Metasurface analogues of electromagnetically induced transparency (EIT) have been a focus of the nanophotonics field in recent years, due to their ability to produce high-quality factor (Q-factor) resonances. Such resonances are expected to be useful for applications such as low-loss slow-light devices and highly sensitive optical sensors. However, ohmic losses limit the achievable Q-factors in conventional plasmonic EIT metasurfaces to values <~10, significantly hampering device performance. Here we experimentally demonstrate a classical analogue of EIT using all-dielectric silicon-based metasurfaces. Due to extremely low absorption loss and coherent interaction of neighbouring meta-atoms, a Q-factor of 483 is observed, leading to a refractive index sensor with a figure-of-merit of 103. Furthermore, we show that the dielectric metasurfaces can be engineered to confine the optical field in either the silicon resonator or the environment, allowing one to tailor light–matter interaction at the nanoscale.
Electromagnetically induced transparency (EIT) is a concept originally observed in atomic physics and arises due to quantum interference, resulting in a narrowband transparency window for light propagating through an originally opaque medium1. This concept was later extended to classical optical systems using plasmonic metamaterials2,3,4,5,6,7,8,9,10, among others11,12, allowing experimental implementation with incoherent light and operation at room temperature. The transparent and highly dispersive nature of EIT offers a potential solution to the long-standing issue of loss in metamaterials as well as the creation of ultra-high-quality-factor (Q-factor) resonances, which are critical for realizing low-loss slow-light devices2,3,6,10, optical sensors13,14 and enhancing nonlinear interactions15.
The classical analogue of EIT in plasmonic metamaterials relies on a Fano-type interference16,17 between a broadband ‘bright’-mode resonator, which is accessible from free space, and a narrowband ‘dark’ mode resonator, which is less-accessible, or inaccessible, from free space. If these two resonances are brought in close proximity in both the spatial and frequency domains, they can interfere resulting in an extremely narrow reflection or transmission window. Due to the low radiative loss of the dark mode, the Fano resonance can be extremely sharp, resulting in complete transmission, analogous to EIT2,3,4,5,6,7,8,9,10, or complete reflection13, from the sample across a very narrow bandwidth. However, the main limitation of metal-based Fano-resonant systems is the large non-radiative loss due to ohmic damping, which limits the achievable Q-factor17 to <~10.
High-refractive-index dielectric particles offer a potential solution to the issue of material (non-radiative) loss. Such particles exhibit magnetic and electric dipole, and higher order, Mie resonances while suffering from minimal absorption loss, provided the illumination energy is sub-bandgap18,19,20,21,22. For instance, dielectric Fano-resonant structures based on oligomer antennae23, silicon (Si) nanostripe24 and asymmetric cut-wire metamaterials25,26 have been demonstrated with Q-factors up to 127.
In this article, we describe the development of Si-based metasurfaces possessing sharp EIT-like resonances with a Q-factor of 483 in the near-infrared regime. The high-Q resonance is accomplished by employing Fano-resonant unit cells in which both radiative and non-radiative damping are minimized through coherent interaction among the resonators combined with the reduction of absorption loss. Combining the narrow resonance linewidth with strong near-field confinement, we demonstrate an optical refractive index sensor with a figure-of-merit (FOM) of 103. In addition, we demonstrate unit-cell designs consisting of double-gap split-ring resonators that possess narrow feed-gaps in which the electric field can be further enhanced in the surrounding medium, allowing interaction with emitters such as quantum dots.
Design and characterization
The schematic of the designed dielectric metasurface is shown in Fig. 1a. The structure is formed from a periodic lattice made of a rectangular bar resonator and a ring resonator, both formed from Si. The rectangular bar resonator serves as an electric dipole antenna, which couples strongly to free-space excitation with the incident E-field oriented along the x axis. The collective oscillations of the bar resonators form the ‘bright’ mode resonance. The ring supports a magnetic dipole mode wherein the electric field is directed along the azimuthal direction, rotating around the ring’s axis. The magnetic dipole mode in the ring cannot be directly excited by light at normal incidence, as the magnetic arm of the incident wave is perpendicular to the dipole axis; however, it can couple to the bright-mode bar resonator. Furthermore, the ring resonators interact through near-field coupling, resulting in collective oscillation of the resonators and suppression of radiative loss, forming the ‘dark’ mode of the system.
The interference between the collective bright and dark modes form a typical 3-level Fano-resonant system17, as illustrated in Fig. 1b. The response of the dielectric metasurface is similar to the collective modes found in asymmetric double-gap split-ring resonators, in which the asymmetry in the rings yields a finite electric dipole moment that can couple the out-of-plane magnetic dipole mode to free space27,28,29,30,31,32. In our case, coupling to free space is provided by the bright-mode resonators, which are placed in close proximity to the symmetric dark-mode resonators. Numerical simulations of the structure were carried out using commercially available software (CST Microwave Studio) using the finite-element frequency-domain solver (see Methods). The simulated transmittance, reflectance and absorption spectra of the designed structure are shown in Fig. 1c, where a distinct EIT-like peak can be observed at a wavelength of 1,376 nm. In these simulations, the resonators are sitting on a quartz substrate and embedded in a medium with a refractive index of n=1.44, matching the experiments described below. We have also used the dielectric function of Si as determined using ellipsometry and assumed an infinitely large array, resulting in a Q-factor that reaches 1,176 (see Methods for details on the extraction of the Q-factor). Furthermore, the peak of the transparency window approaches unity, demonstrating the potential to realize highly dispersive, yet lossless, ‘slow-light’ devices.
The designed structure was fabricated by starting with a 110-nm-thick polycrystalline Si (refractive index n=3.7)-thin film deposited on a quartz (SiO2) (n=1.48) wafer. The structure was patterned using electron-beam lithography (EBL) for mask formation followed by reactive-ion etching (RIE). A scanning electron microscope (SEM) image of a fabricated sample is shown in Fig. 1d,e. Before optical measurements, the resonator array was immersed in a refractive-index-matching oil (n=1.44) within a polydimethylsiloxane flow cell (see Methods for details). The experimentally measured transmittance, reflectance and absorption spectra, plotted in Fig. 1f, were acquired by illuminating the sample with normal-incident white light with the electric field oriented along the long axis of the bar resonator. A peak transmittance of 82% was observed at a wavelength of 1,371 nm with a Q-factor of 483, as determined by fitting the dark-mode resonance to a Fano line shape (see Methods and Supplementary Fig. 1). The shape of the measured spectra have good agreement with the simulation, although the Q-factor and peak transmittance are reduced. This is most likely due to imperfections within the fabricated sample, which introduce scattering loss and break coherence among the resonators. The role of coherence will be further addressed below. Furthermore, additional loss in the Si arising from surface states created during reactive-ion etching leads to slightly increased absorption in the array compared with theory. It should also be noted that the use of index-matching oil is not needed to achieve such high Q-factors. Designs comprised of the resonators placed on a quartz substrate and surrounded by air are presented in Supplementary Fig. 2; Supplementary Note 1.
The response of the metasurface can be qualitatively understood by applying the widely used coupled harmonic oscillator model33,34, described by the following equations,
where x1 and x2 represent the amplitudes of the collective modes supported by oscillators 1 (bright mode) and 2 (dark mode), respectively. γ1 and γ2 are the damping rates, given by γ=γR+γNR where γR and γNR are the radiative and non-radiative decay rates, respectively. ω0 is the central resonant frequency of oscillator 1, δ is the detuning of resonance frequency of oscillator 1 and 2 and g is the bright-mode dipole-coupling strength to the incident electric field E0. κ is the coupling coefficient between oscillators 1 and 2 and given the close proximity of the resonators, it should be considered an effective coupling coefficient that takes into account interaction between the bright-mode atom and its two nearest neighbours.
Of particular interest is the value of γ2 that reflects the damping of the collective dark mode and plays a large role in dictating the linewidth of the EIT-like resonance. The radiative damping term, γR2, is minimized due to the collective oscillations of the array, mediated by near-field coupling between the unit cells. One consequence of utilizing collective modes is that the value of γR2 is inversely proportional to the size of the array due to the fact that the discontinuity at the edges of the array allows for light leakage to free space27,28. While collective modes have been utilized in past demonstrations of plasmonic EIT metamaterials to realize extremely small γR2 values, the Q-factors have intrinsically been limited by the ohmic loss in the metal. By replacing the resonator constituents with lossless dielectrics, the non-radiative damping term γNR2 can also be minimized, resulting in the large increase in the Q-factor and peak transmittance.
Equally important is the role of the coupling coefficient, κ, in realizing a high-Q-factor resonance for this system. It has previously been shown that the slope of dispersion is inversely proportional to κ2 (ref. 2). In the limit of γ2→0, reduction of κ will result in a monotonic increase of the Q-factor until κ=0 is reached, at which point the Fano resonance will vanish, leaving only the bright-mode resonance. In our system, the magnetic field from the bright-mode resonator is inducing the dark-mode resonance, as illustrated in Fig. 2a. Thus, as the spacing between the resonators (g1) is increased the coupling coefficient decreases, resulting in an increase in the Q-factor (Fig. 2c,d) and strong magnetic and electric field localization (Fig. 2b). At a spacing of g1=74 nm, the Q-factor reaches a value of ~30,000 which is indicative of the fact that both radiative and non-radiative losses in the system are minimal, resulting in a situation wherein γ2~0. However, losses in the Si primarily arising from surface states created during etching will ultimately limit the Q-factor, as has been demonstrated in microcavities35. Such losses are not included in these calculations. It is also important to realize that the bright-mode resonator is also interacting with the dark-mode resonator in the adjacent unit cell (D2), inducing a magnetic field that is 180° out of phase with the excitation from the bright-mode resonator within its own unit cell. Therefore, when the gap between the bright-mode resonator and adjacent dark-mode resonators are equal (g1=75 nm, Δ=g2−g1=0) the fields destructively interfere and κ goes to zero, resulting in elimination of the Fano resonance, as can be observed in Fig. 2c and in the magnetic and electric field profiles in Fig. 2b.
At the transmission peak the energy in the array is concentrated in the collective dark mode with the magnetic dipoles in each of the split-rings oscillating coherently as shown in Fig. 3a. The array size thus becomes an important factor in the overall Q-factor of the metasurface due to the fact that lattice perturbations at the array’s edge break the coherence27,28, leading to strong scattering of light into free space and broadening of the resonance peak. To characterize this effect, we fabricated arrays of five different sizes, consisting of 400 to 90,000 unit cells (SEM image of the test samples are shown in Fig. 3b). In the measurement, we used a × 5 objective for illumination and a × 50 objective for collection with an aperture in the conjugate image plane on the transmission side to confine the collection area to 15 μm × 15 μm. The measured spectra are shown in Fig. 3c and we observe that the Q-factor increases with increasing array size, saturating as we approach 90,000 unit cells, as is shown in Fig. 3d. The saturation of the Q-factor indicates the limit imposed by both incoherent radiative loss arising from inhomogeneities and non-radiative loss arising due to finite absorption in the Si. As expected, the required unit-cell number needed to achieve spectral convergence is larger than that reported in coherent plasmonic metamaterials due to the reduction in the non-radiative component.
Photonic crystal cavities possessing higher Q-factors have been reported36, although they lack the spatial homogeneity present in the metasurface outlined here. Diffractive-guided mode structures can also exhibit extremely high Q-factors37, although in our case we have the additional freedom of engineering the local field enhancement through modification of the dark-mode resonators. For instance, this can be done by placing symmetric feed-gaps in the resonator forming a double-gap split-ring, as shown in Fig. 4a. In this case, the azimuthally oriented field located in the gap is enhanced by a factor of εd/εs (Fig. 4b), where εd and εs are the permittivities of the resonator and surrounding medium, respectively. For the design depicted in Fig. 4, this results in an electric field enhancement of 44 in the gap region. Having the advantages of both a sharp spectral response and a strongly enhanced field in the surrounding substance allows the metasurface to serve as an ideal platform for enhancing interaction with the surrounding medium. To investigate the response of such structures, samples were made using the same processes as described above and measured in n=1.44 index-matching oil. An SEM image of the sample is shown in Fig. 4c. The simulated and experimentally measured transmittance curves are shown in Fig. 4d and result in theoretical and experimentally measured Q-factors of 374 and 129, respectively. The lower theoretical Q-factor, compared with the ring geometry, is due to the fact that the electric fields are not equal in the two arms of the split-ring due to the asymmetry of the unit cell. This results in radiation loss to free space as the electric dipole moments do not fully cancel one another. The decrease in the experimental Q-factor, compared with theory, is attributed to more imperfections in the sample arising from the inclusion of the gaps, ultimately resulting in increased scattering from the structure. Single-gap split-ring dark-mode resonators were also explored and are described in Supplementary Fig. 3; Supplementary Note 2. More details regarding the field profiles of each of the metasurface variations can be found in Supplementary Fig. 4.
Due to their narrow linewidths, one interesting application of these metasurfaces is optical sensing. Optically resonant sensors are characterized by both the linewidth of the resonance (Δλ) as well as the shift in the resonance per refractive-index-unit change (S). These two values comprise the FOM that is given by FOM=S/Δλ (ref. 38). The highest-demonstrated FOMs for Fano-resonant-localized surface plasmon resonance (LSPR) sensors are on the order of 20 (refs 13, 38, 39). Here, we examine the FOM of the ring-resonator metasurfaces and to further increase the sensitivity of our metasurface to local index changes, we etched a 100-nm-tall quartz pillar below the Si resonators such that the field overlap in the surrounding dielectric can be further promoted, as illustrated in Fig. 5a. The transmittance spectra of the metasurface when immersed in oil with different refractive indices, from 1.40 to 1.44, are presented in Fig. 5b, and it can be seen that a substantial movement in the peak position is realized despite the small index change. A linear fit of the shift in the resonance peak (Fig. 5c) leads to a sensitivity of S=289 nm RIU−1, which is comparable, but slightly lower, than the best Fano-resonant plasmonic sensors. The slight decrease in sensitivity is due to the fact that the index contrast, and corresponding field enhancement, at the dielectric metasurface–oil interface is still lower than that found in plasmonic structures. However, when combining the sensitivity with an average resonance peak linewidth Δλ of only 2.8 nm, we arrive at an FOM of 103, which far exceeds the current record for Fano-resonant LSPR sensors. With further optimization of fabrication and more stringent control of the resonator coupling, FOMs on the order of 1,000 should be within reach. We also characterized the performance of the double-gap split-ring metasurface, finding it has a higher sensitivity (S=379 nm RIU−1) due to the increased modal overlap with the surrounding material. However, the experimentally measured FOM is reduced to 37 due to the broader linewidth. More details can be found in Supplementary Fig. 5; Supplementary Note 3.
In conclusion, dielectric metasurfaces can be used to significantly improve upon the performance of their plasmonic counterparts in mimicking EIT due to their greatly reduced absorption loss, resulting in sensing FOMs that far exceed previously demonstrated LSPR sensors. With proper design, such metasurfaces can also confine the optical field to nanoscale regions, opening the possibility of using such metasurfaces for a wide range of applications including bio/chemical sensing, enhancing emission rates, optical modulation and low-loss slow-light devices.
The numerical simulations (transmittance/reflectance and field distributions) presented in the manuscript were carried out using a commercially available software (CST Microwave Studio 2013) using the finite-element frequency-domain solver with periodic boundary conditions for each unit cell. The dimensions and material properties of the metasurface and the background are specified in the main text. Both normal-incident TE00 (polarization along the long axis of the bar antenna) and TM00 (polarization perpendicular to the long axis of the bar antenna) modes were defined at the incident and receiving ports to ensure that any polarization conversion is accounted for. At least 10 mesh steps per wavelength were used to ensure the accuracy of the calculated results. In addition, we reproduced the results using another commercially available full-wave simulation tool (Lumerical) using a finite-difference time-domain solver.
We used a Fano model to extract the Q-factor of the EIT resonance from the dielectric metasurface. The experimentally measured transmittance Texp was fitted to a Fano line shape given by , where a1, a2 and b are constant real numbers; ω0 is the central resonant frequency; γ is the overall damping rate of the resonance. The experimental Q-factor was then determined by Q=(ω0/2γ). The fit was performed over the wavelength range from 1,367 to 1,380 nm as this model only encompasses the Fano line shape and does not include the fit to the background resonance provided by the bright mode. We used a fitting method identical to the one used in a recent demonstration of Si-based chiral metasurface25, therefore rendering the reported Q-factors in both cases comparable. The fit is shown in Supplementary Fig. 1.
Polycrystalline Si was chosen as the resonator material due to its high index and small absorption in the near-infrared frequencies. The Si was deposited on a 4-inch quartz wafer using a low-pressure chemical vapour deposition horizontal tube furnace. The metasurfaces were created by a sequential process of EBL, mask deposition, lift-off and RIE. In the EBL process, we employed a 10-nm chromium charge-dissipation layer on top of the PMMA resist. The total pattern size was ~225 μm × 225 μm, written using a JEOL 9300FS 100 kV EBL tool. A fluorine-based inductively coupled plasma RIE recipe involving C4F8, SF6, O2 and Ar gas flows was used to etch the poly-Si layer creating the metasurface layer. Polydimethylsiloxane flow cells were used to immerse the metasurface in the refractive-index-matching oils (Cargille Labs) for all the spectroscopy and sensing measurements. The samples were washed thoroughly after each measurement with isopropyl alcohol followed by placing them in a vacuumed desiccator for 1 h to ensure that no residual oil was left after each measurement.
A custom-built free-space infrared microscope was used to measure the transmittance, reflectance and absorption spectra of the metasurfaces. Light from a tungsten/halogen lamp was focused through a long-working distance objective (Mitutoyo, × 5, 0.14 numerical aperture) with the numerical aperture of the objective further cut down to 0.025 by an aperture at its back focal plane to restrict the incident angle to near-normal. The transmittance spectrum (T) was normalized with the transmittance of the white light through an unpatterned quartz substrate. The reflectance spectrum (R) was normalized to reflectance of a gold mirror, and the absorption of the sample is determined as A=1−T−R.
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This work was funded by the Office of Naval Research under programmes N00014-12-1-0571 and N00014-14-1-0475. A portion of this research was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. A portion of this work was also performed at the Vanderbilt Institute of Nanoscale Science and Engineering, we thank the staff for their support.
The authors declare no competing financial interests.
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Yang, Y., Kravchenko, I., Briggs, D. et al. All-dielectric metasurface analogue of electromagnetically induced transparency. Nat Commun 5, 5753 (2014). https://doi.org/10.1038/ncomms6753
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