
Citation: | Huang YJ, Xiao TX, Chen S, Xie ZW, Zheng J et al. All-optical controlled-NOT logic gate achieving directional asymmetric transmission based on metasurface doublet. Opto-Electron Adv 6, 220073 (2023). doi: 10.29026/oea.2023.220073 |
Since the information processing efficiency for traditional electron-based computing technology with excessive Ohmic loss is intrinsically limited by the RC delay as well as the data transfer speed among different modules, optical computing is a promising alternative1, 2. Due to its unique properties of ultrahigh processing speed, ultralow power consumption and parallel operation capability for ref.3, 4, optical computing has been treated as a potential platform to meet the demands for large calculation amount and low-cost energy consumption. Akin to its electron-based counterpart, logic operations are also required in optical circuits to lay the foundation for the implementation of computing. Therefore, constructing and exploring all-optical logic gates (LGs) with robust performance, complete logic function and ease of implementation is now a hotspot in the fields of optics, plasmonics and photonics5.
To date, although many related works have been reported to achieve all-optical logic operations based on linear or nonlinear optical effects, their performances are still limited by their intrinsic drawbacks. For nonlinear cases6-8, since the optical LGs are mostly based on the third-order nonlinear susceptibility that heavily depends on the precise manipulation of control light and pump light, the robustness for these devices can hardly meet the requirements for practical applications. For linear cases, the methodologies mainly include interference effects and on-chip plasmonic effects9-12. The limitation for the former one is the rigid interference conditions and complicated optical paths, which lead to performance instability as well as device cumbersome11, 12, while the latter one is restricted by stringent demand for the size of input beams to avoid cross talk and false output9, 10.
Metasurface, as a kind of artificial surface composed of subwavelength unit cells, has attracted much attention in recent years due to its unique properties such as small footprints, flexible functions and planar geometries13-17. By ingeniously aligning the meta atoms and choosing proper materials, many novel phenomena and applications have been witnessed including electromagnetic absorption18-23, flat lensing24-28, surface cloaking29, 30, polarization control31-36 and meta-hologram37-40. Recently, metasurface-based all-optical LGs were also proposed that have already manifested many exotic advantages over the traditional counterparts due to their more compact structures and higher operation efficiency5, 41-43. However, most of the presented works only realized basic LGs with “AND”, “OR” or “NOT” operations, while additional logic operations will be needed for practical application.
Here, in order to further enhance the operation robustness and miniature of the optical device, we propose a metasurface-based all-optical LG with simple yet generalized methodology. Distinct from previously reported works that need specific manipulations for the incident light, this designed all-optical LG exhibits a highly efficient response simply under plane wave incidence according to its incident direction and spin state. Besides, it possesses multiple-input-output states that behave as a controlled-NOT (CNOT) LG. Similar to its quantum counterpart44, 45, control signal (CS) ε1 and target signal (TS) ε2 are two basic elements in the all-optical CNOT LG. Mathematically, such operation can be described as:
|ϵ1⟩|ϵ2⟩→|ϵ1⟩|ϵ1⊕ϵ2⟩, | (1) |
where ε1,2=0 or 1 describes their incident states and ⊕ denotes the logic modulation. As shown in Eq. (1), the input CS determines the change of TS and the value of CS is invariant during the operation. Therefore, the CNOT LG can be expressed by the unitary operation:
|00⟩|01⟩|10⟩|11⟩|00⟩|01⟩|10⟩|11⟩(1000010000010010). | (2) |
Equation (2) shows that if the input CS equals “0”, the output TS maintains its value. Otherwise, the output TS will be altered accordingly (“0” to “1” or “1” to “0”). To further present the working mechanism of the proposed metasurface-based CNOT LG, Fig. 1 shows the far-field responses after incident light passing through the metasurface doublet under different conditions. It can be inferred that four diverse responses can be obtained, which perfectly match with the demand for aforementioned CNOT LG. In this case, CS is the spin state of incident light, while its incident direction is TS.
To illustrate the mechanism for the aforementioned all-optical CNOT LG, we begin with the analysis of a typical anisotropic unit cell as shown in Fig. 2(a). According to the theory of geometric phase (also known as Pancharatnam-Berry phase)46, when plane wave E impinges on such transparent optical scatterer, the transmission electromagnetic field E' can be linked with E by a Jones matrix as
E′=(cosδ2isinδ2e−2iφisinδ2e2iφcosδ2)E, | (3) |
where δ is the phase difference between orthogonal linear polarizations, φ is the orientation angle between the unit cell main axis and x axis. Therefore, Eq. (3) can be further simplified as
E′=cos(δ2)E−isin(δ2)×[⟨E|ERR⟩exp(−i2φ)|L⟩+⟨E|ELL⟩exp(i2φ)|R⟩], | (4) |
where |L⟩ and |R⟩ denote left- (LCP) and right-handed circularly polarized (RCP) waves, respectively. The first term in the right side of Eq. (4) indicates that a part of the output beam keeps the same polarization as the incidence without phase shift, while the second term shows that another part of the output beam will reverse its spin and acquire an extra phase shift depending on φ, which is defined as geometric phase. Thus, in order to increase the operation efficiency, the ideal unit cell for most of the geometric phase based metasurfaces is a high-performance half wave plate (HHWP) with δ=π and the co-polarized transmitted waves are generally treated as noises. Since incident light with opposite spins will experience reversed phase shifts, these metasurfaces exhibit conjugated directional performance as shown in
To break the spin-dependent directional transmission conjugation, we propose a metasurface doublet with a metasurface (M1) composed of HHWP unit cells at the front side and another metasurface (M2) composed of low-performance half wave plate (LHWP) unit cells with δ=π/2 at the back side. In the simulation, the device is all-silicon with permittivity obtained from measurement49 and the details are given in the Experimental section. It can be inferred from Fig. 2(b) and 2(f) that the polarization conversion ratio (defined as the transmittance of cross-polarized light to transmitted light) at 28.3 THz is larger than 98% for HHWP unit cell and about 50% for LHWP unit cell. Besides, the simulated phase delays in Fig. 2(b) and 2(f) are well accorded with the geometric phase that the implemented phase θ of the unit cells is solely dependent on their orientation angle φ with θ=±2φ,where ± is determined by the incident spin. Therefore, the transmitted light can be fully manipulated by the HHWP unit cells, while only half of the transmitted light is manipulated by the LHWP unit cells.
In order to achieve highly efficient all-optical CNOT LG, M1 is designed as a convex lens for LCP front (RCP back) incidence with focal distance f1, and M2 is also designed as a convex lens for LCP front (RCP back) incidence with focal distance f2. Therefore, due to the transmission conjugation of the geometric phase, both metalenses are concave lenses for RCP front incidence and LCP back incidence with focal distances –f1 and –f2, respectively. In this case, the transmitted field under certain incident direction and spin state can be calculated simply by geometric optics50.
To further illustrate this issue, Fig. 3 depicts corresponding numerical results based on vectorial diffraction theory51. In this case, the phase delay and the transmitted amplitude of the metasurface doublet are retrieved from the simulated results for the unit cells. The diameter of the metasurface doublet is d1=6 mm, the focal distances f1 and f2 are set as 3d1 and 9d2. It can be inferred that focal spots can be observed at two locations at z=18 mm (f1, white dashed lines) and 27 mm (f3, blue dashed lines), which matches well with the results calculated by geometric optics. The calculated intensity contrast ratio (ICR) is defined as ICR=I1/I0, where I1 and I0 indicate the intensity at a certain position, and the subscripts (1 or 0) are according with those in the insets of Fig. 3. The calculated
As a proof of concept, corresponding experiments are carried out as shown in Fig. 4. Figure 4(a) depicts SEM images of the fabricated M1 and M2 with negligible surface roughness and vertical sidewalls with a sidewall angle >80° (details of the fabrication process is given in the Experimental section). The schematic illustration of the measurement setup is shown in Fig. 4(b) and the optical path in experiment is shown in
In fact, except for the above mentioned case, the focal spot can also be shaped by adding extra phase shifts. For example,
In fact, from the perspective of geometric optics, the proposed device in Fig. 3 can also be treated as a spin-selective directional metalens. Different from previously reported works with symmetrical and fixed imaging performance24, 25, the proposed metasurface doublet has the capability to adjust the focal distance (as shown in Fig. 3(c) and 3(d)) or achieve dual imaging at two image planes (as shown in Fig. 3(b)), which may find many exciting applications for chiral sensing and imaging57-59. Besides, since the polarization conversion ratios for the fabricated HHWP and LHWP unit cells may differ from the simulated results due to the imperfection of fabrication, we also discuss the influence of such deviation on the performance of the proposed devices in the Supplementary information.
In summary, we propose a simple yet powerful design methodology to achieve an all-optical CNOT LG with metasurface doublet. By ingeniously aligning two metasurfaces with different polarization conversion ratios and phase distributions, multiple input-output performance can be realized depending on the incident spin state and direction. Both theoretical and measured results demonstrate the robustness and broadband nature of the designed device. Furthermore, a CNOT LG-based Janus metasurface is also characterized and shows that the asymmetric electromagnetic transmission can be achieved for orthogonal circularly polarized incidence. Since the design method is derived from geometric optics, it can be easily extended to other part of the spectrum, which will enable more fascinating applications in optical computing, chiral optics and electromagnetic communications.
Numerical simulation: Considering the symmetry of the structure, to reduce the amount of calculation, the simulated results in Fig. 2 were obtained using the finite element method in CST Microwave Studio with unit cell boundaries in xy directions and open boundary in z direction. A fine tetrahedral mesh was applied with adaptive mesh refinement to ensure the accuracy of the results. The magnetic field distributions were calculated by using the build-in magnetic field monitors in CST Microwave Studio.
Device fabrication: The schematic diagram of the fabrication process is shown in
This work is supported by the National Natural Science Foundation of China (12104326, 12104329 and 62105228), Natural Science Foundation of Sichuan Province (2022NSFSC2000) and the Opening Foundation of State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering. P. Müller-Buschbaum acknowledges funding by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany´s Excellence Strategy – EXC 2089/1 – 390776260 (e-conversion) and TUM.solar in the context of the Bavarian Collaborative Research Project Solar Technologies Go Hybrid (SolTech). T. Xiao is grateful for the support from the China Scholarship Council (CSC).
Y. Huang and T. Xiao proposed the original idea. L. Li and P. Müller-Buschbaum supervised the project. Z. Xie, J. Zheng and J. Zhu participated the discussion of the research. S. Chen, Y. Su and W. Chen carried out the experiments and collected the data. Y. Huang, K. Liu and M. Tang analyzed all data. Y. Huang and L. Li wrote the paper. All authors discussed the results and commented on the manuscript
The authors declare no competing financial interests.
†These authors contributed equally to this work
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Supplementary information for All-optical controlled-NOT logic gate achieving directional asymmetric transmission based on metasurface doublet |
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Schematic for the proposed all-optical CNOT LG. (a–d) Far-field responses under different incident conditions that correspond to (a) no focus, (b) two foci, (c) one focus with small focal distance and (d) one focus with large focal distance. The corresponding truth-table is shown in the inset with spin state as CS and incident direction as TS, which is perfectly matched with that in Eq. (2).
Unit cells for the CNOT LG metasurface doublet. (a, e) Schematic for HHWP and LHWP unit cells, respectively. P=4.5 μm, h=6 μm, l1=3.7 μm, w1=1.2 μm, l2=2.9 μm and w2=2.05 μm. (b, f) Corresponding polarization conversion ratio (left panel) and phase delay (right panel) with different φ for cross-polarized waves at 28.3 THz under LCP incidence. (c, g) Corresponding transmittance at φ=0 (solid lines) and φ=π/4 (dashed lines) from 27–29 THz. (d, h) Corresponding magnetic field distributions at –28.3 THz.
Numerical far-field results in x-z plane under different incident conditions. (a) Front RCP incidence. (b) Front LCP incidence. (c) Back RCP incidence. (d) Back LCP incidence. The insets show the 2D normalized intensity distributions at z=18 mm (white dashed lines) and 27 mm (blue dashed lines). When a focal spot can be observed at certain focal plane, the corresponding truth table is “1”, otherwise the truth table is “0”.
Experiment for the asymmetric transmission metasurface doublet. (a) SEM images for the front (left) and back (right) side of the metasurface. (b) Schematic illustration of the measurement setup. LP: linear polarizer. λ/4: quarter wave plate. BE: beam expander. SA: sample. (c–f) Intensity distributions at z=18 mm and 27 mm. (c) Front RCP incidence. (d) Front LCP incidence. (e) Back RCP incidence. (f) Back LCP incidence.
Demonstration of the directional Janus metasurface for orthogonal polarizations. (a) Schematic flow chart of the design process. FFT: fast Fourier transformation. IFFT: inverse fast Fourier transformation. (b–e) Calculated and measured far-field images at the same image plane under different incident conditions. (b) Front RCP incidence. (c) Front LCP incidence. (d) Back RCP incidence. (e) Back LCP incidence.