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Abstract
We propose a new generation of reprogrammable multi-functional bias encoded metasurfaces for dynamic wave manipulation using liquid crystals (LC). This metadevice is an array of unit-cells based on LCs to provide the desired phase steps based on its large birefringence property. The presented 3-bit coding metasurface (CM) use 8 states of "000"-"111" to control and manipulate the scattered wave at λ=1.4µm for several applications. The metasurface is introduced in detail and followed by several examples to show its versatility. Steered pencil, regular, and focused vortex beams with different topological charges are realized. The theoretical predictions are confirmed by numerical simulations. The proposed CM enables the realization of multifunctional optical wavefront manipulation and future intelligent optical devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials, which are materials with engineered properties consist of subwavelength unit-cells, exhibiting properties to manipulate the amplitude, phase, and polarization of electromagnetic waves which can not be obtained by natural materials [1–5]. Due to their bulky size, inevitable material losses, and fabrication difficulties, the metasurfaces, (as a 2D counterpart of metamaterials) which are made of arrays of planar metallic or dielectric structures, have shown great promise for practical applications [6–12]. The concept of digital metamaterials has been introduced, which utilize digital codes that realize the desired permittivity [13]. The simplest case is a 1-bit coding metasurface, which employs “0" and “1" coding particles in order to realize the inverse phases of 0$^\circ$ and 180$^\circ$. Universally an N-bit coding metasurface (CM) includes $2^N$ coding particles to provide discrete phase distribution with a step of $\phi =360^\circ /2^N$. This concept has been adopted to realize anomalous reflections, broadband diffusions [14], anisotropic digital metasurface [15], and multi-functional metasurfaces [16–20].
The orbital angular momentum (OAM) carried by vortex waves has a phase cross-section of $\exp (il\phi )$ where $l$ can take any integer value [21,22]. The transmission capacity of optical communication can be increased without occupying additional bandwidth by using OAM due to the orthogonality of its eigenstates [23]. Multi-bit coding sequences helped CM to generate complex wave steering functionalities such as OAM. However, there are still critical bottlenecks, since only a few works reported near-infrared (NIR) reprogrammable vortex beam realizations [24,25]. A-state-of-the-art coding metasurface employs complex coding particles $\exp (j\phi )$, through several respective coding patterns known as the addition theorem [26]. Furthermore, by applying the convolutional principle [27], the scattering pattern shift can be achieved. Therefore, by means of these two theorems, multiple pencil beam, vortex beam, and their combination with distinct topological charges have provided feasible opportunities. Each of the aforementioned capabilities may be realized by acquiring a suitable CM. However, many of the presented CMs are confined to a specific application and are not usable for other cases.
Active elements and field-programmable gate arrays have enabled the CM to be digitally controlled in a programmable manner. This has led to extensive applications such as dynamically-tunable absorbers [28], anomalous deflectors [3], and tunable focusing lenses [29], which have been applied in numerous frequency ranges. More recently, various works reported tunable coding metasurfaces by means of active materials such as pin diodes; however their capabilities are restricted to microwave frequencies [30]. Coding metasurface based on micro-electromechanical system (MEMS) [31] and Schottky diode [32] schemes have been used for real-time manipulation of electromagentic waves for frequencies up to THz. Nevertheless, it confined them for tuning capabilities that rely on the nonlinear properties of the compositing materials and their availability exclusively for laboratory experiments. Beside, tunable thin layers such as graphene, vanadium dioxide, and indium tin oxide have been employed to achieve multi-functional active metasurfaces [30,33–39]; however, they suffer high intrinsic losses and a difficult fabrication process, particularly in optical frequencies.
The liquid crystal (LC) is a promising candidate for tunable and dynamic metamaterials as an active ingredient due to its broadband non-linearity and birefringence, which can be externally controlled by temperature, light, and electric or magnetic fields [40–43]. LC has some advantages such as low loss and ease of fabrication compared to other tunable materials; however, it has a slower switching time. The typical time response of the LC is of the order of 1ms, which is well suitable for many multifunctional applications from anomalous refraction to vortex beam generation [44,45]. Importantly, in homogeneously aligned nematic LCs, the time for the Freedericksz transition for a vertically applied voltage is proportional to the square of the LC layer thickness. Therefore, response times of LC optical devices are considerably shorter than that of LC THz devices. Fast establishing solid-state light detection and ranging (LIDAR) and holographic display technologies need spatial light modulators (SLMs) to meet the ever-increasing customer demands. The most critical drawback of conventional LC-based SLMs is their large pixel size. On the other hand, LC-based metasurface can act as an SLM with sub-wavelength pixel size, and by changing the LC molecule’s orientation, the resonances can be tuned. LC-based metasurface SLM permits a reduction of the LC layer thickness essential to gain the necessary phase alternation by more than half as compared to the traditional SLMs [46].
In this paper, a liquid crystal-based 3-bit coding metasurface (LCCM) is presented at $\lambda$=1.4 $\mu$m, which can be used in several real-time applications. By changing the external voltage bias via an FPGA platform, the employed unit-cells can be dynamically arranged in different coding sequences between eight digital states of “000" -“111". To demonstrate the versatility and flexibility of the proposed LCCM structure, the steered pencil beams, OAMs with four different modes, and focused vortex beam, are all presented and verified through theoretical predictions and numerical simulations. Furthermore, the superposition of several patterns and beam shifting have been demonstrated by the addition theorem and convolution method. To the author’s best knowledge, this is the first multi-bit programmable LC-based CM at optical frequencies. The proposed method would address some crucial challenges at optical regimes, and pave the way for dynamic optical wavefront engineering and future practical multifunctional applications.
2. Design of the liquid crystal coding metasurface
Figure 1 depicts a sketch of unit-cells of the liquid crystal integrated metasurface. It is composed of a gold layer deposited under the LC material, which is sandwiched between a thick glass substrate and a metallic patch located on the top of the substrate. The dimensions are $l_1 = 223$ nm, $h_1=15$ nm, $h_2=230$ nm, $h_3=210$ nm, $h_4=80$ nm, $h_5=100$ nm, and $P=300$ nm. The LC is composed of anisotropic molecules whose orientations will be varied by applying an external electrical field. Upon illumination by a linearly polarized light, the permittivity of the nematic LC can be expressed as [47].
In the above equation, $\theta$ is the angle between the incident wave electric field and the LC director. In the unbiased state ($\varepsilon _{\perp }$), by coating both the top and bottom boundary surfaces of LC with a thin layer of polyimide (Pi) film, the long axes of the molecules will be directed parallel to the surface of the substrate (perpendicular to the director axis $\hat {n}$) due to the static action of a polymer layer [48]. By increasing the biasing voltage, the maximum relative permittivity ($\varepsilon _{\parallel }$) in the saturation state can be achieved while the long axis of the molecules is aligned parallel to the director axis $\hat {n}$ [49]. The periodicity of subwavelength unit-cells is $P=300$ nm. The glass is assumed to have relative permittivity of 2.25. The optical behavior of gold is characterized by Drude model in the NIR spectral region as:
Fig. 1. Schematic diagram of real-time wave-manipulation coding metasurface showing dimensions of the LCCM unit-cell. A coding sequence that is generated by a computer can translate to voltage biases by an FPGA and its functions can dynamically be controlled by the FPGA.
Table 1. All 8-step phases with the related permittivities of liquid crystal and a distinct color for each of them.
3. Results and discussions
Verification of the proposed metasurface consisting of reprogrammable unit-cells based on the LC is presented in this section. Under the illumination of the NIR linearly polarized wave, and assigning specific coding sequences to the unit-cells, the proposed LCCM has the possibility of generating pre-determined patterns by merely changing the biasing voltage controlled by an external field-programmable gate array. The following subsections present steered pencil beams, vortex beams with four different OAM modes, focused vortex beams with four OAM modes, and finally superposition and convolution of different patterns. It is worth mentioning that a metasurface with a fixed structure is used in each example. Different design goals are achieved by only altering the cells’ bias. Also, all the results presented in the following were obtained by full-wave electromagnetic simulation of the full-structure of the LCCM consisting of a finite array of the unit-cells.
3.1 Phase-gradient LCCM
By engineering the lateral phase gradient, one can direct the pencil beam in a pre-determined direction. To keep the periodic response of the unit-cells indicated in Table 1, the metasurface comprises an $N \times N$ array of $M \times M$ identical unit-cells that form a so-called super-cell. Using a 3-bit LCCM provides more freedom for any desired directions. The reflected angels can be calculated by generalized Snell law:
Suppose that a plane wave normally incident on the LCCM, and the desired pencil beam directions are ($\theta =24.4^\circ$, $\varphi =135^\circ$) and ($\theta =11.9^\circ$, $\varphi =135^\circ$). Accordingly, the aforementioned variables should be $M = 2$ and $M = 4$, $\Delta \varphi _y$=-$\pi$/4, $\Delta \varphi _x = \pi$/4 at 214 THz. Figure 2 shows the arrangement of the unit-cells for the steered beams at $\varphi =135^\circ$, and the resulted pencil beams in the predetermined directions. We observe good agreement between the theoretical predication and the numerical results. This example demonstrates that the instantaneous access to an anomalous reflection with outgoing directions is realized with our designed LCCM architecture. As can be observed, by changing the size of the lattices, beam steering functionality in real time can be realized which has applications in optical wireless communications and tracking systems.
Fig. 2. Steered pattern of the designed phase-gradient LCCMs for the direction of $\phi =135^\circ$ and $\theta$= (a) $24.4^\circ$ and (b) $11.9^\circ$
3.2 Generating vortex beams
To further show the versatility of our proposed reconfigurable LCCM architecture, four optical vortex wavefront with different topological charges are planned. To this end, the coding metasurface has been encoded by a spiral coding sequence, and the phase distribution of the metasurface can be calculated as:
where $l$ is the topological charge, $\varphi$ is the azimuth angle, and $y$ and $x$ are the distances between the centers of the unit-cells and center of the metasurface. Note that the arrangement of the cells is composed of 8 and 16 sectors, for $\mid l \mid = 1$ and $\mid l \mid = 2$, respectively, and the successive phase step from one sector to another is $\pm 45^\circ$. Under the illumination of a linear plane wave on the metasurfaces, the electric field distributions recorded for OAM modes of l=-2, -1, 1, 2 in the far-field with the dimensions of 10800 nm$\times$10800 nm are shown in Figure 3(a)-(d). The produced doughnut-shape vortex patterns for each mode are shown in Figure 3(e)-(l), which validate this capability of the proposed LCCM. We observe that the patterns are ring-shaped with high intensity and an approximate 15 dB drop in the center (in comparison to highest amplitude in the annular zone). In this example, the encoded metasurface contains 36 $\times$ 36 unit-cells with an overall size of $10.8 \times 10.8\,\mu {m^2}$. The ability to instantaneously switch between different topological charges in real time is provided by our LCCM architecture that can enable applications in wideband OAM based multi-user system where the beam’s topological charges identify the routing.Fig. 3. (a)-(d) Electric field distribution, and (e)-(h) Top view and (i)-(l) 3D view of simulated far-field patterns of the generated vortex beam, respectively, with different topological charge orders of l=-2, l=-1, l=1 and l=2.
3.3 Parabolic spiral LCCM
To further exhibit the multi-functional potential of the proposed LCCM, the focused vortex beam with coding sequences in the pattern of a parabolic spiral is presented. This application allows concentration of the incident plane wave onto a pre-determined point in a vortex shape pattern, and also switch the focal point ($z_{focal}$) and topological charge order in real time. The phase pattern of the metasurface for this purpose is computed as:
which $l$ is the OAM mode, $y$ and $x$ are the distances between the center of the unit-cells and the center of the metasurface, and $\lambda$ is the operating wavelength. Four focused vortex beam extracted from the proposed LCCM for topological orders of $l$=-2, -1, 1 and 2, are shown in the focal points of 10000 nm, 7000 nm, 6500 nm and 8500 nm, respectively. Figure 4(a)-(d) represent the required 2D spiral-parabola phase map for realizing the corresponding digital states, where it is shown that for $\mid l \mid =1$, 8 arcs (phases), and for $\mid l \mid =2$, 16 arc (phases) are twisted to each other. In this example, the encoded metasurface contains 36 $\times$ 36 unit-cells with an overall size of $10.8 \times 10.8\, \mathrm {\mu m^2}$. The simulated electric field distributions in the sampling planes at the corresponding focal lengths (see Figure 4(e)-(h)) exhibit the capability and flexibility of the proposed LCCM to generate optically focused vortex beams with different topological charges and focal lengths.Fig. 4. (a)-(d) Phase map profile, and (e)-(h) the electric field distribution of the focused vortex beams, respectively, with l=-2, l=-1, l=1 and l=2 (from left to right).
3.4 Superposition and convolution
Due to the fact that the coding pattern and the scattering pattern are a Fourier transform pair [26,50], the principle of scattering pattern shift could be defined as:
Fig. 5. (a) Superposition of two tilted gradient pattern. (b) Convolution of an OAM beam with mode of l=-2 with a chessboard pattern.
Recently, it has been shown that the addition of two different functions by superposition will provide a mixed coding pattern which achieves both functionalities simultaneously. It employs the complex coding particle $e^{j\varphi }$ to add two separated scattering patterns by:
where $\varphi _3$ is the phase requirement for the superimposed CM. Let us consider two metasurfaces driven by gradient coding sequences along different directions to produce two single beams along ($\theta$=12$^\circ$, $\phi$=315$^\circ$) and ($\theta$=24.4$^\circ$, $\phi$=225$^\circ$) directions, respectively. Exploiting the superposition operation leads to an LCCM structure incorporating both the above-mentioned gradient codes satisfactorily to generate two scattered beams pointing at the predetermined directions as shown in Figure 5(a). Once again, we observe that all the practical functionalities discussed throughout this paper can be instantaneously interchanged to another function by digitally and dynamically changing the spatial voltage distribution controlled by an FPGA platform.4. Biasing and fabrication possibility
For biasing the cells, we can use the structure shown in Fig. 6(a) consisting of a gold patch with a dimension of $223 \times 223 ~ \mathrm {nm^2}$ with a lattice spacing of 230 nm on a glass substrate covered with 5 nm of Indium-Tin-Oxide (ITO), which can be fabricated by a standard electron-beam lithography method. Since the ITO has low resistance electrical contacts without blocking light, the presence of ITO does not have any considerable effect on the scattering response of the metasurfaces. The simulated reflection amplitude and phase response of the unit-cells for two states of LC permittivities with and without ITO layers are depicted in Fig. 6(b) and Fig. 6(c) showing a negligible effect of the ITO on the responses. In these simulations, the near-IR permittivity of the ultra-thin ITO film was given from [51,52]. It should be noted that for ultra-thin ITO films, the imaginary part of the electric permittivity trends towards zero. The transparent ITO layer inhibits charge accumulation during the electron-beam lithography process and also acts as one of the two electrodes required to apply the electric voltage to the LC cell. For applying the positive voltages to the top electrodes, we can use transparent ITO nano-wires since they do not impact the reflection characteristics of the structure considerably [53,54]. Moreover, ITO films covers almost the entire cell’s surface; however, small gaps are needed to have a DC isolation between neighboring electrodes.
Fig. 6. (a) Schematic representation of LCCM after inserting ITO thin layer which act as a positive electrode to apply DC bias voltage. (b) Top view of LCCM. (c), (d) Simulated reflection amplitude and phase of LCCM for two different permitivies of LC (3.4 and 5.8).
It is worth mentioning that since the bias voltage is applied between the top ITO electrode covering almost the entire cell’s surface and the bottom of the gold film, the bias electric field would have an almost uniform distribution. The electric field is distorted between neighbor areas biased with different voltages. But since all designs used super-cells consisting of several identical cells, which are biased using the same voltage, distortions in the bias field appear only in small areas between two adjacent super-cells, which is negligible compared to the super-cell areas.
Notice that the accurate height of the gap between the two electrodes can be extracted from the measured Fabry-Perot oscillations of the unit-cell without the liquid crystal. After infiltration with the liquid crystal at a specified temperature, the LCCM can be fixed in a home-built white-light transmittance setup and can be connected to an adjustable function generator that supplies a sinusoidal AC voltage. In the experiments, the light from a halogen lamp should first transmit a polarizer to produce linear-polarized light and then consecutively concentrated onto the LCCM. After excitation by x-polarization of light, the reflected emerging light spectrum can be detected with an optical spectrum analyzer and consequently, a CCD image of the LCCM can be recorded.
5. Conclusion
This work presented a design concept for a novel multi-mission bias encoded metasurface at optical frequencies incorporating LC as a phase change material. This work was motivated by the ever-increasing demands of integrating multiple diversified functionalities into one single device. By tuning the LC permittivity from 2 to 6 at a wavelength of 1400 nm through an external voltage bias in real time, eight reflection phase responses of 0, $\pi /4$, $\pi /2$, $3\pi /4$, $\pi$, $5\pi /4$, $3\pi /2$, and $7\pi /4$ were achieved to mimic eight digital states of “000" - “111". The versatility of the LCCM structure has been validated through several demonstrative examples from anomalous reflection to focused wavefront carrying OAM with different topological charges, which were dynamically interchangeable. The simulation results corroborate well with our theoretical predictions where the superposition theorem and convolution operation were adopted for realizing several fundamental objectives from multiple pencil beams in predetermined directions to emitting arbitrarily-oriented multiple vortex beams with different OAM modes. We believe that the integrated structural design of our proposed LCCM is a promising candidate to meet future demands of intelligent optical industrial applications and multifunctional devices.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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