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Abstract
In this work, a simple dielectric metasurface hologram is proposed and designed by combining the electromagnetic vector analysis method and the immune algorithm, which can realize the holographic display of dual wavelength orthogonal-linear polarization light in visible light band, solve the problem of low efficiency of the traditional design method of metasurface hologram, and effectively improve the diffraction efficiency of metasurface hologram. The titanium dioxide metasurface nanorod based on rectangular structure is optimized and designed. When the x-linear polarized light with wavelength of 532 nm and y-linear polarized light with wavelength of 633 nm are incident on the metasurface respectively, different display output images with low cross-talk can be obtained on the same observation plane, and the transmission efficiencies of x-linear and y-linear polarized light are as high as 68.2% and 74.6% respectively in simulation. Then the metasurface is fabricated by Atomic Layer Deposition method. The experimental results are consistent with the design results, which proves that the metasurface hologram designed by this method can completely realize the feasibility of wavelength and polarization multiplexing holographic display, and has potential application value in holographic display, optical encryption, anti-counterfeiting, data storage and other fields.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Holography is an optical technology for recording and reconstructing light wavefront [1], which shows great potential in the next generation imaging technology. The traditional hologram can be generated by the interference between the reference beam and the scattered beam of the target object, and the phase information of the hologram can also be obtained by numerical simulations [2]. Traditional holograms rely on specific surface structure to achieve local phase change, which faces the challenges of limited imaging efficiency and complicated manufacturing, it is difficult to achieve high-efficiency multiplex holographic display [3–5].
Metasurface is an optical device composed of artificially manufactured subwavelength nanostructures, which can arbitrarily modulate the amplitude, phase and polarization of incident light [6–13]. The metasurface hologram can provide high-quality reconstructed images with subwavelength resolution, and has the advantage of larger viewing angle, higher Spatial Bandwidth Product (SBP) and far-field suppression of high-order diffraction [14–17]. Therefore, many types of metasurface holograms have been proposed [18–17]. Among them, the full-color metasurface holograms need to rely on the phase control of the wavelength, and different wavelengths need different metasurface phases, which is extremely challenging. Therefore, in the initial research stage, many literatures used the method of composite structure to form unit pixel. Wang et al. [22] used four silicon rectangular columns to form unit pixel of the metasurface. The polarization conversion efficiency of the rectangular columns of each size to the circularly polarized light of red, green and blue is different, so as to modulate the phase of the light for a specific wavelength. The metasurface can realize the holographic display of red, green and blue. The measured diffraction efficiencies of red, green and blue are 18%, 5.2%, 3.6% respectively. Each pixel of the metasurface is composed of a plurality of rectangular columns, which increases the size of the pixel, thereby reducing the display resolution and the diffraction efficiency of three wavelengths [5,23]. In order to improve the resolution and diffraction efficiency, and reduce the complexity of the meta-atom, scholars further proposed the single structure meta-atom of unit pixel. Each meta-atom needs to function for three colors simultaneously which may result in color cross-talk. Huang et al. [24] proposed an aluminum Metal-Insulator-Metal (MIM) three-layered reflective metasurface, which realized the red green blue wavelength multiplexing holographic display. The transmission of the metasurface is around 50%. The diffraction efficiencies for blue, green and red are 0.59%, 0.54%, and 0.69% respectively in simulation. The efficiency obtained from measurement for green is around 0.3%. Qin et al. [25] proposed the aluminum elliptical hole structure metasurface, which realized the transmission type full-color holographic display. Wan et al. [26] used the aluminum elliptical hole structure metasurface to add the phase offset to the hologram corresponding to the red, green and blue wavelengths, thus realizing the red, green and blue wavelength multiplexing holographic display. The diffraction efficiencies for red, green and blue light are around 1%, 2.8%, and 0.4% respectively in simulation. At present, the metasurface multi-wavelength holographic display is mainly facing some problems, such as relatively complex meta-atom, low diffraction efficiency and wavelength cross-talk.
In this work, a highly diffraction efficiency wavelength and polarization multiplexing dielectric metasurface hologram is proposed. The metasurface meta-atom can independently control the phase of two orthogonal-linear polarized light with different wavelengths, which can solve the problems of low transmission efficiency and wavelength cross-talk of the existing transparent wavelength multiplexing metasurface, and can effectively reduce the complexity of multiplexing holographic metasurface. In order to realize multi-wavelength multiplexing holographic display using the simple structure metasurface, it is necessary to select appropriate meta-atom to meet the phase and transmittance requirements of different wavelength modulation at the same time. Therefore, it is necessary to build a complete structure database of meta-atom that can cover all phase requirements. This paper proposes an innovated method to combine the theory of electromagnetic vector analysis with the global optimization algorithm, establish the scientific evaluation function through the self-made correlation program, and establish the structure database of meta-atom by using the optimization method, so as to meet the phase requirements of different holographic displays. This method can greatly improve the search efficiency of the structure parameters of meta-atom, improve the design efficiency and performance of multi-wavelength multiplexing holographic metasurfaces, also solve the cross-talk problem, improve the diffraction efficiency and reduce the structural complexity.
The dual wavelength and dual polarization multiplexing metasurface hologram constructed in this paper can reconstruct different holograms for 532 nm x-linear polarized light and 633 nm y-linear polarized light. The transmission efficiencies of x-linear and y-linear polarized light can reach 68.2% and 74.6%, respectively in simulation. The simple structure of the metasurface hologram proposed in this paper has the advantage of high diffraction efficiency, low cross-talk, and high feasibility, which can be applied to the fields of information encryption, optical security and many other circumstances in optical applications.
2. Theoretical analyses
2.1 Principle of holographic metasurface
In this work, the holographic metasurface is designed by using the characteristics of single structure metasurface meta-atom with different phase control ability to orthogonal-linear polarized light. The schematic diagram of the designed dual wavelength, orthogonal-linear polarization multiplexing holographic display of the metasurface meta-atom structure is shown in Fig. 1(a). The metasurface is composed of periodically arranged rectangular meta-atoms. Figure 1(b) is a schematic diagram of holographic display of the metasurface at 532 nm wavelength and 633 nm wavelength with orthogonal-linear polarization. After the x-linear polarized light with the wavelength of 532 nm and the y-linear polarized light with the wavelength of 633 nm are vertically incident on the metasurface at the same time, the reconstructed output green “SZU” character and red bull head image are displayed in the far field.
Fig. 1. (a) Schematic of unit cell structure considering of TiO2 meta-atom on the SiO2 substrate (b) Schematic of hologram metasurface at wavelength of 532 nm and 633 nm with orthogonal-linear polarizations.
The classical Gerchberg-Saxton (GS) phase recovery algorithm [27] is used to calculate the phase of holograms required for the holographic image corresponding to two different wavelengths. Because the phase is continuously distributed, considering the actual processing ability and diffraction efficiency, it is necessary to quantify the phase hologram. According to the relationship between the diffraction efficiency and the quantization order, the phase of the two holograms is discretized by the eighth order. Finally, the phase of the same pixel of the two holograms is represented by the rectangular meta-atom, so as to obtain the metasurface that simultaneously provides the phase distribution required for the corresponding two holograms.
Due to the low absorption of titanium dioxide (TiO2) at the visible wavelength, TiO2 is used as the metasurface structure material to obtain higher transmission efficiency. Figure 1 (a) shows the schematic diagram of metasurface meta-atom structure. The unit cell has a period (P) of 500 nm in both directions, while the TiO2 meta-atoms, which are centered in the unit cells, have a thickness(H) of 650 nm, a length of L, a width of W. As the base material, SiO2 has a refractive index of nsio2 = 1.45.
When an arbitrarily polarized incident light is perpendicular to the metasurface meta-atom along the Z axis, the components ${E_{tx}}$ and ${E_{ty}}$ of the transmitted electric field in the x and y directions can be expressed by the transmission matrix T and the incident electric fields ${E_{ix}}$ and ${E_{iy}}$, as shown in Eq. (1) [7]:
Here, ${t_{xx}}$ and ${t_{yy}}$ are the components of the transmission matrix T in the same polarization direction, and ${t_{xy}}$, ${t_{yx}}$ are the components of the transmission matrix T in the orthogonal polarization direction. When the incident light is linear polarized, ${t_{xy}} = {t_{yx}} = 0$. According to Eq. (1), when the incident light is x-linear polarized, the corresponding x-linear polarized transmitted light is ${E_{tx}} = {t_{xx}}{E_{ix}} = \left|{{t_{xx}}} \right|{e^{i{\varphi _x}}}{E_{ix}}$, ${\varphi _x}$ is the transmission phase of the meta-atom. When the incident light is y-linear polarized, the corresponding transmitted y-linear polarized light is ${E_{ty}} = {t_{yy}}{E_{iy}} = \left|{{t_{yy}}} \right|{e^{i{\varphi _\textrm{y}}}}{E_{iy}}$, ${\varphi _y}$ is the transmission phase of meta-atom. Therefore, when the width W of meta-atom is fixed, the phase of the element is mainly controlled by the length L of meta-atom under the incidence of x-linear polarized light. Similarly, when the length L of meta-atom is fixed, the phase of meta-atom is mainly controlled by the width W of meta-atom under the incidence of y-linear polarized light. According to Eq. (1), the corresponding transmission phase can be obtained by changing the size (L, W) of the meta-atom under double wavelengths and double-linear polarized light. Through the reasonable design of L and W parameters, the phase response of the rectangular meta-atom under the incidence of x-linear polarized light and y-linear polarized light can all cover the range of 0-2π, so it is possible to obtain the transmission phase required for dual-wavelengths and dual-polarizations holographic display.
2.2 Immune algorithm optimize the meta-atom of metasurface
Immune algorithm [28] is an optimization algorithm imitating the biological immune system to solve the multimodal function optimization problem. The immune algorithm uses the group search strategy and iterative calculation to finally obtain the optimal solution of the problem with a large probability. The immune algorithm is better in solving the distributed complex problems, with better intelligence and better convergence to the global optimal solution in the solution-searching procedure.
In order to find the two parameter values of L and W corresponding to the phase required by the hologram, the conventional method is to obtain the relationship between L, W and the phase of the meta-atom by scanning the changes of L and W, which often requires a lot of calculation time. In this work, the immune algorithm [28] combined with finite-difference time-domain (FDTD) is used to optimize the L and W of meta-atom which required by the holograms, which can greatly reduce the calculation time. In order to obtain the appropriate size parameters of meta-atoms, the meta-atoms at the metasurface pixels $({x,y} )$ can simultaneously represent the phases of the corresponding positions of the two holograms ${\varphi _1}({x,y} )$ and ${\varphi _2}({x,y} )$, and ensure that the meta-atoms have relatively high transmission efficiency. This paper establishes a scientific evaluation function $\Delta ({x,y} )$ to assist selection. The evaluation function can be expressed as [29]:
Here ${\varphi _x}({x,y} )$ and ${\varphi _y}({x,y} )$ is the transmission phase value corresponding to 532 nm wavelength, x-linear polarized light and 633 nm wavelength y-linear polarized light when the length and width of the meta-atom are $L({x,y} )$ and $W({x,y} )$, respectively. ${t_x}({x,y} )$ and ${t_y}({x,y} )$ are the transmission efficiency corresponding to 532 nm wavelength x-linear polarized light and 633 nm wavelength y-linear polarized light when the length and width of the meta-atom are $L({x,y} )$ and $W({x,y} )$, respectively. The first and second terms of Eq. (2) consider that the rectangular meta-atom at $({x,y} )$ can simultaneously represent the phase of the corresponding positions of the two holograms, and the third and fourth terms consider the transmission efficiency of the rectangular meta-atom. The smaller value of the evaluation function $\Delta ({x,y} )$, the smaller deviation between ${\varphi _x}({x,y} )$, ${\varphi _y}({x,y} )$ and ${\varphi _1}({x,y} )$, ${\varphi _2}({x,y} )$ is obtained, i.e., the phase of the meta-atom on the pixel on the hologram is close to the phase of the hologram, and the maximum transmission efficiency of the meta-atom is ensured, the closer length and width of the meta-atom is to the ideal value.
We have two different holograms at two wavelengths, the meta-atom has two phases at two wavelengths. According to the phase retrieval algorithm, the phase distributions of two holograms corresponding to two different wavelengths are calculated. The meta-atom structures corresponding to two holograms were obtained by immune algorithm combined with FDTD algorithm. The whole optimization scheme is shown in Fig. 2. Firstly, the immune algorithm is applied to generate an initial meta-atom population in the whole search space, that is, to generate a variety of meta-atom structures, and then the FDTD algorithm is called to calculate the corresponding phase and t transmission efficiency of each meta-atom structure at different wavelengths. The phase and transmission efficiency of each meta-atom structure is evaluated by formula (2) to calculate out the evaluation function value, and the smallest evaluation function value has corresponding meta-atom structure. Through continuous optimization, we can determine whether all the phases of two hologram can find the corresponding meta-atom structures. When the judgment is true, the entire meta-atom database can completely correspond to two holograms, and the optimization is completed. If not, the immune algorithm will mutate the population to generate new species, and then evaluate and filter until all the meta-atom structures corresponding to two holograms are found, and the meta-atom database is established. Finally, the most suitable meta-atoms for each pixel of hologram are selected from the meta-atom database to form the metasurface device.
3. Simulation and discussions
We use 512 × 512 pixels holographic image: “SZU” character and red bull head image. By using GS algorithm to calculate the phase of two holograms at 532 nm and 633 nm wavelength. The phase distribution obtained for the hologram is shown in Fig. 3(a)(c).
Fig. 3. Simulated phase distribution of the two hologram (a) Phase distribution of “SZU” character hologram. (b) Enlarged phase distribution of the upper-right corner of (a). (c) Phase distribution of red bull head image hologram. (d) Enlarged phase distribution of the upper-right corner of (c).
A suitable meta-atom is selected from the constructed metasurface meta-atom database to represent the phase of the same pixel of the two holograms, so as to obtain the designed metasurface. The distributions of lengths and widths of the designed metasurface meta-atoms are shown on Fig. 4(a)(b).
Fig. 4. (a) Lengths distribution of metasurface meta-atoms. (b) Widths distribution of metasurface meta-atom (c) Simulated holographic image at wavelength of 532 nm and 633 nm with orthogonal-linear polarizations.
Figure 5 shows the distribution of transmission efficiency and phase of the incident light with 532 nm x-linear polarization and 633 nm y-linear polarization for eight metasurface meta-atoms randomly selected from the metasurface. The lengths and widths of the eight randomly selected meta-atoms of metasurface are listed in Table 1.
Fig. 5. Transmission and phase of the randomly selected meta-atoms from the metasurface, N is the number of meta-atoms.
Table 1. The lengths and widths of the randomly selected meta-atoms from the metasurface
Figure 4(c) shows the simulated holographic images of the metasurface with 532 nm x-linear polarization and 633 nm y-linear polarization incident light on the receiving screen. According to the transmission efficiency corresponding to the structural parameters of each pixel in the metasurface, the average transmission efficiencies of 532 nm x-linear polarized light and 633 nm y-linear polarized light are 68.2% and 74.6% respectively.
4. Experimental result
In this work, the metasurface is fabricated by the method of Atomic Layer Deposition (ALD). An experimental device was built to test the metasurface device. As shown in Fig. 6, two beams of different wavelengths with orthogonal-linear polarization were vertically incident on the metasurface, and orthogonal-linearly polarized light was obtained by rotating the polarization directions of the two polarizers. The 532 nm x-linear polarized and 633 nm y-linear polarized beams were combined through a beam splitter prism, and then vertically incident on the designed metasurface. The holographic image was received with a white screen.
Figure 7(a) shows the scanning electron microscope (SEM) scanning of the metasurface sample. The metasurface sample size is 256 um by 256 um, and the period of metasurface meta-atom is 500 nm. When 532 nm x-linear polarized light and 633 nm y-linear polarized light are incident on the metasurface at the same time, the holographic image presented on the receiving screen is shown in Fig. 7(b). The holographic images generated by the metasurface, and one can see that the red bull image and the green “SZU” character have high accuracy, low distortion and without the obvious cross-talk of the red “SZU” character and the green bull image. The measured cross-talk is around 1%. Because the phase of the metasurface is only close to the ideal value, and part of the transmitted light does not participate in the generation of the holographic image, a bright zero order spot appears in the center of the reconstructed holographic image plane. We found the ∼40% of transmitted light form the zero-order spot, and ∼60% of transmitted light generates the desired image. As can be seen from Fig. 7(b). Figure 7(c)(d) shows the holographic image presented on the receiving screen when 532 nm x-linear polarized light and 633 nm y-linear polarized light are separately incident on the metasurface. Due to the shielding of the zero-order light spot, the Red Bull image and the green “SZU” character are clearer and have higher resolution. The measured transmission efficiencies reach ∼60% and ∼67% at the wavelength of 532 nm and 633 nm. The diffraction efficiency is defined as the power of reconstructed image divided by the power of incident light. We block the zeroth order diffraction to measure the optical power of the images. Measured diffraction efficiencies are ∼18% and ∼21% at wavelength of 532 nm and 633 nm.
Fig. 7. (a) Scanning electron microscope image of fabricated structures (b), (c), (d) Holographic images obtained experimentally from the fabricated metasurface. The far field images captured by a digital camera on a screen (b) The wavelength of green (532 nm) and red (633 nm) and the pair of orthogonal-linear polarizations (x polarization and y polarization) simultaneously illuminate (c) x-linear polarized 532 nm light (d) y-linear polarized 633 nm light.
The experimental results show that the metasurface device can realize the incidence of 532 nm x-linear polarized light and 633 nm y-linear polarized light respectively, and reconstruct different holographic images, which are consistent with the simulation results in this paper.
5. Conclusion
In summary, the immune optimization algorithm combined with the finite-difference time-domain method (FDTD) is used to design and produce a simple structure of metasurface hologram composed of rectangular cylinder meta-atoms. The holographic display output of dual wavelength and dual polarization multiplexing is realized in the visible light band. The experimental results show that the designed metasurface hologram can display bright and clear holographic images under the simultaneous illumination of 532 nm plane wave with x polarization and 633 nm plane wave with y polarization. The transmission efficiencies are 68.2% and 74.6% in simulation, ∼60% and ∼67% in measurement. The metasurface has the advantage of simple structure, easy fabrication, suppression of the cross-talk between wavelengths, and high diffraction efficiency, which provides a new way for the practical application of the metasurface in optical storage, security devices, full-color display and many other applications.
Funding
National Natural Science Foundation of China (61275167); Shenzhen Higher Institution Stability Support Plan (20200812103045003); The Basic Research Project of Shenzhen (JCYJ20170817101827765, JCYJ20180305125430954).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the authors on reasonable request, see author contributions for specific data sets.
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