Generation and manipulation of THz waves are of vital importance to advance THz technology. Nonlinear metasurfaces allow effective integration of both processes into a single compact device. However, the existing THz generator-manipulators offer limited control over the generated field. Here, we demonstrate that coupling between meta-atoms provides additional degrees of freedom: achiral coupling can provide full control over the amplitude of the generated THz field, while chiral coupling makes the THz generation sensitive to the handedness of the pump polarization. Based on chiral coupling, we realize meta-molecules that only generate THz waves when pumped with circularly polarized light of one handedness. This enables independent generation of different holograms with left-handed and right-handed pump light. As an example, we generate THz beams with different orbital angular momenta with a handedness-selective metasurface.
Article
Controlling THz generation in nonlinear metasurfaces through coupling: amplitude-tuning, handedness-selectivity and holography
https://doi.org/10.21203/rs.3.rs-2074443/v1
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Terahertz (THz) waves are a frontier for communication1,2, sensing3 and imaging technologies4,5. The development of these fields relies on advances in THz generation, manipulation and detection. Conventionally, these processes are performed separately by different components. This provides flexibility but prevents the construction of compact systems. Integration of multiple processes into a single device is the key to miniaturize THz systems. Nonlinear metasurfaces are attracting growing interest for simultaneous THz generation and manipulation6–11, as the amplitude, phase and polarization of the nonlinear radiation can in principle be controlled by meta-atom design. This provides a route to nonlinear holography and increased functionalities. However, these existing THz generator-manipulators offer limited control over the generated field.
In metasurfaces, coupling among spatially separate resonant elements provides a way to tailor the electromagnetic response without requiring modification of the coupled units. Coupling in linear metasurfaces has led to many fascinating optical functionalities, such as electromagnetically induced transparency (EIT)12–14, PT symmetry breaking15,16, and resonance splitting17–19, etc. It is expected that this design freedom may be exploited to facilitate the control of nonlinear effects. In this work, we introduce EIT coupling into nonlinear metasurfaces to control THz generation upon infrared pumping. Here, nonlinear THz emission arises from the second-order nonlinearity of the magnetic dipole resonance (MDR) of a split-ring resonator (SRR). The MDR can be excited directly by the incident field or indirectly through near-field coupling. By tailoring either the indirect excitation through coupling (I) or the interference between both excitation routes (II), THz generation through difference frequency generation (DFG) in the SRR can be controlled. Here, we consider two types of coupled meta-molecules: achiral meta-molecules (type I) that provide control over the amplitude of THz emission (Fig. 1a), and chiral meta-molecules (type II) that are sensitive to the handedness of the pump polarization (Fig. 1b). Importantly, the chiral meta-molecules can be optimized to provide giant nonlinear circular dichroism (NLCD), where THz generation occurs only for either left-handed or right-handed circularly polarized (LCP or RCP) pumping. Such left-handed or right-handed meta-molecules enable the multiplexing of independent Pancharatnam-Berry (PB) meta-holograms revealed separately by LCP and RCP pumping. We illustrate this with a handedness-selective nonlinear THz spin-orbital interaction device that generates beams with different orbital angular momentum in response to circularly polarized infrared pump light of opposite handedness (Fig. 1c). The proposed approach provides an avenue towards various highly integrated THz generation devices with multiple tailorable functionalities.
The MDR of an isolated U-shaped SRR is responsible for THz generation6. It can be excited directly by a pumping beam with the electric field polarized perpendicular to the SRR’s symmetry axis (↔, x-polarization). However, this mode cannot be excited directly by the electric field oriented along the SRR’s symmetry axis (↕, y-polarization). On the other hand, indirect excitation of the MDR becomes possible through coupling if another resonator is placed nearby in a way that disturbs the SRR’s symmetry.
Controlling the amplitude of THz generation through coupling. In order to excite and enable the control of the MDR of SRRs by y-polarized light, we place a pair of SRRs symmetrically on the left and right sides of a bar resonator (type-I meta-molecule, Fig. 2a). While incident x-polarized light will excite the MDR of both SRRs directly and in phase, incident y-polarized light first excites the electric dipole resonance of the bar resonator (bright mode), which then couples through near-fields to the SRRs and excites their MDRs (dark mode) with a π phase difference between the two SRRs (Fig. 2b). In either case, the MDR leads to in-phase nonlinear currents that flow along the arms of both SRRs, giving rise to the y-polarized THz radiation that interferes constructively in the far-field6. Due to its symmetry, the bar resonator and its electric dipole mode can only support out-of-phase nonlinear currents that do not contribute to far-field THz radiation.
This indirect MDR excitation through coupling between bright and dark modes is usually described as classical analogue of EIT14. In this process, stronger coupling strengthens the MDR excitation but weakens the electric dipole resonance. Thus, the amplitude of the nonlinear THz generation can be controlled by changing the coupling strength via adjusting the position (y-separation ΔS) of the SRRs relative to the bar resonator.
In the experiment, four samples with different ΔS’s are fabricated using e-beam lithography (see Methods). Scanning electron microscopy (SEM) images of the meta-molecules are shown as insets of Fig. 2c. We will focus on y-polarized illumination for the control over the MDR excitation and THz emission, as illustrated by Fig. 2c-g. (For x-polarized illumination the response resembles that of individual SRRs. As illustrated by Fig. 2b, there is little dependence on ΔS as the effects of the MDRs of both SRRs on the bar resonator cancel, see Fig. S1.) Fig. 2c shows the measured linear transmission spectra for y-polarized illumination (see Methods). When ΔS = − 20 nm, only a single broad resonance at 1280 nm occurs. As ΔS increases, an EIT window gradually emerges and becomes more pronounced at ~ 1220 nm, as indicated by the dashed line in Fig. 2c. To quantify the variation of the coupling strength, coupled-mode theory is used to fit the measured transmission spectra, revealing that the coupling coefficient increases monotonically with ΔS (Supplementary Note S1 and Fig. S2). This dependence results from the interplay between the electric and magnetic coupling of bar resonator and SRRs, which changes from destructive to constructive interference as ΔS increases in the studied range20. This trend is also confirmed using numerical simulation, where the MDR at 1220 nm gradually becomes stronger as ΔS increases, as illustrated by the Hz-field distributions in Fig. 2d (Supplementary Note S2 and Fig. S3). It is thus expected that the amplitude of the nonlinear THz generation will increase accordingly.
To experimentally characterize the nonlinear performance, the samples are measured using THz time-domain spectroscopy (see Methods and Fig. S4). The central wavelength of the incident fundamental wave (FW) is initially fixed at 1220 nm, and the pulse width is about 65 fs. Single-cycle THz pulses are detected from all samples, as illustrated in Fig. 2e, indicating broadband THz emission (bandwidths around 2.7 THz). Figure 2e shows that the amplitude of the THz pulses increases dramatically with the increase of the separation. At ΔS = − 20 nm, the THz signal is almost negligible, since the MDR is hardly excited due to weak coupling. As ΔS increases, the THz signal becomes stronger because of the enhanced coupling strength. We observe a 93.8% tuning range of the THz peak-to-peak amplitude ΔE, defined as (ΔEmax − ΔEmin)/ΔEmax with ΔEmax (ΔEmin) representing the measured maximum (minimum) THz peak-to-peak amplitudes of the four samples. The strength of the THz signal ΔE increases monotonically with the retrieved coupling coefficient (Fig. 2f). Further enhancement of the coupling coefficient by increasing ΔS is limited by the localization of the resonance fields. Next, we investigate the nonlinear performance in a broad FW wavelength range from 1160 nm to 1500 nm with a fixed pump fluence (Fig. 2g). Enhanced THz generation with increasing coupling strength is observed throughout the whole wavelength range. These findings are supported by nonlinear numerical simulations based on a Maxwell-hydrodynamic model8 (Supplementary Note S3 and Fig. S5a, S5b). The simulations show that the FW wavelengths of maximum THz generation are very close to the EIT window where the MDR excitation becomes strongest. The spectral dispersion of the measured THz peak-to-peak amplitude (Fig. 2g) closely follows the strength of the MDR (|Hz|2 at the SRR’s center) calculated based on linear simulations (Fig. S3) at different ΔS, which agrees with the nonlinear polarization equation (Supplementary Notes S2 and S3).
Near-field chirality in type-I meta-molecules. In the previous section we have confirmed that the MDRs could be excited directly or indirectly by incident x- or y-polarized pump fields, respectively, as illustrated by Fig. 2b.When the FW pump field contains both x- and y-polarized components (Ex and Ey), constructive and destructive interference between the in-phase (excited directly by Ex) and anti-phase (excited through coupling by Ey) magnetic dipole modes can occur in the two SRRs. In this case, the THz generation in each SRR will be determined by the amplitude contrast r = |Ey/Ex| and phase difference δ = ∠(Ey/Ex) of the incident field components. Under x-polarized illumination, the excitation of both the left and right magnetic dipole resonances (MDRs), ml and mr, can be described by aEx, where a is an invariant complex excitation coefficient. Whereas, under the y-polarized illumination, they can be expressed by ± bEy, where the complex excitation coefficient b is determined by coupling while opposite signs, + and −, apply to different SRRs. Therefore, we have ml = aEx + bEy and mr = aEx − bEy. Thus, when the incident polarization satisfies |a| = |br|, the left (right) MDR will not be excited due to destructive interference at δ + ϕ = π (0) with ϕ =∠(b/a), while the right (left) MDR excitation will be maximized by constructive interference. In particular, for a circularly polarized pump (r = 1 and δ = σπ/2), and meta-molecules satisfying b = ia, left-handed circularly polarized (LCP, σ = −1) pumping will only excite the left MDR, while right-handed circularly polarized (RCP, σ = 1) pumping will only excite the right MDR, providing handedness-selective resonance excitation.
The amplitude relation between a and b depends on the coupling strength and can be adjusted by changing ΔS, while the phase difference between the bright electric and dark magnetic dipole modes is close to π/2 around the dark resonance. Simulations show that the condition is satisfied by ΔS = 130 nm at a pump wavelength of 1130 nm (Fig. S6). However, it should be noted that the handedness-selective MDR excitation can only be observed in the near-field. In the far-field, there is no chiral response, as the type-I meta-molecule has mirror symmetry. Thus, from the nonlinear point of view, the THz emissions will also be the same under LCP and RCP pumping, since the two SRRs exhibit identical nonlinear responses. Nevertheless, this effect provides a route to obtain a far-field nonlinear chiral response by removing one SRR from the achiral type-I unit cell, resulting in the chiral type-II meta-molecule. Though coupling that affects a will emerge under x-polarized pumping in this case, the geometry can be adjusted to achieve handedness-selective MDR excitation in the remaining SRR.
Coupling-controlled nonlinear chiral response. By removing one SRR, we arrive at a type-II meta-molecule that derives a chiral nonlinear response from a planar chiral21–24 arrangement of a single SRR positioned on the left (or right) side of a bar resonator (Fig. 3a). It can be designed to only exhibit THz emission under LCP (or RCP) FW pumping. It is convenient to describe such optimized meta-molecules as left-handed (right-handed). The handedness-selective THz generation is schematically illustrated in Fig. 3b. Meanwhile, the adjustable coupling provides a route to tune the nonlinear chiral response and even to reverse it by changing ΔS. While this controls the amplitude of the generated THz radiation, the THz field remains y-polarized as the THz generation still arises from the MDR in the SRR. To demonstrate this, three samples with different ΔS were fabricated (SEM images shown as insets of Fig. 3c). The measured transmission spectra under y-polarized illumination are shown in Fig. 3c. A noticeable transmission window only occurs at ΔS = 70 nm at ~ 1250 nm, implying significant coupling between the electric dipole resonance and the MDR. At ΔS = − 30 and 20 nm, only single resonance dips are observed, indicating weak coupling. These features are confirmed by the corresponding simulated transmission spectra and near-field MDR intensities (Fig. S7). Simulated Hz-field distributions arising from circularly polarized pumping at 1250 nm wavelength (Fig. 3d) show that the handedness-selectivity of MDR excitation indeed increases as ΔS changes from − 30 nm to 70 nm. The model predicts that the design with ΔS = 70 nm comes close to handedness-selective MDR excitation around the EIT wavelength, where only LCP pumping excites the MDR of the SRR strongly (Fig. S7e), implying pump-handedness-selective THz generation.
Figure 3e shows the measured THz intensities (square of the THz peak-to-peak amplitudes) of the three samples under LCP and RCP pumping in a FW wavelength range of 1160 nm to 1500 nm at a fixed pump fluence. The FWs are incident from the back side (substrate side) of the samples. We observe broadband nonlinear chiral responses that are in agreement with the above expectations. The difference between the THz intensities generated by LCP and RCP pumping increases with ΔS. To quantify the nonlinear chiral response, we calculate the NLCD defined by NLCD = 
is the THz intensity under LCP (RCP) pumping. The broadband NLCD is clearly largest for the case of ΔS = 70 nm (Fig. 3f), whose maximum approaches 0.9 at ~ 1350 nm pump wavelength.
For ΔS = − 30 and 20 nm, the overall NLCDs have a similar magnitude but opposite signs (Fig. 3f). Notably, the reversed chiral response is observed for structures that are not enantiomers. This phenomenon arises from the electric (and magnetic) coupling of bar resonator and SRR (Fig. S8). Electric coupling dominates when the SRR is located close to an end of the bar resonator, where opposite signs of the oscillating charges yield MDR excitation with a π phase difference for SRR placed near opposite bar ends. Thus, the coupling-mediated MDR excitation due to incident y-polarized electric field Ey changes sign as the SRR is shifted from one bar end to the other, while the direct MDR excitation due to Ex does not change significantly. This switches between constructive and destructive interferences between these contributions to MDR excitation, causing the observed NLCD reversal. We also carry out nonlinear numerical simulations onto the above type-II meta-molecules, where the results agree well with the measurements (Supplementary Note S3 and Fig. S5c, S5d).
While NLCD can be reversed by changing ΔS, the simpler and more obvious approach is to reverse the planar chirality of the meta-molecule by moving the SRR from the left of the bar resonator to the right, resulting in the mirror-image meta-molecule (enantiomer). This situation is approximated by illuminating the front (structured side) of the sample instead of its back (substrate side), as shown by the reversed NLCDs (Fig. 3f) for illumination from the front (Fig. 3g) and back (Fig. 3e).
Handedness-selective nonlinear meta-holography. In contrast to traditional nonlinear optics, nonlinear metasurfaces offer the flexibility to locally engineer amplitude and phase of the generated light. Handedness-selective THz generation provides an opportunity to generate multiplexed holograms by LCP and RCP pumping by interleaving left-handed and right-handed meta-molecules. To demonstrate this, we realize a metasurface that generates THz beams with different orbital angular momentum upon LCP and RCP pumping (Fig. 1c). The device is based on handedness-selective type-II meta-molecules, which are mirror-images of each other, where left-handed (right-handed) meta-molecules are highlighted green (orange). The generated THz radiation is controlled by rotating the meta-molecules, which changes the nonlinear PB phase8,25 (Fig. 4a). For meta-molecule rotation by an angle + θ, the generated RCP and LCP THz waves acquire + θ and − θ phases irrespective of the handedness of the incident FW. Our device (Fig. 4b) consists of left-handed and right-handed meta-molecules that are rotated clockwise and anticlockwise by θl = −φ and θr = 2φ and then arranged into ring distributions of different radii, where φ is the azimuth angle. Therefore, the device will generate the LCP and RCP THz vortex beams with OAMs of l = 1 and − 1 under LCP FW pumping, while the RCP FW pumping will generate vortex beams with OAMs of l = − 2 and 2.
Figures 4c-f show the measured amplitude and phase distributions of the generated LCP and RCP THz beams under the LCP and RCP FW pumping (see Methods). We observe donut-shaped amplitude profiles and vortex phase profiles, which are characteristic for vortex beams. The detected field distributions are the same across the studied spectral range of 0.8 to 1.4 THz, indicating broadband THz vortex beam generation. It should be noted that the RCP and LCP THz beams are generated simultaneously. Their superposition actually forms a linearly polarized vector beam with the local polarization azimuth following the orientation of the SRR arms. Thus the device could also serve as a pump-handedness-selective vector beam generator. To avoid the superposition, an additional linear phase gradient can be added to the design, which would deflect the circularly polarized THz beams of opposite handedness by opposite angles. Indeed, nearly arbitrary THz Poincaré beams could be generated by designing handedness-selective OAMs and pumping with elliptically polarized FWs simultaneously with tunable intensity contrast and time delay26,27.
Handedness-selective generator-manipulators can not only combine the functionality of two meta-holograms and THz generation in a single device consisting of a functional layer of nanoscale thickness, but also offer an improved spatial resolution by more than two orders of magnitude. For comparison, the unit cells of typical linear THz metasurfaces are ~ 100 µm in size24, while the nonlinear THz generation studied here occurs in meta-molecules with a size of only 550 nm.
Besides nonlinear PB phase control, our coupling-based designs also provide a robust route for achieving continuous and broadband control over the amplitude of the THz emission. For example, these meta-molecules may be arranged on an interface to form amplitude distributions of gratings, zone plates and holograms. Moreover, such amplitude modulation may be combined with the nonlinear PB phase for simultaneous control over amplitude and phase of the emitted THz waves for more complex and high-quality manipulation of THz radiation. In particular, pump-polarization-selective THz generation can in principle be engineered for any chosen pump polarization.
While the coupling strength between meta-atoms in our meta-molecules was fixed at the time of fabrication, we note that nanomechanical photonic metamaterials28 (e.g. based on NEMS) offer a route to dynamic control over such coupling. Nanomechanical THz generator-manipulators could in principle switch the nonlinear THz emission on and off or offer dynamic control over pump-handedness-selectivity. Compared to MEMS THz metamaterials29–31, the much smaller characteristic dimensions of photonic metamaterial nonlinear THz generators imply that the moving parts can be orders of magnitude smaller, lighter and therefore faster. Nanomechanical photonic metamaterials with fundamental mechanical resonances at up to 150 MHz have been reported32 (though ~ 1 MHz is more typical), implying that sub-microsecond response times should be feasible. This indicates an opportunity to develop fast THz modulators.
In summary, we have demonstrated a coupling between meta-atoms provides control over terahertz emission by nonlinear metasurfaces, including control over the amplitude of the THz field and pump-polarization-selective THz generation. In particular, we have realized meta-molecules that generate THz waves only for pumping with circularly polarized light of one handedness or the other, corresponding to nonlinear circular dichroism of approximately unity. We have shown experimentally that this enables the generation of two independent THz meta-holograms revealed by LCP and RCP pumping, in a single device of nanoscale thickness with very high spatial resolution (~ 500 meta-molecules per wavelength). The nonlinear metasurface acts as a spin-selective terahertz vortex/vector beam generator. Our method demonstrates how coupling provides a useful degree of freedom in engineering nonlinear effects in metasurfaces and opens a gateway towards compact functional and multi-functional nonlinear THz photonic devices.
Sample fabrication. The metasurfaces are fabricated by a sequential process of electron beam lithography (EBL), electron beam evaporation and lift-off. First, the metasurface patterns are created using a JEOL 9300FS 100 kV EBL tool on a 5 nm ITO-coated fused quartz substrate of 0.7 mm thickness, where the thin ITO layer can prevent local charge accumulation during lithography and enhance the nonlinear THz generation8. Next, 3 nm Ti and 40 nm Au films are successively deposited using e-beam evaporation. At last, lift-off and cleaning processes are performed to obtain the metasurfaces.
Linear transmission measurement. The linear transmission spectra of all samples are measured using a custom-built infrared microscope. Near infrared light emitted from a stabilized tungsten infrared light source (Thorlabs, SLS202L/M) passes through a linear polarizer and is then focused onto the metasurface by an objective lens. The transmitted light is guided and collimated into a spectrometer (Princeton Instruments, Acton SpectraPro SP-2300). The reference spectrum is the transmitted light from an un-patterned area on the same substrate.
Nonlinear measurement. All the nonlinear measurements are performed using a custom-built THz time-domain spectroscopy (TDS) system (Fig. S4). It is pumped by a Ti: sapphire femtosecond laser amplifier (Coherent, Legend Elite Duo) with central wavelength of 800 nm, pulse duration of 35 fs, and a repetition rate of 1.0 kHz. The laser light is split into two beams by a beam splitter (BS). One is guided to a 1-mm-thickness 110-cut ZnTe crystal after passing through a beam expander composed by two lenses (L1 and L2), serving as the probe beam. The other is injected into an optical parameter amplifier (OPA, Coherent OperA Solo) to generate a near infrared femtosecond laser beam, which serves as the pump beam. The central wavelength of the pump beam can be continuously tuned from 1160 nm to 2000 nm. To control the pump polarization, a half-wave plate (HWP), a linear polarizer (P1) and a super achromatic quarter-wave plate (SQWP) are inserted before the sample. The emitted THz wave is collected and focused by two parabolic mirrors (PM1 and PM2) with 2- and 4-inches focal lengths, respectively. Two THz linear polarizers P2 and P3 are inserted between them to measure the THz polarization components, in which P3 is fixed to allow transmission of only the horizontally polarized component while P2 is rotated to allow transmission of either − 45° or 45° polarized components. After passing through a polished 2-mm-thickness silicon wafer, that is used to combine the THz and optical probe beams, the combined beams are incident onto the ZnTe crystal. Based on the electro-optical effect, the polarization state of the probe beam will be modulated by the transient THz electric field, which changes form linearly polarized to slightly elliptically polarized. By shining the transmitted probe beam onto an iris, a quarter-wave plate (QWP) and a Wollaston prism (WP) in sequence, the transient THz field, which is proportional to the intensity difference between the two orthogonally polarized beams from the WP, can be extracted using a balance detection (BD) technique. At last, by gradually controlling the time delay between the probe beam and the THz pulse through scanning the delay line, the time-domain THz waveform is retrieved. To measure the transverse field distributions of the THz beam, the ZnTe crystal and the iris are mounted on a motorized two-dimensional translation stage and raster scanned in the x-y plane.
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant Nos. 61735012, 62025504, 62075158, 61875150, 61935015, 62005193, 11974259, 62271004, 62231003 and U20A20164); the Tianjin Municipal Fund for Distinguished Young Scholars (18JCJQJC45600); the UK's Engineering and Physical Sciences Research Council (Grant No. EP/T02643X/1); H2020 ERC Consolidator Grant (648783). Following a period of embargo, the data from this paper will be available from the University of Southampton ePrints research repository: https://doi.org/10.5258/SOTON/D2310
Conflict of interest
The authors declare no competing interests
Contributions
X.Z. and J.H. conceived the idea; Q.W. and Q.X. designed and fabricated the samples; Q.W. carried out the numerical simulations; Q.W. and X.F. performed the measurements; Q.W., X.Z., Q.X., X.F., Y.L., L.N. and E.P. analyzed the data; Q.W., X.Z. and E.P. wrote the manuscript with input from J.G., Q.Y., M.F., Z.H. and S.Z.; X.Z., J.H. and W.Z. supervised the project; all authors discussed the results and prepared the manuscript.
- Nagatsuma, T., Ducournau, G., Renaud, C. C. Advances in terahertz communications accelerated by photonics. Nat. Photonics 10, 371–379 (2016).
- Kleine-Ostmann, T., Nagatsuma, T. A Review on Terahertz Communications Research. J. Infrared Millim. Terahertz Waves 32, 143–171 (2011).
- Beruete, M., Jauregui-Lopez, I. Terahertz Sensing Based on Metasurfaces. Adv. Opt. Mater. 8, 1900721 (2020).
- Chan, W. L., Deibel, J., Mittleman, D. M. Imaging with terahertz radiation. Rep. Prog. Phys. 70, 1325–1379 (2007).
- Dobroiu, A., Otani, C., Kawase, K. Terahertz-wave sources and imaging applications. Meas. Sci. Technol. 17, R161-R174 (2006).
- Luo, L. et al. Broadband terahertz generation from metamaterials. Nat. Commun. 5, 3055 (2014).
- Keren-Zur, S., Tal, M., Fleischer, S., Mittleman, D. M., Ellenbogen, T. Generation of spatiotemporally tailored terahertz wavepackets by nonlinear metasurfaces. Nat. Commun. 10, 1778 (2019).
- Lu, Y. et al. Integrated Terahertz Generator-Manipulators Using Epsilon-near-Zero-Hybrid Nonlinear Metasurfaces. Nano Lett. 21, 7699–7707 (2021).
- McDonnell, C., Deng, J., Sideris, S., Ellenbogen, T., Li, G. Functional THz emitters based on Pancharatnam-Berry phase nonlinear metasurfaces. Nat. Commun. 12, 30 (2021).
- McDonnell, C., Deng, J., Sideris, S., Li, G., Ellenbogen, T. Terahertz Metagrating Emitters with Beam Steering and Full Linear Polarization Control. Nano Lett. 22, 2603–2610 (2022).
- Zdagkas, A. et al. Observation of toroidal pulses of light. Nat. Photonics 16, 523–528 (2022).
- Zhang, S., Genov, D. A., Wang, Y., Liu, M., Zhang, X. Plasmon-induced transparency in metamaterials. Phys. Rev. Lett. 101, 047401 (2008).
- Liu, N. et al. Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit. Nat. Mater. 8, 758–762 (2009).
- Gu, J. et al. Active control of electromagnetically induced transparency analogue in terahertz metamaterials. Nat. Commun. 3, 1151 (2012).
- Lawrence, M. et al. Manifestation of PT Symmetry Breaking in Polarization Space with Terahertz Metasurfaces. Phys. Rev. Lett. 113, 093901 (2014).
- Li, S. et al. Exceptional point in a metal-graphene hybrid metasurface with tunable asymmetric loss. Opt. Express 28, 20083–20094 (2020).
- Romero, I., Aizpurua, J., Bryant, G. W., García de Abajo, F. J. Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers. Opt. Express 14, 9988–9999 (2006).
- Luk'yanchuk, B. et al. The Fano resonance in plasmonic nanostructures and metamaterials. Nat. Mater. 9, 707–715 (2010).
- Manjappa, M., Srivastava, Y. K., Cong, L., Al-Naib, I., Singh, R. Active Photoswitching of Sharp Fano Resonances in THz Metadevices. Adv. Mater. 29, 1603355 (2017).
- Liu, X. et al. Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode. Appl. Phys. Lett. 100, 131101 (2012).
- Fedotov, V. A. et al. Asymmetric propagation of electromagnetic waves through a planar chiral structure. Phys. Rev. Lett. 97, 167401 (2006).
- Plum, E., Fedotov, V. A., Zheludev, N. I. Planar metamaterial with transmission and reflection that depend on the direction of incidence. Appl. Phys. Lett. 94, 131901 (2009).
- Chen, S. et al. Giant Nonlinear Optical Activity of Achiral Origin in Planar Metasurfaces with Quadratic and Cubic Nonlinearities. Adv. Mater. 28, 2992–2999 (2016).
- Wang, Q. et al. Reflective chiral meta-holography: multiplexing holograms for circularly polarized waves. Light:Science & Applications 7, 219–227 (2018).
- Li, G. et al. Continuous control of the nonlinearity phase for harmonic generations. Nat. Mater. 14, 607–612 (2015).
- Jiang, Z. H, et al. A Single Noninterleaved Metasurface for High-Capacity and Flexible Mode Multiplexing of Higher-Order Poincare Sphere Beams. Adv. Mater. 32, 1903983 (2020).
- Liu, M. et al. Broadband generation of perfect Poincare beams via dielectric spin-multiplexed metasurface. Nat. Commun. 12, 2230 (2021).
- Zheludev, N. I., Plum, E. Reconfigurable nanomechanical photonic metamaterials. Nat. Nanotechnol. 11, 16–22 (2016).
- Zhu, W. M. et al. Switchable Magnetic Metamaterials Using Micromachining Processes. Adv. Mater. 23, 1792–1796 (2011).
- Zhu, W. M. et al. Microelectromechanical Maltese-cross metamaterial with tunable terahertz anisotropy. Nat. Commun. 3, 1274 (2012).
- Manjappa, M. et al. Reconfigurable MEMS Fano metasurfaces with multiple-input-output states for logic operations at terahertz frequencies. Nat. Commun. 9, 4056 (2018).
- Karvounis, A., Ou, J.-Y., Wu, W., MacDonald, K. F., Zheludev, N. I. Nano-optomechanical nonlinear dielectric metamaterials. Appl. Phys. Lett. 107, 191110 (2015).
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