Abstract
Plasmonic nanostructures hold promise for the realization of ultrathin subwavelength devices, reducing power operating thresholds and enabling nonlinear optical functionality in metasurfaces. However, this promise is substantially undercut by absorption introduced by resistive losses, causing the metasurface community to turn away from plasmonics in favour of alternative material platforms (e.g., dielectrics) that provide weaker field enhancement, but more tolerable losses. Here, we report a plasmonic metasurface with a qualityfactor (Qfactor) of 2340 in the telecommunication C band by exploiting surface lattice resonances (SLRs), exceeding the record by an order of magnitude. Additionally, we show that SLRs retain many of the same benefits as localized plasmonic resonances, such as field enhancement and strong confinement of light along the metal surface. Our results demonstrate that SLRs provide an exciting and unexplored method to tailor incident light fields, and could pave the way to flexible wavelengthscale devices for any optical resonating application.
Introduction
Metallic nanostructures are essential to many applications in photonics, including biosensing^{1}, spectroscopy^{2,3}, nanolasing^{4}, alloptical switching^{5}, nonlinear optical processes^{6}, and metasurface technologies^{7,8,9}. These plasmonic elements form flexible components with geometrydependent responses and have many desirable properties, such as the possibility to confine light to subwavelength scales and large localfield enhancements^{9,10}. Metals also possess intrinsic nonlinear optical constants that are many orders of magnitude larger than dielectric materials^{11}.
When structured at the subwavelength scale^{8,9,12}, individual nanostructures exhibit localized surface plasmon resonances (LSPRs), where electromagnetic fields couple to the freeelectron plasma of a conductor at a metal–dielectric interface^{6,10}. Depending on its shape, an individual nanoparticle may be polarized by an incident light beam, acting as a lossy dipole antenna^{13} and trapping light for a short period of time. In contrast to other photonic resonant devices such as whispering gallery mode resonators, microring resonators, or photonic crystals^{14,15,16}, resonating dipoles in a metasurface can easily be accessed by a beam propagating in free space and require only a subwavelength propagation region for operation. Therefore, a plasmonic metasurface resonator enables a series of specialized optical responses, including phasematchingfree nonlinear optical effects^{6,17}, strongly localized field enhancements^{9}, multimode operation^{18}, and a spatially localized optical response^{7}. Such a metasurface with a large quality factor (Qfactor) could be used as a cavity for applications that need increased light–matter interactions, small mode volumes, large field enhancements, and large optical nonlinearities, such as an ultraflat nanolaser with a large transverse mode size^{4,19} or frequency conversion applications (e.g., nonlinear harmonic generation^{20} or THzwave generation^{21}). One frequently cited limitation of LSPRbased metasurfaces are their low Qfactors (e.g., Q < 10) due to the intrinsic Ohmic losses present in metals at optical frequencies^{10,22,23,24}. As the Qfactor is related to the light–matter interaction time as well as to enhancements to the electric field, it is typically desirable to maximize this quantity^{14}. Low Qfactors therefore make many potential applications of plasmonicsbased metasurface devices impractical, and new methods for obtaining large Qfactor resonances in a metasurface have long been sought after.
The optical response of coupled plasmonic nanoresonators has been a topic of intense study^{25}. Notably, plasmonic metasurfaces of large periodically arranged nanostructures support collective resonances called surface lattice resonances (SLRs)^{26,27,28,29,30,31,32}. Here the individual responses from the surface plasmons of many individual nanostructures form a collective response that couples to inplane diffraction orders of the periodic array^{26,30}. As a consequence, a relatively highQ resonance can emerge at an optical wavelength λ_{SLR} ≈ nP, close to the product of the refractive index of the background medium n and the lattice period P^{26,32}. Recent theoretical studies of this platform have predicted Qfactors on the order of 10^{3} by properly engineering the dimensions of the individual nanostructures and the period of the lattice^{31,32,33}, hinting at the possibility of combining the aforementioned benefits of metals with long interaction times provided by high Qfactors. However, to date, the highest experimentally observed Qfactor in an SLRbased metasurface is 430^{34}. The disparity between theory and experiment has been attributed to a variety of reasons, including poor spatial coherence of light beams^{28,35}, small array sizes^{30,31,36}, fabrication imperfections^{30,31}, and the addition of an adhesion layer^{37}.
Inspired by this discrepancy, here we perform a detailed investigation to determine the dominant factors that most drastically affect the observed Q of an SLRbased metasurface: the nanostructure geometry, the array size, and the spatial coherence of the probing light source. Using the results of this study, we demonstrate a plasmonic metasurface capable of supporting ultrahighQ SLRs.
Results
The metasurface in consideration consists of a rectangular array of rectangular gold nanostructures embedded in a homogeneous silica glass (n ~ 1.45) environment (Fig. 1a). The lattice constant P_{y} = 1060 nm was selected to place the SLR wavelength in the telecommunication window; P_{x} = 500 nm was reduced from a square lattice, increasing the nanoparticle density and consequently increasing the extinction ratio of the resonance. The overcladding is carefully matched to the substrate material to ensure a symmetric cladding index, as it has been shown that the Q of an SLR may be affected by the homogeneity of the environment^{26,38,39}. As shown by the numerical predictions in Fig. 1b, for an xpolarized beam, this metasurface is expected to support an LSPR at λ_{LSPR} = 830 nm and an SLR of the first type around λ_{SLR} = 1550 nm (See Supplementary Sec. S2: SLR type). The SLR linewidth is substantially narrower than that of the LSPR, corresponding to a much higher Qfactor. Incidentally, the inset field profiles in Fig. 1b also reveal that the SLR provides a more significant field enhancement, with \( {E}_{\max }({\lambda }_{{\rm{SLR}}}) \sim 3 {E}_{\max }({\lambda }_{{\rm{LSPR}}})\). Figure 1c shows an image of the fabricated device with dimensions matching those of the simulations. The measured transmission spectra are presented in Fig. 1d, closely matching the predicted spectrum. Notably, the full width at halfmaximum of the linewidth is only Δλ = 0.66 nm, corresponding to a Qfactor of Q = 2340. This value exceeds the record for plasmonic metasurfaces by an order of magnitude^{34,37,40} and is among the highest reported in a metasurface. It is roughly within a factor of two of semianalytic calculations performed using the lattice sum approach (LSA), where Q ~ 5000 (see “Methods” for details). In order to observe this value for the Qfactor, both the metasurface and the measurement apparatus needed to be arranged with a few considerations in mind, which we describe in greater detail below.
The role of nanoparticle polarizability
First, the individual structures need to be engineered to exhibit the appropriate response at λ_{SLR}. The optical response of a nanostructure can be approximated using the polarizability of a Lorentzian dipole,
where A_{0} is the oscillator strength, ω_{0} = 2πc/λ_{LSPR} corresponds to the nanoparticle resonance frequency, and γ is the damping term. These quantities all depend on the particle geometry^{12} (here the length L_{y} and width L_{x} of a rectangular bar). The contribution of the particle lattice to the polarizability can be introduced using the LSA^{39,41}:
where α^{*}(ω) is known as the effective polarizability of the entire metasurface and S(ω) corresponds to the lattice sum. This latter term depends only on the arrangement of the lattice. An SLR appears approximately where S(ω) exhibits a pole, at ω_{SLR} = (2πc/λ_{SLR}). At this spectral location, the individual responses of all of the nanostructures contribute cooperatively^{41}.
Equation (2) may be used to predict the optical response of the entire metasurface, including the behavior of its many resonances, as a function of the geometry of its nanostructures (see “Methods”): by changing the geometry of a nanostructure^{12,42}, its individual resonance wavelength λ_{LSPR}, oscillator strength A_{0}, and damping constant γ are all modified. In turn, adjusting these values changes the polarizability of the nanostructures throughout the spectrum, including at the SLR wavelength α(ω_{SLR}), and therefore also the response of the entire metasurface at this wavelength α^{*}(ω_{SLR}). Here we adjust the above parameters by changing the dimensions of the nanostructures (see “Methods”), while the parameters could be alternatively modified by considering altogether different nanostructure shapes, such as nanorings, nanorods, or core–shell nanoparticles^{42}. By contrast, the spectral location of the SLR wavelength is dictated mainly by the lattice period and the background index λ_{SLR} ≈ nP^{32,43,44}. In other words, the lattice configuration governs the presence of the SLR, and the nanostructure geometry dictates its coupling efficiency to free space. Indeed, recent theoretical studies in this platform have shown Qfactors on the order of 10^{3} by properly selecting the dimensions of the individual nanostructures^{31,33}.
We reproduce this dependence in this platform explicitly by plotting the calculated transmission of a metasurface (see “Methods”) as a function of nanostructure resonance wavelength λ_{LSPR} (Fig. 2). (The dependence of the SLR behavior on particle dimensions, which is connected to the resonance wavelength, is also demonstrated using fullwave simulations in Supplementary Sec. S3: Dependence of SLR behavior on particle dimensions.) Here we hold the oscillator strength A_{0} and damping term γ constant and slowly increase the nanoparticle resonance wavelength λ_{LSPR}. Note that the resonance position differs slightly from the position of the dip due to the incorporation of a longwavelength correction^{45}. In Fig. 2b, c, the SLR wavelength does not change substantially from its location around λ_{SLR} = 1542 nm; however, the extinction ratio ΔT and the linewidth Δλ of the resonance change dramatically. In Fig. 2d, we plot the extracted Qfactors for these SLRs and for other values of A_{0}, as well (see Supplementary Sec. S1: Qfactor extraction for the fits). Based on wellestablished relationships between nanoparticle geometry and polarizability^{10,46}, this A_{0} range corresponds to a change in nanoparticle volume of roughly 20%. We find that, for every given value of A_{0}, there is a corresponding λ_{LSPR} for which light couples optimally to the lattice resonance at λ_{SLR} and produces the highest Qfactor. The optimal conditions are therefore found in the balance between increasing α relative to P_{y} (i.e., increasing coupling strength) and maintaining a large spectral gap between λ_{LSPR} and λ_{SLR} (i.e., limiting Ohmic losses associated with metallic nanoparticles). The tradeoff between coupling and loss is a traditional one for optical resonators and is reproduced in the SLRbased metasurface platform^{47}.
Effect of array size
Next, we study the dependence of the Qfactor on the array size. For certain metasurfaces, it has already been predicted that larger array sizes lead to better device performance^{36,48}. This dependence makes some intuitive sense—since highQ operation requires low absorption losses, we are required to operate the device far from the LSPR. However, at a sufficiently far operating wavelength, the scattering crosssection is also small, resulting in each antenna scattering very weakly. Consequently, far from the LSPR, one requires a sufficiently large number of scatterers to build up the resonance. Equivalently, the standing wave mode in an SLR consists of counterpropagating surface waves; therefore, a larger array provides an expanded propagation length in the cavity to support these modes.
To examine the dependence of Q on the number of nanostructures explicitly, we fabricated and characterized a series of devices of increasing array size. Figure 3 shows the resulting transmission spectra, as well as their corresponding semianalytic predictions. The observed Qfactors increase monotonically as a function of array size (Fig. 3b—see Supplementary Sec. S1: Qfactor extraction for the fits). In the smallest array (300 × 300 μm^{2}), the SLR is almost imperceptible. This trend might help explain the relatively low Q values observed in previous studies^{9,30,31,36} where array sizes were typically no larger than 250 × 250 μm^{2}, likely due to the relatively slow writespeed of the electronbeam lithography process necessary for fabrication^{26,37}. By contrast, our devices have array sizes reaching up to 600 × 600 μm^{2} (see Supplementary Sec. S4: Image of the device).
The role of spatial coherence
Finally, it is of critical importance to consider all aspects of the characterization system in order to get an accurate measurement of the Qfactor. In particular, we have found that the spatial coherence of the probe beam was critical to obtaining a clean measurement of the dip in transmission indicating a resonance. A spatially coherent beam, such as a laser, excites every region of the metasurface in phase, producing a resonance feature that is both deeper and narrower compared to using a spatially incoherent source. Additionally, the higherorder modes of the lattice are more sensitive to angular variance in the measurements, leading to broader peaks when using incoherent sources^{35}. Furthermore, in our particular experiment, the transmitted signal from our coherent supercontinuum source was both brighter and could also be better collimated than our incoherent thermal source. Therefore, the light collected from the metasurface array could be isolated with a smaller pinhole in the image plane, selecting the signal coming from nanostructures at the center of the array with a more uniform collective response.
In Fig. 3, we compare the performance of the metasurface when illuminated using different light sources: a broadband supercontinuum laser (i.e., a wellcollimated coherent source), and a tungstenhalogen lamp. The comparison between these measurements indicates that the Q increases with the coherence of the light source—using the thermal light source reduces the Qfactor by a factor of 2–5 when compared to the laser. Additionally, it decreases the resonance coupling strength, as is evident from the reduced extinction ratio of the SLRs. Figure 3b summarizes the Qfactors extracted from these measurements and compares them to numerical predictions. LSA calculations predict that Qfactors increase as a function of array size; this trend continues for both smaller and larger devices than those probed experimentally. Note that, even when using an incoherent source, the largest array still produces a very large Qfactor (Q ~ 1000). The observation of such a high Q using an incoherent source reinforces the validity of our aforementioned metasurface design criteria—that is, the importance of the choice of nanostructure geometry and of the array size.
In some of the measurements, the value for the normalized transmittance can be seen to exceed unity (i.e., T > 1). We speculate that this is because the nanostructures aid in coupling to the substrate, reducing the reflections from the first interface.
Discussion
Despite promising results, Fig. 3b also highlights some discrepancies between the simulation and the experiment for the largest arrays, notably reducing the measured Qfactors. This disparity could be due to multiple reasons, which we enumerate below. First, the prediction produced by the LSA might be overestimating the Q by assuming that each nanoparticle is excited with a constantvalued local field. This assumption cannot be entirely correct for a Gaussian beam and a finite array, where particles closer to the boundaries of the array feel a weaker local field than the particles near the center. Second, the fabrication procedure produces stitching errors, which become more important for larger arrays. This added disorder might contribute to the reduction in Q. Lastly, the Qfactors might be limited due to additional measurement considerations, such as the finite coherence length of the light source or imperfections with the collimation.
In this work, we only looked into rectangular nanoparticles in rectangular lattices. Based on LSA calculations and the discretedipole approximation (DDA) used in previous work^{26,39,44,49,50}, it is evident that any particle geometry (e.g., cylindrical, rectangular, or triangular) that can be approximated by dipoles with the same Lorentzian parameters A_{0}, λ_{LSPR}, and γ will yield an identical SLR Qfactor. For nanoparticles that cannot be modeled by dipoles—regardless of the particle geometry—the SLR Qfactor will be the same provided that the polarizability at λ_{SLR} remains the same. Regarding different lattice configurations, the spectral responses of other lattice geometries such as hexagonal, orthorhombic, and kagome are likely to be different than the rectangular lattice design we have adopted. However, lattice sums can be computed for these regular lattices, and therefore they can also be treated using our method. Therefore, strategies presented in this work are largely blind to the specific lattice arrangements, and its conclusions will be helpful in obtaining resonances with largeQ factors in other geometries.
The Qfactors for the type of device presented here could be further increased, however, by considering larger arrays or by further optimizing the nanostructure dimensions—instead of rectangles, a more intricate nanostructure shape could tailor the Lorentzian dipole coefficients A_{0}, λ_{LSPR}, and γ more independently to allow for optimal coupling and higher extinction ratios. These shapes include Lshaped antennas^{51}, splitring resonators^{52}, and others that also exhibit higherorder moments^{53,54}. Alternatively, a nanoparticle with a large aspect ratio could increase coupling to more neighboring particles using outofplane oscillations^{44}. Finally, the metasurface shown here can be combined with other established methods to enable multiple simultaneous resonances^{39,50,55}.
Table 1 contains a short survey of the literature on metasurface nanocavities. Other than the reported Qfactors, we have included, when available, information that is relevant to compare their work against ours, such as the operating wavelength, the material platform, the array size, and the type of light source used. Our work demonstrates the highest Q by an order of magnitude among metasurfaces with plasmonic components and is exceeded only by metasurfaces that incorporate a bound state in the continuum (BIC).
To summarize, we have fabricated and experimentally demonstrated a plasmonic metasurface nanoresonator with a high Qfactor, which is in excellent agreement with numerical predictions. Our work presents the experimental demonstration of a highQ plasmonic metasurface nanoresonator with an orderofmagnitude improvement over prior art (see Table 1). We have found that the observed Qfactor obtained from an SLR may be limited by a poor choice of nanostructure dimensions, a small array size, or poor spatial coherence of the source illumination; we hypothesize that one or many of these factors may have been the cause for the low Qfactors reported in previous experiments featuring SLRs. Additionally, our device follows simple design principles that can be easily expanded upon to enable multiple resonances to fully tailor the transmission spectrum of a wavelengthscale surface. Our result highlights the potential of SLRbased metasurfaces and expands the capabilities of plasmonic nanoparticles for many optical applications.
Methods
Simulations
Finitedifference time domain (FDTD)
Fullwave simulations were performed using a commercial threedimensional FDTD solver. A single unit cell was simulated using periodic boundary conditions in the inplane dimensions and perfectly matched layers in the outofplane dimension. The structures were modeled using fully dispersive optical material properties for silica^{56} and for gold^{57}. Minimal artificial absorption (\({\rm{Im}}(n)\ \sim \ 1{0}^{4}\)) was added to the background medium to reduce numerical divergences.
Lattice sum approach
The LSA is a variant of the DDA method^{58}. It is a semianalytic calculation method that has been found to produce accurate results for plasmonic arrays^{39,41,44}. The main assumption in LSA when compared to DDA is that the dipole moments of all interacting nanoparticles are assumed to be identical^{44}. The main benefit of using LSA for our application compared to alternatives such as FDTD is its capability to model finitesized arrays with an arbitrary number of nanostructures, by assuming that the overall response of the array closely follows the responses of the nanoparticles at the center of the array. By comparing simulations performed using the LSA against the DDA, this assumption has also been found to be quite accurate^{44}. Its rapid simulation time makes it a useful tool for iterating many simulations to study trends and behaviors of entire metasurfaces, especially for finite array effects, such as the effect of array size on the Qfactor.
Using the LSA approach, the dipole moment p of any particle in the array is written as
where the effect of interparticle coupling is incorporated in the lattice sum \({{S}}\) and α^{*} is the effective polarizability. This equation produces Eq. (2) in the main text. The calculations presented in this work also incorporate a modified longwavelength correction^{45}:
where k is the wavenumber in the background medium k = (2πn/λ) and l is the effective particle radius. Also here, minimal artificial absorption (\({\rm{Im}}(n)=6\times 1{0}^{4}\)) was added to the refractive index n = 1.452 of the background medium to reduce numerical divergences associated with the approach when considering large arrays^{41}. We set l = 180 nm for all calculations. The static polarizability of the nanoparticle is given by
where A_{0} is the oscillator strength, ω_{0} = 2πc/λ_{LSPR} corresponds to the nanoparticle resonance frequency, and γ is the damping term.
For a planar array of N dipoles, the lattice sum term \({{S}}\) is
where r_{j} is the distance to the jth dipole and θ_{j} is the angle between r_{j} and the dipole moment p.
The optical transmission spectra can be obtained by using the optical theorem, \({\rm{Ext}}\propto k{\rm{Im}}({\alpha }^{* })\)^{59}:
where P_{x} and P_{y} are the lattice constants along the x and y dimensions, respectively.
To produce the plots in Fig. 1d, we performed an LSA calculation using the following parameters for the single dipole: λ_{LSPR} = 780 nm; A_{0} = 3.46 × 10^{−7} m^{3}/s, γ = 8.5 × 10^{13} s^{−1}. LSA parameters were determined by matching to FDTD data. The lattice constants were P_{x} = 500 nm and P_{y} = 1067.5 nm. The total array size was 600 × 600 μm^{2}, corresponding to N_{x} = 1200 × N_{y} = 562 nanostructures, respectively. The LSA calculations in Fig. 3 used these same parameters but varied the total number of nanostructures.
To calculate the figures in Fig. 2a, c, we performed a series of LSA calculation using the following parameters for the particle: A_{0} = 3.98 × 10^{−7} m^{3}/s, γ = 1/[2π(2.1 fs)] ≈ 7.6 × 10^{13} s^{−1}. The dipole resonance wavelengths λ_{LSPR} were 800, 833, 866, 900, 933, 966, and 1000 nm, respectively. Based on the performed FDTD simulations, these resonance wavelengths could correspond to rectangular gold nanostructures with widths of L_{x} = 110, 120, 130, 140, 150, 160, and 170 nm, respectively, if L_{y} = 190 nm, and t = 20 nm. (Note that, in the main text, L_{y} = 200 nm). See Supplementary Sec. S3: Dependence of SLR behavior on particle dimensions for the corresponding simulations. The lattice constants were P_{x} = 500 nm and P_{y} = 1060 nm, respectively. The total array size was 600 × 600 μm^{2}, corresponding to N_{x} = 1200 × N_{y} = 567 nanostructures, respectively. To obtain Fig. 2d, a series of LSA calculations were performed for many values of λ_{LSPR} ranging from 800 to 1000 nm, and the Qfactors were extracted from the results using a fit to a Lorentzian. The curves in Fig. 2d come from repeating this procedure with oscillator strengths of A_{0} = 3.98 × 10^{−7}, 4.38 × 10^{−7}, and 4.77 × 10^{−7} m^{3}/s.
Device details
We fabricated different metasurface devices with array sizes of 300 × 300, 400 × 400, 500 × 500, and 600 × 600 μm^{2}, with a corresponding number of participating nanostructures of 600 × 284, 800 × 378, 1000 × 472, and 1200 × 567, respectively. The lattice constants of the rectangular arrays are P_{x} = 500 nm × P_{y} = 1060 nm. The dimensions of the rectangular gold nanostructures are L_{x} = 130 nm × L_{y} = 200 nm, with a thickness of t = 20 nm. The lattice is embedded within a homogeneous background n ≈ 1.46.
Fabrication
The metasurfaces are fabricated using a standard metal liftoff process. We start with a fused silica substrate. We deposit a silica undercladding layer using sputtering. We then define the pattern using electronbeam lithography in a positive tone resist bilayer with the help of a commercial conductive polymer. The mask was designed using shapecorrection proximity error correction^{60} to correct for corner rounding. Following development, a thin adhesion layer of chromium (0.2nm thick) is deposited using ebeam evaporation, followed by a layer of gold deposited using thermal evaporation. Liftoff is performed, and a final protective silica cladding layer is deposited using sputtering. The initial and final silica layers are sputtered using the same tool under the same conditions to ensure that the environment surrounding the metasurface is completely homogeneous. Before characterization, the surface of the device is then covered in indexmatching oil. The backside of the silica substrate is coated with an antireflective coating to minimize substraterelated etalon fringes.
Characterization
See Supplementary Sec. S5: Experimental setup for a schematic of the experimental setup.
Coherent light measurements
To measure the transmission spectra, we floodilluminated all of the arrays in the sample using a collimated light beam from a broadband supercontinuum laser source. The wavelength spectrum of the source ranges from λ = 470 to 2400 nm. The beam comes from normal incidence along the zdirection with light polarized in the xdirection. The incident polarization is controlled using a broadband linear polarizing filter. Light transmitted by the metasurface is then imaged by a f = 35 mm lens, and a 100μm pinhole is placed in the image plane to select the desired array. The transmitted light is collected in a large core (400 μm) multimode fiber and analyzed using an optical spectrum analyzer and is normalized to a background trace of the substrate without gold nanostructures. The resolution of the spectrometer is set to 0.01 nm.
Incoherent light measurements
Here the experiment goes as above, but the samples are excited using a collimated tungstenhalogen light source (ranging from λ = 300 to 2600 nm) and a 400μm pinhole.
Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Code availability
The code used to analyze the data and the related simulation files are available from the corresponding author upon reasonable request.
References
 1.
Anker, J. et al. Biosensing with plasmonic nanosensors. Nat. Mater. 7, 442–453 (2008).
 2.
Nie, S. & Emory, S. R. Probing single molecules and single nanoparticles by surfaceenhanced Raman scattering. Science 275, 1102–1106 (1997).
 3.
Willets, K. A. & Van Duyne, R. P. Localized surface plasmon resonance spectroscopy and sensing. Annu. Rev. Phys. Chem. 58, 267–297 (2007).
 4.
Azzam, S. I. et al. Ten years of spasers and plasmonic nanolasers. Light Sci. Appl. 9, 90 (2020).
 5.
Ren, M. et al. Nanostructured plasmonic medium for terahertz bandwidth alloptical switching. Adv. Mater. 23, 5540–5544 (2011).
 6.
Kauranen, M. & Zayats, A. V. Nonlinear plasmonics. Nat. Photonics 6, 737 (2012).
 7.
Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).
 8.
Won, R. The rise of plasmonic metasurfaces. Nat. Photonics 11, 462–464 (2017).
 9.
Meinzer, N., Barnes, W. L. & Hooper, I. R. Plasmonic metaatoms and metasurfaces. Nat. Photonics 8, 889–898 (2014).
 10.
Maier, S. A. Plasmonics: Fundamentals and Applications (Springer, 2007).
 11.
Boyd, R. W. Nonlinear Optics 4th edn (Academic, 2020).
 12.
Oldenburg, S. J., D., A. R., Westcott, S. L. & Halas, N. J. Nanoengineering of optical resonances. Chem. Phys. Lett. 288, 243–247 (1998).
 13.
Novotny, L. & Van Hulst, N. Antennas for light. Nat. Photonics 5, 83–90 (2011).
 14.
Zhang, X., Choi, H. S. & Armani, A. M. Ultimate quality factor of silica microtoroid resonant cavities. Appl. Phys. Lett. 96, 153304 (2010).
 15.
Ji, X. et al. Ultralowloss onchip resonators with submilliwatt parametric oscillation threshold. Optica 4, 619–624 (2017).
 16.
Asano, T., Ochi, Y., Takahashi, Y., Kishimoto, K. & Noda, S. Photonic crystal nanocavity with a Q factor exceeding eleven million. Opt. Express 25, 1769 (2017).
 17.
Krasnok, A., Tymchenko, M. & Alù, A. Nonlinear metasurfaces: a paradigm shift in nonlinear optics. Mater. Today 21, 8–21 (2018).
 18.
Celebrano, M. et al. Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation. Nat. Nanotechnol. 10, 412–417 (2015).
 19.
Zhou, W. et al. Lasing action in strongly coupled plasmonic nanocavity arrays. Nat. Nanotechnol. 8, 506–511 (2013).
 20.
Michaeli, L., KerenZur, S., Avayu, O., Suchowski, H. & Ellenbogen, T. Nonlinear surface lattice resonance in plasmonic nanoparticle arrays. Phys. Rev. Lett. 118, 243904 (2017).
 21.
Luo, L. et al. Broadband terahertz generation from metamaterials. Nat. Commun. 5, 3055 (2014).
 22.
Choi, D.Y. et al. Imagingbased molecular barcoding with pixelated dielectric metasurfaces. Science 360, 1105–1109 (2018).
 23.
Sain, B., Meier, C. & Zentgraf, T. Nonlinear optics in alldielectric nanoantennas and metasurfaces: a review. Adv. Photonics 1, 1 (2019).
 24.
Koshelev, K. et al. Subwavelength dielectric resonators for nonlinear nanophotonics. Science 367, 288–292 (2020).
 25.
Nordlander, P., Oubre, C., Prodan, E., Li, K. & Stockman, M. I. Plasmon hybridization in nanoparticle dimers. Nano Lett. 4, 899–903 (2004).
 26.
Auguié, B. & Barnes, W. L. Collective resonances in gold nanoparticle arrays. Phys. Rev. Lett. 101, 143902 (2008).
 27.
Chu, Y., Schonbrun, E., Yang, T. & Crozier, K. B. Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays. Appl. Phys. Lett. 93, 181108 (2008).
 28.
Kravets, V., Schedin, F. & Grigorenko, A. Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles. Phys. Rev. Lett. 101, 087403 (2008).
 29.
Vecchi, G., Giannini, V. & Rivas, J. G. Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas. Phys. Rev. B 80, 201401 (2009).
 30.
Kravets, V. G., Kabashin, A. V., Barnes, W. L. & Grigorenko, A. N. Plasmonic surface lattice resonances: a review of properties and applications. Chem. Rev. 118, 5912–5951 (2018).
 31.
Khlopin, D. et al. Lattice modes and plasmonic linewidth engineering in gold and aluminum nanoparticle arrays. J. Opt. Soc. Am. B 34, 691 (2017).
 32.
Zou, S., Janel, N. & Schatz, G. C. Silver nanoparticle array structures that produce remarkable narrow plasmon line shapes. J. Chem. Phys. 120, 10871–10875 (2004).
 33.
Zakomirnyi, V. I. et al. Refractory titanium nitride twodimensional structures with extremely narrow surface lattice resonances at telecommunication wavelengths. Appl. Phys. Lett. 111, 123107 (2017).
 34.
Deng, S. et al. Ultranarrow plasmon resonances from annealed nanoparticle lattices. Proc. Natl. Acad. Sci. USA 117, 23380 (2020).
 35.
Li, S. Q. et al. Ultrasharp plasmonic resonances from monopole optical nanoantenna phased arrays. Appl. Phys. Lett. 104, 231101 (2014).
 36.
Rodriguez, S. R. K., Schaafsma, M. C., Berrier, A. & Gomez Rivas, J. Collective resonances in plasmonic crystals: size matters. Phys. B Condens. Matter 407, 4081–4085 (2012).
 37.
LeVan, Q. et al. Enhanced quality factors of surface lattice resonances in plasmonic arrays of nanoparticles. Adv. Opt. Mater. 7, 1801451 (2019).
 38.
Auguié, B., Bendana, X. M., Barnes, W. L. & de Abajo, F. J. G. Diffractive arrays of gold nanoparticles near an interface: critical role of the substrate. Phys. Rev. B 82, 155447 (2010).
 39.
Reshef, O. et al. Multiresonant highQ plasmonic metasurfaces. Nano Lett. 19, 6429–6434 (2019).
 40.
Thackray, B. D. et al. Supernarrow, extremely high quality collective plasmon resonances at telecom wavelengths and their application in a hybrid grapheneplasmonic modulator. Nano Lett. 15, 3519–3523 (2015).
 41.
Markel, V. A. Divergence of dipole sums and the nature of nonLorentzian exponentially narrow resonances in onedimensional periodic arrays of nanospheres. J. Phys. B 38, L115–L121 (2005).
 42.
Teperik, T. & Degiron, A. Design strategies to tailor the narrow plasmonphotonic resonances in arrays of metallic nanoparticles. Phys. Rev. B 86, 245425 (2012).
 43.
Offermans, P. et al. Universal scaling of the figure of merit of plasmonic sensors. ACS Nano 5, 5151–5157 (2011).
 44.
Huttunen, M. J., Dolgaleva, K., Törmä, P. & Boyd, R. W. Ultrastrong polarization dependence of surface lattice resonances with outofplane plasmon oscillations. Opt. Express 24, 28279–28289 (2016).
 45.
Jensen, T., Kelly, L., Lazarides, A. & Schatz, G. C. Electrodynamics of noble metal nanoparticles and nanoparticle clusters. J. Cluster Sci. 10, 295–317 (1999).
 46.
Huang, C.p, Yin, X.g, Huang, H. & Zhu, Y.y Study of plasmon resonance in a gold nanorod with an LC circuit model. Opt. Express 17, 6407–6413 (2009).
 47.
McKinnon, W. R. et al. Extracting coupling and loss coefficients from a ring resonator. Opt. Express 17, 17010 (2009).
 48.
Zundel, L. & Manjavacas, A. Finitesize effects on periodic arrays of nanostructures. J. Phys. Photonics 1, 015004 (2019).
 49.
Huttunen, M. J., Rasekh, P., Boyd, R. W. & Dolgaleva, K. Using surface lattice resonances to engineer nonlinear optical processes in metal nanoparticle arrays. Phys. Rev. A 97, 053817 (2018).
 50.
Huttunen, M. J., Reshef, O., Stolt, T., Dolgaleva, K. & Boyd, R. W. Efficient nonlinear metasurfaces by using multiresonant highQ plasmonic arrays. J. Opt. Soc. Am. B 36, 118 (2019).
 51.
Husu, H., Mäkitalo, J., Laukkanen, J., Kuittinen, M. & Kauranen, M. Particle plasmon resonances in lshaped gold nanoparticles. Opt. Express 18, 16601–16606 (2010).
 52.
Corrigan, T. D. et al. Optical plasmonic resonances in splitring resonator structures: an improved LC model. Opt. Express 16, 19850–19864 (2008).
 53.
Barnes, W. L. Particle plasmons: why shape matters. Am. J. Phys. 84, 593–601 (2016).
 54.
Alaee, R., Rockstuhl, C. & FernandezCorbaton, I. An electromagnetic multipole expansion beyond the longwavelength approximation. Opt. Commun. 407, 17–21 (2018).
 55.
Baur, S., Sanders, S. & Manjavacas, A. Hybridization of lattice resonances. ACS Nano 12, 1618–1629 (2018).
 56.
Palik, E. D. Handbook of Optical Constants of Solid (Academic, 1985).
 57.
Johnson, P. & Christy, R. Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972).
 58.
Oldenburg, S. J., D., A. R., Westcott, S. L. & Halas, N. J. Discretedipole approximation for scattering calculations. J. Opt. Soc. Am. A 11, 1491–1499 (1994).
 59.
Jackson, J. D. Classical Electrodynamics 3rd edn (Wiley, 1999).
 60.
Schulz, S. A. et al. Quantifying the impact of proximity error correction on plasmonic metasurfaces [Invited]. Opt. Mater. Express 5, 2798–2803 (2015).
 61.
Rodriguez, S. R. et al. Coupling bright and dark plasmonic lattice resonances. Phys. Rev. X 1, 021019 (2011).
 62.
Kravets, V. G., Schedin, F., Kabashin, A. V. & Grigorenko, A. N. Sensitivity of collective plasmon modes of gold nanoresonators to local environment. Opt. Lett. 35, 956–958 (2010).
 63.
Yang, A. et al. Realtime tunable lasing from plasmonic nanocavity arrays. Nat. Commun. 6, 6939 (2015).
 64.
Yang, Y., Kravchenko, I. I., Briggs, D. P. & Valentine, J. Alldielectric metasurface analogue of electromagnetically induced transparency. Nat. Commun. 5, 5753 (2014).
 65.
Singh, R. et al. Ultrasensitive terahertz sensing with highQ Fano resonances in metasurfaces. Appl. Phys. Lett. 105, 171101 (2011).
 66.
Wu, C. et al. Fanoresonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers. Nat. Mater. 11, 69–75 (2011).
 67.
Campione, S. et al. Broken symmetry dielectric resonators for high quality factor fano metasurfaces. Nano Lett. 3, 2362–2367 (2016).
 68.
Ha, S. T. et al. Directional lasing in resonant semiconductor nanoantenna arrays. Nat. Nanotechnol. 13, 1042–1047 (2018).
 69.
Liu, Z. et al. HighQ quasibound states in the continuum for nonlinear metasurfaces. Phys. Rev. Lett. 123, 253901 (2019).
Acknowledgements
Fabrication in this work was performed in part at the Centre for Research in Photonics at the University of Ottawa (CRPuO). The authors acknowledge support from the Canada Excellence Research Chairs (CERC) Program, the Canada Research Chairs (CRC) Program, and the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery funding program. M.S.B.A. acknowledges the support of the Ontario Graduate Scholarship (OGS), the University of Ottawa Excellence Scholarship, and the University of Ottawa International Experience Scholarship. O.R. acknowledges the support of the Banting Postdoctoral Fellowship of the NSERC. Y.M. was supported by the Mitacs Globalink Research Award. M.J.H. acknowledges the support of the Academy of Finland (Grant No. 308596) and the Flagship of Photonics Research and Innovation (PREIN) funded by the Academy of Finland (Grant No. 320165).
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M.S.B.A., O.R., and M.J.H. conceived the basic idea for this work. O.R. and M.S.B.A. performed the FDTD simulations. M.J.H., M.S.B.A., and O.R. performed the lattice sum calculations. O.R. and G.C. fabricated the device. M.Z.A. and M.J.H. designed the preliminary experimental setup. M.S.B.A. and Y.M. carried out the measurements. O.R., M.S.B.A., and Y.M. analyzed the experimental results. J.U., B.T.S., J.M.M., M.J.H., R.W.B., and K.D. supervised the research and the development of the manuscript. M.S.B.A. and O.R. wrote the first draft of the manuscript. All coauthors subsequently took part in the revision process and approved the final copy of the manuscript. Portions of this work were presented at the 2020 SPIE Photonics West Conference in San Francisco, CA.
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BinAlam, M.S., Reshef, O., Mamchur, Y. et al. UltrahighQ resonances in plasmonic metasurfaces. Nat Commun 12, 974 (2021). https://doi.org/10.1038/s41467021211962
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