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Second harmonic generation in a TMDC metasurface. a Experimentally measured wavelength dependence of the SHG from metasurface C. The second harmonic generation (SHG) was enhanced in the vicinity of magnetic quadrupole (MQ) and electric dipole (ED). b Schematic showing the locations of the SH current source χ 2 . c Calculated second harmonic generation conversion efficiency (η SHG ) by employing fullwave nonlinear simulations. The patterned region is the spectral range not accessible by the laser in our experiments. d SHG conversion efficiency calculated using quasi-normal modes couple-mode theory. e Spatial overlap between the induced nonlinear current source J NL and eigenfields of the calculated quasi-normal modes ~ E m . f Schematic of the modal overlap of nonlinear current source and eigenfields.
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Nonlinear light sources are central to a myriad of applications, driving a quest for their miniaturisation down to the nanoscale. In this quest, nonlinear metasurfaces hold a great promise, as they enhance nonlinear effects through their resonant photonic environment and high refractive index, such as in high-index dielectric metasurfaces. However,...
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... full-wave nonlinear simulations have been performed in order to investigate the tapering angle effect of the following three meta-atom shapes: (i) cone, (ii) truncated cone, (iii) vertical cylinder, on the THG conversion efficiency (in either direction forward and backward) and the results are presented in Supplementary Fig. 5 of Supplementary Information. The THG directionality is quite similar in truncated shapes, cone and truncated conical meta-atoms. ...
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... test the influence of the resonant modes on the SH enhancement, we examined the wavelength dependence of the SHG from metasurface C. For this purpose, we scan the wavelength of the infra-red pump beam in the range of 1200-1600 nm. The measured SH spectra for different pump wavelengths are shown in Fig. 5a. Two peaks of SH emissions can be observed when the SH wavelength is in the vicinity of the MQ and ED QNMs. The SH enhancement, however, is significantly higher at the position of the MQ mode at 1400 nm, despite the stronger far-field scattering at the position of the ED mode. This feature of the SH enhancement can be explained by ...
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... response. The analysis of these four scenarios is discussed in detail in the Supplementary Information (see Supplementary Fig. 6). Among these four scenarios, the first one best describes our experimental SH response. Namely, the SH response is a result of the interference of the SHG from the top and bottom layers of the MoS 2 , as depicted in Fig. 5b. This is in stark contrast to the surface SHG emission from nanostructures made of centrosymmetric materials, such as silicon metasurfaces 54 . In such nanostructures, the second harmonic emission originates mainly from their sidewalls, where the symmetry is broken. In our TMDC metasurface, the dominant contribution is from the top and ...
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... corresponding simulations for the wavelength dependence of the SH efficiency from metasurface C are presented in Fig. 5c. A good agreement can be observed with the measured SHG (Fig. 5a). We note that our theoretical calculations show the strongest SHG at the position of the MD mode, which is not accessible by our tunable pump laser. To quantify this wavelength dependence, we further performed coupled-mode analysis on the nonlinear wave interactions. The ...
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... corresponding simulations for the wavelength dependence of the SH efficiency from metasurface C are presented in Fig. 5c. A good agreement can be observed with the measured SHG (Fig. 5a). We note that our theoretical calculations show the strongest SHG at the position of the MD mode, which is not accessible by our tunable pump laser. To quantify this wavelength dependence, we further performed coupled-mode analysis on the nonlinear wave interactions. The SHG efficiency depends upon the coupling between the SH light and ...
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... Fig. 5d, we also show the calculated SHG conversion efficiency using the coupled QNM theory, Eq. (4), as well as the contributions of each of the three QNMs to the overall ...
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... along the x-axis and the co-polarised component of the SHG. We can clearly observe that the SHG displays peaks of efficiency that are associated only with the two magnetic modes, while SH light coupling with ED-like mode is significantly inhibited. This result is in qualitative agreement with the full-wave nonlinear numerical simulations (Fig. 5c) and our experimental observations (Fig. ...
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... component of the SHG. We can clearly observe that the SHG displays peaks of efficiency that are associated only with the two magnetic modes, while SH light coupling with ED-like mode is significantly inhibited. This result is in qualitative agreement with the full-wave nonlinear numerical simulations (Fig. 5c) and our experimental observations (Fig. ...
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... reason behind the dominant role of magnetic modes over the electric mode is better clarified by inspecting the overlap integrals that appear in the expressions of η m . In Fig. 5e, we show the spatial distribution of the eigenmodes ~ E m along with the induced nonlinear surface currents J NL . When the SH is tuned to the wavelengths of the magnetic QNMs, ~ λ MD and ~ λ MQ , the spatial overlap between the nonlinear source and the eigenfield is optimal on both the top and bottom surface (see MQ and MD in Fig. ...
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... of η m . In Fig. 5e, we show the spatial distribution of the eigenmodes ~ E m along with the induced nonlinear surface currents J NL . When the SH is tuned to the wavelengths of the magnetic QNMs, ~ λ MD and ~ λ MQ , the spatial overlap between the nonlinear source and the eigenfield is optimal on both the top and bottom surface (see MQ and MD in Fig. 5e). On the contrary, this overlap is very weak for the ED mode (see ED in Fig. 5e). Although the ED mode displays strong field localisation at the centre of the meta-atom's volume, the eigenfield is less intense at the top and bottom surfaces, where the nonlinearity is present. In addition, the SH coupling to the ED mode is frustrated by ...
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... with the induced nonlinear surface currents J NL . When the SH is tuned to the wavelengths of the magnetic QNMs, ~ λ MD and ~ λ MQ , the spatial overlap between the nonlinear source and the eigenfield is optimal on both the top and bottom surface (see MQ and MD in Fig. 5e). On the contrary, this overlap is very weak for the ED mode (see ED in Fig. 5e). Although the ED mode displays strong field localisation at the centre of the meta-atom's volume, the eigenfield is less intense at the top and bottom surfaces, where the nonlinearity is present. In addition, the SH coupling to the ED mode is frustrated by the fact that the nonlinear current source J NL at ~ λ ED has odd parity, while ...
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... the top and bottom surfaces, where the nonlinearity is present. In addition, the SH coupling to the ED mode is frustrated by the fact that the nonlinear current source J NL at ~ λ ED has odd parity, while the eigenfield ~ E ED has even parity. This difference in the parity of the mode leads to a tiny overlap integral, as shown in the schematic of Fig. ...
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... Arbitrarily manipulating the fundamental parameters of light is one of the main targets in nanophotonics, and metasurfaces provide an operational platform for this objective. Metasurfaces are two-dimensional planar devices with artificial subwavelength unit cells that can modulate the amplitude, phase, polarization and other parameters of electromagnetic waves [1][2][3][4][5][6][7][8][9][10][11]. Once traditional metasurface devices are fabricated, their optical response cannot be adjusted. ...
The enhancement of electromagnetic field with high Q factor in metasurfaces has attracted extensive attention of researchers. Magneto-optical metasurfaces (MOMS) provide approaches with controllable magnetic fields to modulate the optical response, which contributes towards the magneto-optical Kerr effect in nanophotonic devices. However, it is challenging for MOMS to obtain narrow spectra peak with high Q factors. Here, we propose MOMS-supported quasi-bound states in the continuum (quasi-BIC) and theoretically investigate the evolution process from BIC to quasi-BIC. By applying an external magnetic field, the BIC in our proposed metasurface can be transformed into a quasi-BIC with finite Q factor up to 33 620. Meanwhile, the quasi-BIC shows magnetization-related circular dichroism with a vortex point in the polarization graph, based on time-reversal symmetry breaking in the magneto-optical material under the condition of external magnetic field. The quasi-BIC also maintains nearly unity reflection and almost zero absorption, showing a promising future in sensing. Our results enrich the light control mechanisms of MOMS and provide a unique opportunity for applications requiring flexible tunability and high Q factors, such as sensors, laser sources, filters and chiral-related elements.
... resonances in centrosymmetric multilayer TMD nanostructures has shown a remarkable enhancement in SHG [30][31][32] . Furthermore, the SHG intensity of TMD monolayers placed on external metasurfaces has been substantially boosted 33,34 . ...
Second-order nonlinearity in solids gives rise to a plethora of unique physical phenomena ranging from piezoelectricity and optical rectification to optical parametric amplification, spontaneous parametric down-conversion and the generation of entangled photon pairs. Monolayer transition metal dichalcogenides, such as MoS2, exhibit one of the highest known second-order nonlinear coefficients. However, the monolayer nature of these materials prevents the fabrication of resonant objects exclusively from the material itself, necessitating the use of external structures to achieve the optical enhancement of nonlinear processes. Here we exploit the 3R phase of a molybdenum disulfide multilayer for resonant nonlinear nanophotonics. The lack of inversion symmetry—even in the bulk of the material—provides a combination of massive second-order susceptibility, extremely high and anisotropic refractive index in the near-infrared region (n > 4.5) and low absorption losses, making 3R-MoS2 highly attractive for nonlinear nanophotonics. We demonstrate this by fabricating 3R-MoS2 nanodisks of various radii, which support resonant anapole states, and observing substantial (>100-fold) enhancement of second-harmonic generation in a single resonant nanodisk compared with an unpatterned flake of the same thickness. The enhancement is maximized at the spectral overlap between the anapole state of the disk and the material resonance of the second-order susceptibility. Our approach unveils a powerful tool for enhancing the entire spectrum of optical second-order nonlinear processes in nanostructured van der Waals materials, thereby paving the way for nonlinear and quantum high-index transition metal dichalcogenide nanophotonics.
... Several works demonstrate switching of diffraction behaviour by tuning the input polarization [38], [39], allowing for different routing schemes. In many situations, it is desirable to reduce diffraction, which can be achieved with exploiting selection rules [40] or having subwavelength unit cell for all wavelengths [41]. Highefficiency nonlinear conversion generally requires strong field enhancements in the nonlinear region, which can be characterized by the Q-factor of the resonance, its matching with the pulse bandwidth, and the overlap between high Q-factor modes. ...
Sum frequency generation (SFG) has multiple applications, from optical sources to imaging, where efficient conversion requires either long interaction distances or large field concentrations in a quadratic nonlinear material. Metasurfaces provide an essential avenue to enhanced SFG due to resonance with extreme field enhancements with an integrated ultrathin platform. In this work, we formulate a general theoretical framework for multi-objective topology optimization of nanopatterned metasurfaces that facilitate high-efficiency SFG and simultaneously select the emitted direction and tailor the metasurface polarization response. Based on this framework, we present novel metasurface designs showcasing ultimate flexibility in transforming the outgoing nonlinearly generated light for applications spanning from imaging to polarimetry. For example, one of our metasurfaces produces highly polarized and directional SFG emission with an efficiency of over 0.2 cm ² GW ⁻¹ in a 10 nm signal operating bandwidth.
... Metasurfaces based on 2D materials have the advantages of a high refractive index, ultrathin thickness, tunable features, high-Q resonance, and enhanced nonlinear response. [140][141][142][143][144][145][146][147] Significant nonlinear effects were observed in 2D metasurfaces compared with monolayer and few-layers of 2D materials alone. Popkova et al. 141 reported nonlinear exciton-Mie resonance coupling and second-order nonlinear effects using bulk MoS 2 . ...
... Even though the nonlinear metasurfaces operate at a subdiffraction regime for the fundamental wave, the emission of multiple diffractive beams at the nonlinearly generated harmonics restricts directional emission from such metasurfaces. This issue was addressed in a recent paper by Nauman et al., 145 The aforementioned nonlinear metasurfaces have mainly been used to investigate the common nonlinear optical effects such as SHG and THG through exploiting the physics of Mie resonance. However, the excitation of high-Q resonances at the fundamental wave frequencies is important to further improve the efficiency of second-and third-order nonlinear effects and to generate higher-order nonlinear processes. ...
... Specifically, only utilizing bulk TMD platforms enables the integration of a resonant microcavity and excitonic materials into a single nanostructured system, making the realization of self-hybridized exciton-polaritons feasible [25]. To date, the nanopatterned bulk TMDs have been reported to support various microcavity resonances such as Fabry-Pérot resonances, surface lattice resonances, guided-mode resonances, and Mie resonances [26][27][28][29][30]. When the energy of these resonances is tuned across the TMD excitons, the nontrivial anticrossing behavior with a large Rabi splitting energy is observed, which thus affirms the occurrence of self-hybridized exciton-polaritons induced by the strong coupling between the resonant microcavity and the exciton itself [28,30]. ...
Bulk transition metal dichalcogenides (TMDs) have found widespread applications on nanophotonics, condensed matter physics, and quantum optics, due to their high refractive index and stable excitonic response at room temperature. In this paper, based on the finite-element method simulations, we demonstrate that the high refractive index enables the fabrication of bulk WS2 into high-quality-factor metasurfaces that support chiral quasibound states in the continuum (Q-BICs). Interestingly, the Q-BIC resonance can in turn hybridize with excitons in the WS2 metasurface itself. The self-hybridized exciton-polaritons, induced by the strong coupling between a Q-BIC and excitons, exhibit a typical anticrossing behavior with the Rabi splitting up to 136.5 meV. Such remarkable anticrossing behavior is also well elucidated by the coupled oscillator model. Intriguingly, we numerically verify that the self-hybridized exciton-polaritons are photonic spin-controlled, attributed to the chiral Q-BIC with the circular dichroism approaching 0.91. Therefore, we can control the exciton-photon interaction by simply changing the helicity of incident light. We believe that the outstanding self-hybridized exciton-polaritons in a WS2 metasurface itself, without external microcavities, could pave the way for large-scale, low-cost integrated polaritonic devices at room temperature. Additionally, the chiral Q-BIC will enrich the toolbox for engineering exciton-photon interactions in bulk TMDs and other semiconductors. The photonic spin-controlled self-hybridized exciton-polaritons would find utility in ultrafast all-optical switches, modulators, chiral light-emitting devices, and valleytronic devices.
... Nanophotonic systems based on hBN have been successfully realized in various configurations 3 , including photonic crystals 4 , waveguides 5 , and optical metasurfaces 6 , further harnessing unique properties of hBN such as native visible quantum sources 7 , and infrared phonon-polaritons 8 . Similarly, vdW materials have been employed as metasurfaces for non-linear optics 9 , broad spectral tunability 6 as well as strong light-matter coupling 10 , and hold great promise for technological scale-up via largearea production methods 11 . The identification of optically active spin defects in hBN 12,13 has paved the way for leveraging vdW materials as quantum optical systems 14 . ...
Van der Waals (vdW) materials, including hexagonal boron nitride (hBN), are layered crystalline solids with appealing properties for investigating light-matter interactions at the nanoscale. hBN has emerged as a versatile building block for nanophotonic structures, and the recent identification of native optically addressable spin defects has opened up exciting possibilities in quantum technologies. However, these defects exhibit relatively low quantum efficiencies and a broad emission spectrum, limiting potential applications. Optical metasurfaces present a novel approach to boost light emission efficiency, offering remarkable control over light-matter coupling at the sub-wavelength regime. Here, we propose and realise a monolithic scalable integration between intrinsic spin defects in hBN metasurfaces and high quality (Q) factor resonances, exceeding 10², leveraging quasi-bound states in the continuum (qBICs). Coupling between defect ensembles and qBIC resonances delivers a 25-fold increase in photoluminescence intensity, accompanied by spectral narrowing to below 4 nm linewidth and increased narrowband spin-readout efficiency. Our findings demonstrate a new class of metasurfaces for spin-defect-based technologies and pave the way towards vdW-based nanophotonic devices with enhanced efficiency and sensitivity for quantum applications in imaging, sensing, and light emission.
... According to the literature, the refractive indexes of Si 3 N 4, and SiO 2 are assumed as 2.02 and 1.45, respectively [32]. The complex refractive index parameters of Si, bulk and monolayer MoS 2 are based on the experimental data [33,34] (see Fig. 7 in Appendix B). Particularly, the monolayer MoS 2 has a high refractive index with the infinitesimal extinction coefficient in this spectral range [35]. ...
... N-type high-purity Si (99.999%) is purchased from ZhongNuo Advanced Material (Beijing) Technology Co., Ltd and characterized by spectroscopic ellipsometer (RC2D, J. A. Woollam, United States), the optical parameters of Si are shown in Fig. 7(a). While the optical parameters of bulk and monolayer MoS 2 are obtained from the literatures [33,34], as shown in Figs. 7(b) and 7(c). ...
2D materials are promising candidates as nonlinear optical components for on-chip devices due to their ultrathin structure. In general, their nonlinear optical responses are inherently weak due to the short interaction thickness with light. Recently, there has been great interest in using quasi-bound states in the continuum (q-BICs) of dielectric metasurfaces, which are able to achieve remarkable optical near-field enhancement for elevating the second harmonic generation (SHG) emission from 2D materials. However, most studies focus on the design of combining bulk dielectric metasurfaces with unpatterned 2D materials, which suffer considerable radiation loss and limit near-field enhancement by high-quality q-BIC resonances. Here, we investigate the dielectric metasurface evolution from bulk silicon to monolayer molybdenum disulfide ( MoS 2 ), and discover the critical role of meta-atom thickness design on enhancing near-field effects of two q-BIC modes. We further introduce the strong-coupling of the two q-BIC modes by oblique incidence manipulation, and enhance the localized optical field on monolayer MoS 2 dramatically. In the ultraviolet and visible regions, the MoS 2 SHG enhancement factor of our design is 10 ⁵ times higher than that of conventional bulk metasurfaces, leading to an extremely high nonlinear conversion efficiency of 5.8%. Our research will provide an important theoretical guide for the design of high-performance nonlinear devices based on 2D materials.
... Metasurface is characterized as a twodimensional planar device that can modulate the amplitude, phase, polarization and other parameters of electromagnetic waves [1][2][3][4][5][6][7]. Metasurface can modulate these wave parameters by changing geometric parameters [4,8,9]and material compositions of subwavelength unit [10][11][12]. Compared with traditional bulk materials, metasurface exhibits many unique advantages, such as lower loss, smaller footprint, simpler integration, easier fabrication, elaborate modulation, and so on [13,14]. ...
The electromagnetic field enhancement caused by high Q factor resonance can greatly contribute to the magneto-optical Kerr effect of nanophotonic devices. Here we propose a magneto-optical metasurface supporting quasi bound states in the continuum (quasi-BIC) and theoretically investigate the evolution process from BIC to quasi-BIC. By applying external magnetic field, the BIC in our proposed metasurface can transform into quasi-BIC with finite Q factor up to 33620. Meanwhile, the polarization singularity of the quasi-BIC can be tuned by different magnetization directions, based on different time-reversal symmetry breaking phenomena in magneto-optical material under alternating magnetic field. The quasi-BIC in our magneto-optical metasurface keeps Fano reflection peak in parameter sweep, maintaining 99.99% reflection and almost zero absorption. Our results enrich the light control mechanisms of magneto-optical metasurface, and provide a unique opportunity for promising future applications requiring tunability and high Q factors, such as sensing, laser source and filtering.
... 22 Bulk transition-metal-dichalcogenides (TMDCs), i.e., layered van der Waals semiconductors, have emerged as promising nanoresonators for enhancing the light-matter interactions due to the large in-plane refractive index and material anisotropy. [23][24][25] It was demonstrated that the material anisotropy provides an additional degree of freedom for tailoring the magnetic and electric dipole (ED) resonances, 26 and the TMDCs allow for enhancing the nonlinear emission in metasurfaces 27 and deeper subwavelength optical field confinement in waveguides. 28 In this work, we investigate the spin-selective asymmetric transmission of circularly polarized waves in chiral TMDC metasurfaces, and the wavefront shaping for transmitted circularly polarized waves, such as anomalous refraction and spin-selective focusing of light, have also been demonstrated via the merging PB phase. ...
Multidimensional spin-selective manipulation of optical waves is crucial for various intriguing applications in modern nanophotonics, such as quantum-information processing and chiral sensing and imaging. In this work, we observed giant broadband asymmetric transmission of circularly polarized waves and spin-preserving reflection, together with near-unity transmission circular dichroism, in a planar chiral metasurface composed of high-index transition-metal-dichalcogenide nanoantennas with large material anisotropy. The perpendicular and parallel electric and magnetic dipole moments excited in the nanoantennas under circularly polarized waves are explored to account for the asymmetric transmission and optical chirality. Combined with the Pancharatnam–Berry phase, we achieved the wavefront manipulation for transmitted circularly polarized waves with an efficiency approaching 91.5% and spin-selective focusing of an incident light via a metasurface metalens. Our work will pave the way for studying the multidimensional manipulation of optical spins through engineering transition-metal-dichalcogenide-based metasurfaces.
... Among these nonlinearities, second-order nonlinearity has been a critical factor in multiple key optical effects, including second-harmonic generation (SHG) 7 , spontaneous downconversion 8 and the electro-optical effect 9 . These effects serve as the basis for a range of nonlinear devices, including tunable chip-scale sources 10 and high-speed optical signal modulation devices 11 . The amplitude of nonlinear effects in a material is proportional to the second-order susceptibility χ 2 , which is mainly determined by two critical parameters: the dipole dephasing rate and dipole transition moments 12 . ...
Due to their high optical transparency and electrical conductivity, indium tin oxide thin films are a promising material for photonic circuit design and applications. However, their weak optical nonlinearity has been a substantial barrier to nonlinear signal processing applications. In this study, we show that an atomically thin (~1.5 nm) indium tin oxide film in the form of an air/indium tin oxide/SiO2 quantum well exhibits a second-order susceptibility χ² of ~1,800 pm V–1. First-principles calculations and quantum electrostatic modelling point to an electronic interband transition resonance in the asymmetric potential energy of the quantum well as the reason for this large χ² value. As the χ² value is more than 20 times higher than that of the traditional nonlinear LiNbO3 crystal, our indium tin oxide quantum well design can be an important step towards nonlinear photonic circuit applications.
