b). The zoom-in-view phase distribution (100 × 100 pixels) of the lower right corner of Fig. 4(a) and Fig. 4(b) are shown in Fig. 4(c) and Fig. 4(d), respectively. It can be seen that the phase distributions shown in Fig. 4(a) and Fig. 4(b) are opposite, which is consistent with the requirement of asymmetric transmission based on PB phase. With the characteristics of continuous phase control, geometric metasurface provides enough degrees of freedom for phase design in the modified GS algorithm, so it is beneficial to the rapid convergence of the optimization function. The diffraction images of the hologram at a distance of 955 μm calculated by Kirchhoff diffraction principle are shown in Fig. 4(e) and Fig. 4(f), where the holographic images can be seen clearly.
Fig. 4. Phase distribution of the Fresnel-type hologram and the simulated diffraction results. (a, b) Phase profile to reconstruct holographic images of letters ‘U’ and ‘H’, calculated by the modified GS algorithm. (c, d) Partial zoom-in-view (100 × 100 pixels) of the lower right corner (in the dashed box) phase distribution in the total phase distribution. (e, f) Simulated holographic images calculated by the Kirchhoff’s diffraction principle when the operating wavelength is 663 nm and the diffraction distance is 955 μm.
4. Experiment and discussion
To further verify our proposed concept of asymmetric holography based on the single-size nanostructured metasurfaces, a metasurface sample is fabricated by the standard electron-beam lithography (EBL). More details about sample fabrication can be found in Appendix A. The dimensions of the fabricated sample are 170 µm × 170 µm (500 × 500 nanobricks), and the partial scanning electron micrograph (SEM) image of the metasurfaces sample is shown in Fig. 5(a). It can be seen that the size of the nanobrick is basically uniform and the rounding of the corners is not obvious, and the overall quality of the sample is satisfactory. The experimental setup for observation of holographic image is shown in Fig. 5(b). An incident laser beam from the super-continuum light source (YSL SC-pro) is transformed into LP light after passing through the polarizer1, which is then transformed into LCP light by a quarter-waveplate called QWP1. Since the reconstructed images are only sub-millimeter in size, a 50 × (NA = 0.55) optical microscopic object lens is used to observe the images. The circular polarizer composed of QWP2 and polarizer2 is utilized to eliminate co-polarized light. When the LCP light with a wavelength of 663 nm is incident from the forward direction of the sample, the letter ‘U’ appears at a distance of 955 µm from the sample while the letter ‘H’ is at the same distance (955 µm) for backward incidence, which agrees well with the design. To investigate the broadband response of our fabricated sample, we alter the wavelength of the super-continuum laser source from 563 nm to 683 nm by steps of 20 nm. When the wavelength of the incident light changes, the distance between the reconstruction plane and the sample also changes. Under the paraxial approximation, the reconstruction plane distance is inversely proportional to the wavelength of incident light. Therefore, when the incident light is incident from the forward direction of the sample, the distances between sample and the letter ‘U’ for λ = 563, 583, 603, 623, 643, 663, 683 nm are 1124, 1086, 1050, 1016, 984, 955, 927 µm, respectively. In contrast, for backward incidence, the letter ‘H’ appears in the same position as that of letter ‘U’. Simulation and experimental results for the reconstructed images at different wavelengths are shown in Fig. 6(a)–6(n). The experimental results are consistent with the simulation results. Although the hologram is designed for a specific wavelength of 663 nm, due to the dispersion-less characteristic of geometric phase, the holographic images generated by the sample will not be distorted as the wavelength of incident light changes. All the holographic images have high fidelity, which proves that the designed metasurface hologram has strong robustness and wide wavelength response bandwidth.
Fig. 5. Fabricated sample and experimental setup to retrieve the meta-holographic images. (a) The photo of the fabricated metasurface sample. The insets show the partial SEM images. (b) Illustration of the experimental setup to retrieve the transmission-type meta-holographic images. An incident light beam from a super-continuum light source (YSL SC-pro) is converted into LCP light after passing through a linear polarizer and a quarter-wave plate (QWP1). QWP2 and polarizer2 are used to eliminate the unwanted co-polarized light.
Fig. 6. Simulated and experimental results of the asymmetric metasurface hologram. The sample is irradiated with a super-continuum laser source with steps of 20 nm from 563 nm to 683 nm. The sizes of the holographic images by numerical simulations and captured by camera are both 290 × 170 µm2.
5. Conclusion
In summary, we propose an asymmetric transmission-type metasurface for bidirectional holography, enabled with different geometric phase delays when LCP light is incident from forward and backward directions of the metasurface. We experimentally demonstrate this concept when the LCP light is incident from two opposite directions of the metasurface, a pair of independent holographic images can be generated in the Fresnel range, respectively. Compared with other asymmetric metasurface based on multilayer or segmented nanostructures, the proposed single-size nanostructured metasurface has not only design and manufacturing simplicity, but also low crosstalk. Therefore, with the advantages of ultracompactness, simplicity in both design and fabrication, strong robustness and broadband response, the proposed asymmetric metasurface has promising prospects in the fields of data storages, anti-counterfeitings, optical communications, displays and so on.
Appendix A: sample fabrication
Electron beam lithography (EBL) was used to fabricate the metasurface sample on a fused silica substrate coated with α-Si. Firstly, a 380 nm thick layer of α-Si was deposited on a 500 µm fused silica substrate by plasma enhanced chemical vapor deposition (PECVD). Then, 100 nm resist (PMMA, 950 K) was spin-coated and the PEDOT: PSS film was covered as a conductive layer. Then, the Cr mask was exposed by EBL system (Raith 150, acceleration voltage of 30 kV, writing field of 200 µm) to transfer the pattern from the gds file to the photoresist. Then, the 25 nm thick Cr was plated on the sample by electron beam evaporation, and the Cr was stripped by ultrasonic wave in acetone. Next, reactive ion beam etching (RIE) was used to remove α-Si without Cr mask. After etching, the chrome mask was removed. Finally, only the α-Si nanobrick arrays on the fused silica substrate were retained.
Appendix B: dispersion curves of silica and amorphous silicon
Figure 7 shows the dispersion curves of silica and amorphous silicon, used in the design and numerical simulations.
Fig. 7. Refractive index of α-Si and silica. The real part n and imaginary part k of α-Si are represented by red square line and black triangular line, respectively. The real part n of silica is represented by blue dotted line.
Appendix C: phase delay versus orientation angle of nanobrick
Figure 8 shows the phase delay versus orientation angle of nanobrick, illuminated by LCP incident light. As an example, 17 nanobricks with different orientation angles are plotted at the curve knots.
Funding
National Natural Science Foundation of China (11774273, 11904267, 91950110); Fundamental Research Funds for the Central Universities (2042020kf1050).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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