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Abstract
Metasurfaces have shown their unique capabilities to manipulate the phase and/or amplitude properties of incident light at the subwavelength scale, which provides an effective approach for constructing amplitude-only, phase-only or even complexed amplitude meta-devices with high resolution. Most of meta-devices control the amplitude and/or phase of the incident light with the same polarization state; however, separately controlling of amplitude and phase of the incident light with different polarization states can provide a new degree of freedom for improving the information capacity of metasurfaces and designing multifunctional meta-devices. Herein, we combine the amplitude manipulation and geometric phase manipulation by only reconfiguring the orientation angle of the nanostructure and present a single-sized design strategy for a multiplexing meta-hologram which plays the dual roles: a continuous amplitude-only meta-device and a two-step phase-only meta-device. Two different modulation types can be readily switched merely by polarization controls. Our approach opens up the possibilities for separately and independently controlling of amplitude and phase of light to construct a multiplexing meta-hologram with a single-sized metasurface, which can contribute to the advanced research and applications in multi-folded optical anti-counterfeiting, optical information hiding and optical information encoding.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Benefiting from the extraordinary optical responses to the incident light, nanostructured metasurfaces [1–16] have the capabilities of artificial manipulation of lightwave at the subwavelength scale. In the optical manipulations based on metasurfaces, amplitude and phase are the two fundamental optical properties since most optical functional elements and devices are phase-modulated and amplitude-modulated. Among them, rotating the in-plane orientation angles of nanostructures with fixed geometries is a commonly used and effective method to spatially vary the Pancharatnam-Berry (PB) phase (also called geometric phase) of incident circularly polarized (CP) light. In recent years, a variety of geometric phase based optical elements have been proposed, such as metalenses [17–19], meta-gratings [20,21], meta-holograms [22–25], vortex beam generators [26–30] and so on. Regarding to holograms, since a complex-amplitude-modulated hologram can record a three-dimensional (3D) object and it is much more realistic than amplitude-modulated or phase-modulated ones, several complex amplitude manipulation approaches based on nanostructures with varied geometries and orientations [31–33] or a couple of nanostructures [34–36] have been proposed. In their approaches, the amplitude and phase manipulations are realized for the incident light with the same polarization state. Although complex amplitude modulation is of great meaningful, separately controlling the amplitude and phase of incident light with different polarization states can provide a new degree of freedom for the design of multiplexing and multifunctional optical elements.
Recent studies suggest that rotating the orientation angles of anisotropic nanostructures can modulate the amplitude of linearly polarized (LP) light continuously and effortlessly, governed by Malus law. Hence, metasurfaces consisting of nanostructures with different orientations have been reported to construct nanoprints [37–43] and amplitude-only meta-holograms [44,45]. Since geometric phase aforementioned is also dependent on the orientation angles of nanostructures, it is effective to combine Malus-assisted amplitude modulation and geometric phase modulation, and control them separately by employing different polarization controls (LP light for amplitude modulation and CP light for geometric phase modulation), which provides a new route for light manipulation for information multiplexing.
Herein, we present a novel design strategy for multiplexing meta-holograms, which are implemented by constructing a dual-channel meta-hologram with separate manipulation of amplitude and phase of incident light with different polarization states. Figure 1 illustrates the basic concept of the proposed strategy for separate manipulation of amplitude and phase of incident light. It can be seen that one single metasurface consisting of nanostructures with identical geometries but varied orientations can realize two types of optical manipulations (a continuous amplitude manipulation and a two-step phase manipulation), which could be transformed from one type to the other only by switching the polarization states of incident light. Separately manipulating the optical amplitude and phase provides a new mode to advanced light manipulation and can be used to design multiplexing and multifunctional optical elements, which is a simple but useful extension of the long-employed geometric metasurfaces (GEMS). It should be noted that our concept is different from other independent manipulation of amplitude and phase [32], which modulates the amplitude and phase of the incident light with the same polarization state. Therefore, the manipulations of amplitude and phase of their approach are interrelated essentially, that is, two different optical manipulations are not completely separate. When amplitude is modulated, there is no guarantee that phase cannot be modulated and vice versa. As a comparison, in our approach, the phase modulation is irrelevant to the amplitude modulation and one can design a multiplexing metasurface which is an amplitude-only device and a phase-only device all in one. In addition, our strategy can significantly increase information storage density and enhance the information security without adding extra complexity of the design and fabrication, which can be easily applied to other applications such as information storage, anti-counterfeiting, encryption, optical communication, and many other related fields.
Fig. 1. Schematic illustration of manipulating optical amplitude and phase separately. The designed dual-channel multiplexing meta-hologram plays the dual roles: an amplitude-only hologram and a phase-only hologram. The meta-hologram is composed of nanobricks with identical geometric parameters but spatially varied orientations. The inset in the upper left corner is a partial scanning electron microscope (SEM) image of the fabricated meta-hologram sample. The polarization states of incident light are employed as optical keys to decode the information recorded in two channels of the meta-hologram. Specifically, under LP light illumination, an amplitude-only holographic image recorded in channel 1 is reconstructed in the far field. Under CP light illumination, a phase-only holographic image recorded in channel 2 is reconstructed in the far field. The two optical manipulations are independent and do not interfere with each other.
2. Principle of separately manipulating the amplitude and phase via polarization controls
Amplitude manipulation with linearly polarized incident light. Considering an anisotropic nanostructure with orientation angle α (the angle of the short axis of the nanostructure relative to the x-axis), the output electric field of the nanostructure induced by normally incident x-LP light with a Jones vector of $\left[ {\begin{array}{{c}} 1\\ 0 \end{array}} \right]$ (polarized along the x-axis, labeled as PX) or y-LP light with a Jones vector of $\left[ {\begin{array}{{c}} 0\\ 1 \end{array}} \right]$ (polarized along the y-axis, labeled as PY) can be written as
From Eq. (1), we can see that the output field consists of two parts: the co-LP light with the same polarization as that of the incident light and the cross-LP light with the orthogonal polarization. Furthermore, the amplitude modulation rule of the cross-LP light is the same for illuminating the nanostructure with the x- or y-polarized light, which is completely dependent on the first term of the equation.
Phase manipulation with circularly polarized incident light. In case of CP light illumination, mathematically, the transmitted light passing through the nanostructure can be expressed as
With Eqs. (1) and (2), we plot two different curves for amplitude and geometric phase modulation, respectively, as shown in Fig. 2(a). It can be seen that one orientation angle α of the nanostructure could separately modulate the amplitude and phase of incident light, under different polarization controls. Orientation degeneracy of anisotropic nanostructures [46–49] shows a “one-to-many” mapping relationship between orientation angles of nanostructures and modulated intensity, which can be employed to integrate the two functionalities (amplitude modulation and phase modulation) into one metasurface. Specifically, as shown in Fig. 2(a), there are two orientation candidates corresponding to an equal amplitude value except for the maximum/minimum value. The two options of orientation angles can be employed to generate a two-step geometric phase modulation. Consequently, we can obtain a continuous amplitude modulation for the LP incident light and a two-step phase modulation for the CP incident light, merely with a single-sized metasurface, which means that amplitude and phase can be chosen separately. Although the phase value cannot be chosen arbitrarily and independently for one unit-cell, it does not prevent the generation of an arbitrary farfield distribution for hologram, since the effects can average out over the entire element. This indicates that each nanostructure contains two independent information channels for amplitude and phase modulations, respectively. Our concept is quite different from conventional supercell and multilayer design strategies [49], in which each nanostructure contains only one information channel. Therefore, our approach can increase the information density of metasurfaces theoretically.
Fig. 2. Working principles of separately manipulating the optical amplitude and phase, the illustration and the spectral response of a unit-cell nanostructure of the designed metasurface. (a) Amplitude modulation for cross-LP light and phase modulation for cross-CP light versus orientation angle. Two different orientation angles are mapped to an equal amplitude value (marked with green stars), corresponds to a two-step geometric phase modulation (marked with green points). (b) Schematic illustration of an anisotropic nanobrick unit-cell structure. A silver nanobrick is with width W, length L, height H, cell sizes C × C and orientation angle α relative to the x-axis. (c) Simulated transmission and reflection of the designed unit-cell versus wavelength (510 nm ∼ 690 nm). T and R represent the transmissivity and reflectivity for the LP light polarized along the long and the short axes of the nanobrick (labelled with l and s), respectively.
Additionally, as shown in Fig. 2(a), the amplitude-modulated function sin2α can be positive or negative since α varies from 0° to 180°, which can be used to eliminate the unwanted zero-order light that affects the observation of holographic images [44]. Herein, the negative amplitude does not mean the value of the amplitude is opposite, but the direction of the amplitude. That is, for the same amplitude value, the positive value means the direction of the amplitude is positive, and the negative value means the opposite direction. In addition, it can also be interpreted as including a phase term equal to π. Next, we design a nanostructure as an example which can be regarded as a nano-polarizer to implement the multiplexing metasurfaces, as shown in Fig. 2(b). Considering the requirement of investigating the spectrum response and the ease of fabrication in the visible range, metallic silver (Ag) nanobrick is employed and the material of the substrate is silica (SiO2). With the help of CST Microwave Studio software, we elaborately design the geometric parameters of the nanostructure, and a nearly-optimal nano-polarizer is obtained with length L of 160 nm, width W of 80 nm, height H of 80 nm and cell sizes C × C of 300 nm × 300 nm. Figure 2(c) shows the simulated results of the spectral response of the designed nanostructure illuminated by the LP light polarized along two orthogonal directions (the long and short axes of the nanobrick, labelled as l and s), respectively. It can be seen that the transmissivity Ts (95.3%) and reflectivity Rl (92.6%) are above 90% at the designing wavelength of 633 nm, and the unwanted Tl and Rs can be suppressed to be below 2% and 4%, respectively. Hence, the designed nanobrick could function as an ultracompact nano-polarizer in both transmission and reflection modes, and the corresponding transmission axes are the short axis and the long axis of the nanobrick, respectively. The details about the numerical simulation of the unit-cell are provided in the Methods.
3. Design of a dual-channel multiplexing meta-hologram based on separate control of amplitude and phase
As a proof of concept, we design a dual-channel multiplexed meta-hologram composed of the above designed nanostructure to demonstrate the proposed strategy of separately manipulating the amplitude and phase. The dual-channel multiplexing meta-hologram is composed of 500 × 500 nanobricks with identical geometry parameters but spatially varied orientation angles, thus the area of the meta-hologram is 150 × 150 µm2. Patterns of “flower” and “fishbone” are taken as the target images of amplitude-only and phase-only computer-generated holograms (CGHs), respectively. Additionally, the amplitude-only and phase-only CGHs are both designed as Fourier holograms with the same diffraction angle of 30° × 30°.
The flow chart of generating a dual-channel multiplexed meta-hologram is shown in Fig. 3, including three steps. (1) Design of an amplitude-only CGH. At first, according to the target amplitude-only holographic image of “flower”, the amplitude distribution (the interval of definition is [−0.5, 0.5]) of the amplitude-only CGH is calculated by employing the widely used Gerchberg-Saxton (GS) algorithm [50]. The simplified process is shown in Fig. 3(a). It is worth noting that, unlike the GS algorithm for phase-only CGHs, the real part of the complex amplitude is used to iteratively calculate the amplitude profile of the amplitude-only CGH. The amplitude profile is obtained by iteratively applying the inverse fast Fourier transform (iFFT) and fast Fourier transform (FFT), and setting the terminating criterion, until the error between the original target image and the iteratively reconstructed image is less than the preset tolerance. The final amplitude distribution is normalized to a range of [−0.5, 0.5], as depicted in Fig. 3(b). (2) Calculation of the initial orientation distribution. As the designed nanostructure can act as a polarizer, according to Eqs. (1) and (2), the amplitude of the transmitted cross-LP light could be described as Am = (sin2α)/2. Thus, the amplitude distribution of the amplitude-only CGH could be encoded as the initial orientation angles of nanobricks through the equation α = [sin−1(2Am)]/2. (3) Calculation of the final orientation distribution. As shown in Fig. 2(a), each nanobrick of the metasurface has two orientation candidates to generate an equal amplitude, providing a separate two-step phase modulation for the cross-CP light. Then, by employing Simulated Annealing (SA) algorithm [46,51] to reconfigure the orientation angles of nanobricks, the suitable one of the two orientation candidates is chosen to generate the phase profile of the phase-only CGH, as shown in Fig. 3(c). The enlarged amplitude distribution and phase distribution of the same region of the dual-channel multiplexing meta-hologram are shown in Figs. 3(d) and 3(e), respectively. After optimization by SA algorithm, the partial orientation distribution of the dual-channel multiplexing meta-hologram is shown in Fig. 3(f). It can be seen that some nanobricks are rotated to the position shown in the red box, that is, the phase distribution changes. However, according to the orientation degeneracy of amplitude modulation, the corresponding amplitude distribution remains unchanged.
Fig. 3. Flow chart of the dual-channel multiplexing meta-hologram design. (a) Flow chart of the Gerchberg-Saxton (G-S) algorithm based on Iterative Fourier transform to generate an amplitude-only CGH. E denotes the complex amplitude of the target amplitude-only holographic image in the image plane. Then the complex amplitude E1 in the hologram plane is obtained by applying the iFFT. At last, the complex amplitude E2 of the reconstructed holographic image is obtained by applying the FFT. (b) The final amplitude profile of the amplitude-only CGH corresponding to the channel 1 after eliminating the unwanted zero-order diffraction light. (c) Based on the orientation degeneracy, the phase profile of a phase-only CGH is encoded into channel 2 of the same metasurface by employing the SA algorithm. (d) Enlarged amplitude and (e) phase distribution of the same region of the dual-channel multiplexing meta-hologram (red dashed boxes shown in (b) and (c)). (f) Structure schematic of a partial region of the meta-hologram composed of nanobricks with identical geometric dimensions but varied orientation angles. The orientation angles of nanobricks in the red dashed boxes change after employing the SA algorithm, but the corresponding amplitude value remains unchanged.
Hence, by elaborately engineering the orientation angles of nanobricks on a metasurface, an amplitude-only CGH and a phase-only CGH are simultaneously integrated into a single metasurface. The polarization states of incident light could be employed as optical keys to decode the dual-channel information recorded on the meta-hologram. Specifically, the LP incident light could be employed to decode the amplitude-only holographic image in channel 1 and the CP incident light could be employed to decode the other phase-only holographic image in channel 2.
4. Experimental demonstration of the dual-channel multiplexing meta-hologram
The dual-channel multiplexing meta-hologram are fabricated by the standard E-beam lithography (more details about the sample fabrication are presented in Methods). Although the designed meta-hologram can work in both transmitted and reflected spaces, in consideration of the easiness of observing, here we only exhibit the transmission working mode. The fabricated sample is placed into the optical observation setup shown in Fig. 4(a), including a super-continuum laser source (YSL SC-pro), two linear polarizers (P1 and P2), two quarter wave plates (QWP1 and QWP2), an iris and a white screen. A polarizer P1 or a combination of P1 and QWP1 is adopted to transform the light emitted by the laser source to the required linearly or circularly polarized light, respectively. Another polarizer P2 or a combination of QWP2 and P2 is used to filter out the unmodulated co-polarized (co-LP or co-CP) light, respectively. Here, the transmission axis of P2 is orthogonal to that of P1. All of the holographic images are projected onto the white screen placed at a distance of 300 mm away from the meta-hologram sample and captured with a commercial CMOS camera (Nikon5100). In the absence of QWP1 and QWP2, the incident LP light normally irradiates the meta-hologram and the transmitted cross-LP light projects an amplitude-only holographic image into the far field, as shown in Fig. 4(b). After inserting two quarter wave plates, a phase-only holographic images recorded in channel 2 can be observed, as shown in Fig. 4(c).
Fig. 4. Experimental demonstration of the dual-channel multiplexing meta-hologram. (a) Schematic of the experimental setup for capturing the reconstructed holographic images. The transmission axes of the polarizers P1 and P2 are set to be perpendicular to each other to only allow the cross-polarized transmitted light pass through. Quarter wave plates in white dotted box (QWP1 and QWP2) are added for observing the phase-only holographic images recorded in channel 2, which requires the illumination of CP light. (b) The amplitude-only holographic image decoded by the LP incident light in channel 1. The solid and dashed lines at the top right denote the polarization directions of the incident LP light and the transmitted cross-LP light, respectively. (c) The phase-only holographic image decoded by the LCP incident light in channel 2. The operating wavelengths are both 633 nm.
To explore the broadband response, a super-continuum laser source (YSL SC-pro) emitting light with various wavelengths (ranging from 510 nm to 660 nm in steps of 30 nm) is employed to investigate the spectral response. As shown in Fig. 5, under LP incident illumination with various wavelengths range from 510 nm to 660 nm, the amplitude-only holographic images recorded in the channel 1 are decoded. We can see that all holographic images are observed with high fidelity except for varied dimensions.
Fig. 5. Experimentally captured amplitude-only holographic images generated by illuminating the sample with LP light ranging from 510 nm to 660 nm in steps of 30 nm.
Next, by changing the polarization state of incident light, i.e., from linear to circular, the phase-only holographic images recorded in the channel 2 are decoded, as shown in Fig. 6. The reconstructed holographic images with high fidelity verify the feasibility and effectiveness of separately manipulating the amplitude and phase. The unavoidable twin-image appears in the experiments as a result of amplitude modulation [52] and two-step phase modulation [46].
Fig. 6. Experimentally captured phase-only holographic images generated by illuminating the sample with LCP light ranging from 510 nm to 660 nm in steps of 30 nm.
It can be seen that the two information channels are independent to each other for the reason that the amplitude is controlled while the phase modulation is prohibited or vice versa. Furthermore, the proposed dual-channel multiplexing meta-hologram shows strong robustness against wavelength variations and the design strategy is effortless to implement only by engineering the orientation angles of anisotropic nanostructures, bringing great convenience for mass manufacturing and practical applications.
In addition, the efficiencies of the amplitude-only hologram and the phase-only hologram at the various wavelength are measured by using an optical power meter (Thorlabs PM100D). The efficiency of the element is defined as the ratio of the power of the transmitted amplitude-only/phase-only holographic image to the power of the incident beam. At the operating wavelength of 633 nm, the experimentally measured efficiency is about 0.17% and 6% for the amplitude-only meta-hologram and the phase-only meta-hologram, respectively. The efficiency results at the various wavelength are shown in Table 1. It can be seen that if the incident wavelength deviates from 633 nm, the efficiency will decrease, reducing the overall efficiency of the meta-hologram. The efficiency could be improved by applying more precise fabrication procedures or using low-loss dielectric materials (such as TiO2).
Table 1. Measured efficiency results at the various wavelength under two modes
5. Discussions
One remarkable characteristic of our approach is the separate manipulation of amplitude and phase, which provides a new route for multiplexing light manipulation. Hence, a new degree of freedom is available for designing advanced multiplexing meta-holograms. Each nanostructure of the designed dual-channel multiplexing meta-hologram records the information of two independent channels, thus increasing the information density of the multiplexing metasurface. More importantly, the strategy is conducted by reconfiguring the orientation angles of anisotropic nanostructures rather than varying their dimensions, which is promising to bring a technological innovation in designing multiplexing and multifunctional optical elements without adding extra complexity of metasurface design and fabrication.
Another attractive feature of the proposed meta-hologram is that its amplitude/phase modulation is the insensitivity to the operating wavelength. As proved in the theoretical analysis, the nature of phase modulation and amplitude modulation both originate from the orientation of the nanostructure thus the optical modulation is independent of the wavelength of incident light.
At last, our strategy can significantly improve the security and controllability of information. Two different modulation types are switched by controlling the polarization state of the incident light, which requires different orthogonal-polarization optical paths to decode the information recorded in the two channels of the multiplexing meta-hologram. The information cannot be directly obtained without polarization controls, which has potentials in optical information encryption, hiding and anti-counterfeiting, etc.
6. Conclusions
In this paper, we propose a general design strategy of separately manipulating optical amplitude and phase to realize a multiplexing meta-hologram via a single-sized metasurface, merely with polarization controls. Hence each nanostructure of a metasurface can store independent dual-channel information conducted with amplitude and phase modulations, respectively. We experimentally demonstrate this concept by constructing a meta-hologram acting as a continuous amplitude-only hologram and a two-step phase-only hologram simultaneously. Our strategy for multiplexing metasurface design not only increases the information storage density with dual channels but also enhances information security, since the information of each channel is decoded with different optical setups for different polarization controls. Interestingly, the separate manipulation of amplitude and phase originates from the orientations of nanostructures rather than varied geometries, thus the performance is independent of wavelength, which has been experimentally demonstrated over a wide spectral range. With the advantages of increased information density, high security, single-sized design and wavelength insensitivity, the proposed metasurface could find its promising applications in information storage, optical communications, information encryption and anti-counterfeiting, etc.
7. Methods
7.1 Numerical simulations
Commercial CST microwave studio software is used to perform the numerical simulations. As depicted in Fig. 2(b), the nanobrick can be rotated in the xoy plane with an orientation angle α defined as the angle of the short axis of the nanobrick relative to the x-axis. In the simulation, the unit cell condition is employed for x- and y- axes and the open condition is adopted for z-axis, α fixed at 0° and the normal incident plane wave is LP light polarized along the short or long axis of the nanobrick. By optimizing the geometry parameters of the nanostructure, a nano-polarizer structure (which can reflect most of incident light polarized along the long-axis direction while transmits that along the short-axis) with L of 160 nm, W of 80 nm, H of 80 nm and C of 300 nm is obtained and the working wavelength is 633 nm. With these geometric parameters, the spectral response property of the designed unit cell is obtained by sweeping the frequency.
7.2 Sample fabrication
The sample is fabricated on a fused silica substrate by Electron beam lithography (EBL) as following procedures. First, the substrate is spin-coated with positive electron beam resist layer polymethyl methacrylate (PMMA, 950K) at a speed of 4000 rpm and baked on a hotplate at 150 °C for 3 minutes. Next, the wafer is covered with PEDOT: PSS film applied as a conducting layer. Nanobrick structures are defined on the resist film based on the EBL (Raith 150, 30 kV). After the exposure process, the conducting layer is washed away and the exposed resist is developed in the methyl isobutyl ketone (MIBK) and isopropyl alcohol (IPA) 1:3 solutions for 80 seconds at room temperature, dipped in IPA for 30 seconds and blown dry using nitrogen. In order to increase the adhesion of silver and silica substrate, a layer with thickness of 3 nm titanium is deposited firstly. After that, a silver layer with final thickness of 80 nm is deposited by electron beam evaporator. Finally, all of silver nanobricks are obtained on the fused silica substrate through lift-off proceeds in 75 °C hot-acetone.
Funding
National Natural Science Foundation of China (11774273, 11904267, 91950110); Fundamental Research Funds for the Central Universities (2042021kf0018, 2042021kf1043).
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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