For a decade and more, considerable effort has been focused on the engineering of metamaterials - the advancement of fundamental theory and of computational and fabrication techniques [1, 2] - to achieve high-quality resonant responses at technologically-relevant near-infrared and visible wavelengths for applications ranging from negative refraction [3–6] to photovoltaic power generation, electro-/all-optical signal modulation/switching, and biosensing [7–11]. However, the vast majority of metamaterial structures employed here comprise arrays of sub-wavelength metallic (typically split-ring) resonators. These suffer from high inherent energy dissipation due to resistive losses in the metal, especially in the near-infrared to visible range, which severely compromise optical properties and limit potential applications. Numerous efforts have been made to incorporate gain media into metamaterials for loss compensation [12–14] but extremely high pump powers may be needed to compensate the large losses and would unavoidably introduce significant noise and heat. Consequently, there has been growing interest in the development and application of low loss alternatives to metals as plasmonic media [15].

Recently, the Mie resonances of dielectric particles have been proposed as a platform for the engineering of magnetic resonances [16–21], and on this basis magnetic responses have been experimentally realized in metamaterials and photonic crystals fabricated from high permittivity dielectrics such as titanium dioxide and germanium, at microwave and terahertz frequencies [22–24] and more recently in the infrared/optical range [25–27]. Here we experimentally demonstrate another mechanism via which strong visible and near-infrared resonances can be achieved in purely dielectric metamaterials: A magnetic resonance akin to the well-known `trapped mode' of metallic asymmetric split ring (ASR) structures [28] is realized through a coupling between closely spaced, dissimilar dielectric nano-bars within the metamaterial unit cell [29]. These trapped modes are characterized by anti-phased oscillation in the two arms of the unit cell of conduction current / surface plasmon-polariton excitations in metals, or displacement currents in dielectric structures as illustrated schematically in Fig. 1. The scattered electromagnetic fields generated by such current configurations are very weak, with both electric and magnetic dipole radiation components being cancelled via destructive interference. This dramatically reduces coupling to free space and therefore radiation losses. Excitation of such modes relies critically on structural symmetry breaking.

 

Fig. 1 Analogous trapped mode resonances in metallic (left) and dielectric (right) metamaterials (a single sub-wavelength, asymmetric unit resonator of each type being shown) based on the anti-phase oscillation of conduction or displacement currents and consequential excitation of out-of-plane magnetic moments.

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Low-loss media with high refractive indices must be used as a platform for the assembly of dielectric metamaterials in order to minimize absorption losses while ensuring that the metamaterial unit cells are effectively of sub-wavelength size to exclude diffraction effects. Semiconductors such as silicon, germanium, and tellurium are among the best candidates due to their high refractive indices (>3) and relatively low absorption in the optical range. The present study employs silicon, which has a bandgap of 1.1 eV, a refractive index of around 3.5 and low absorption in the near-IR telecommunications wavelength range (see Fig. 2). 160 nm thick amorphous films are deposited by plasma-enhanced chemical vapor deposition (PECVD) at 250°C on glass substrates.

 

Fig. 2 All-dielectric Photonic Metamaterial: (a) Dimensional schematic of a unit cell of an all-dielectric metamaterial, comprising asymmetric silicon nano-bar pairs on silica, which exhibits sharp visible to near-IR `trapped mode' magnetic resonances [h = 160, w = 300, L₁ = 650, L₂ = 750 nm]. The inset to part (b) shows a scanning electron microscope image of the experimental implementation of this design on a 160 nm amorphous silicon film (viewed at an oblique angle to the surface normal; full array size 30 μm × 30 μm). (b) Refractive index of unstructured PECVD amorphous silicon obtained via spectroscopic ellipsometry.

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Dielectric metamaterial structures are then fabricated on these films by focused ion beam (FIB) milling on the basis of the 900 nm square unit cell design illustrated schematically in Fig. 2(a). Each cell contains a dissimilar pair of silicon bars with the same height (the 160 nm thickness of the Si film) and width (300 nm) but different lengths (nominally 650 and 750 nm). The ideal rectangular geometry of Fig. 2(a) is not translated flawlessly to experimental samples, such as shown inset to Fig. 2(b), but the observed imperfections are not found to compromise the essential nature of the metamaterial’s resonant response.

Figure 3 shows measured normal-incidence optical transmission, reflection and absorption spectra for the metamaterial sample introduced in Fig. 2. A pronounced resonance is seen at a wavelength of around 1700 nm for incident light polarized (i.e. with electric field) parallel to the long (x) axes of the silicon nano-bars (solid lines in Figs. 3(a)-3(c)). For y-polarized light (i.e. incident with electric field perpendicular to the long axes of the dielectric bars), the sample’s background level of transmission is somewhat higher, reflection somewhat lower and absorption slightly lower than for the x-polarization, but no resonance features are observed within the measured spectral range. For comparison, x-polarization data are also presented for a ‘symmetric’ control sample in which each unit cell contains two identical 700 nm long silicon bars (160 nm height, 300 nm width and 900 nm array period as for the asymmetric sample). The transmission, reflection and absorption levels here are broadly well-matched to those of the asymmetric sample for the same polarization, but the resonance features are, in keeping with the trapped mode’s essential reliance on structural asymmetry, completely absent.

 

Fig. 3 Near-IR trapped mode resonance in an all-dielectric metamaterial. Absorption (a), reflection (b) and transmission (c) spectra, from microspectrophotometry measurements, for the silicon asymmetric nano-bar metamaterial structure shown in Fig. 2(b) under normally-incident illumination polarized in the x- and y-directions (respectively parallel and perpendicular to the long axes of the bars; plotted with solid and dashed lines), and for a symmetric control sample (all nano-bars of equal dimensions – dotted lines) under x-polarized light.

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Important insight into the nature and origins of the resonance is provided by full-wave electromagnetic numerical simulations (performed using COMSOL MultiPhysics). Figure 4(a) presents simulated spectra for the sample design shown in Fig. 2(a) for normally incident x-polarized light. The calculations assume a silicon refractive index n_Si of 3.5, a substrate index of 1.46, zero absorption in both cases, and ideal rectangular cuboid Si bar shapes. As such the resonance features in the simulated spectra are very sharp, but otherwise (i.e. in terms of the trends in spectral dispersion) correlate well with the experimental data presented in Fig. 3. Figure 2(b) illustrates that the zero-loss assumption is reasonable for an amorphous Si film in the wavelength range under consideration, and the glass substrate can also be considered lossless in this range. The damping of spectral resonance features observed in experiment is therefore attributed to manufacturing imperfections, specifically surface roughness (which introduces scattering losses), gallium contamination from the FIB milling process (introducing absorption), and cell-to-cell inhomogeneity across the array. Unlike their metallic (plasmonic) counterparts, dielectric metamaterials are largely insensitive to geometric complications at the scale of individual (sub-unit cell) elements [29], and indeed, in the present case modeling confirms that trapezoidal deviations from the ideal rectangular cuboid bar shape have little impact on resonance quality.

 

Fig. 4 Numerical modeling of near-IR dielectric metamaterials. (a) Simulated normal incidence x-polarization transmission and reflection spectra for a rectilinear metamaterial silicon-on-silica geometry based on the experimental sample design parameters shown in Fig. 2(a). (b) Magnitude of the x-component of electric field across an asymmetric Si nano-bar unit cell of the metamaterial structure at the resonance wavelength λ_R = 1644 nm, presented for the xy plane bisecting the nano-bars 80 nm above the substrate surface, overlaid with arrows indicating direction and magnitude of displacement current. (c) Corresponding magnitude of the x-component of displacement current presented for the yz symmetry plane of the unit cell, overlaid with arrows indicating direction and magnitude of magnetic field.

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Figures 4(b) and 4(c) show cross-sections of the electric field distribution within a nano-bar pair unit cell of the metamaterial structure at the resonance wavelength. The two bars are excited in anti-phase, with electric polarizations of almost equal amplitude, and thereby display a magnetic mode resonance through electric coupling [30] – anti-parallel displacement currents in the bars, indicated by the arrows overlaid in Fig. 4(b), generate an alternating ‘antiferromagnetic’ arrangement of out-of-plane magnetic moments, illustrated by the magnetic field arrows overlaid in Fig. 4(c). Similar resonances have been extensively studied in metallic planar metamaterials with a broken structural symmetry [28, 31].

As in metallic metamaterials composed of asymmetric split rings [28], the quality of trapped-mode resonances in dielectric metamaterials can be increased by reducing the asymmetry of the resonant elements. However, as the radiation losses are very low, losses are the limiting quantity on achievable quality factor Q ( = λ_r/Δλ where λ_r is the resonance frequency and Δλ is the half-maximum linewidth) in such metamaterials. In Fig. 4(a), the quality factor of the trapped mode resonance is approximately 230. Figure 5 illustrates how this value decreases as losses, introduced via non-zero values for the imaginary part of the assumed silicon refractive index, increase.

 

Fig. 5 The impact of absorption loss and asymmetry on dielectric metamaterial trapped mode resonance quality. (a) Simulated transmission, reflection and absorption spectra for the same metamaterial geometry [and the same x-polarized normally-incident illumination conditions] employed in Fig. 4 with non-zero values of the silicon absorption coefficient k: solid lines assume n_Si = 3.5 + 0.02i; dashed lines n_Si = 3.5 + 0.1i. (b) Resonance quality factor Q as a function of unit cell asymmetry α (defined as ΔL/L₂ where ΔL is the difference between nano-bar lengths L₁ and L₂; L₂ being the larger of the two) for zero and non-zero absorption levels as labeled. The inset shows Q as a function of absorption coefficient k at α = 0.133 (L_{1, 2} = 650, 750 nm).

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Remarkably, for n_Si = 3.5 + 0.02i the resonance retains a quality factor of ~91 and even at n_Si = 3.5 + 0.1i, Q ~30 - a value that would be considered good for a metal ASR metamaterial in the VIS/NIR wavelength range [31]. Indeed, based on the measured parameters for PECVD films presented in Fig. 2(b) a silicon metamaterial resonant at λ = 700 nm, where n_Si = 3.87 + 0.006i, may present trapped mode resonances with Q values approaching 100. The experimental metamaterial sample presented here has a resonance quality factor of ~15 but crucially this is limited not by the intrinsic properties of the medium from which it is made (as is the case in metallic structures at visible and near-infrared wavelengths) but by the manufacturing process (as described above). Thus, with improvements in fabrication technique, visible and near-IR resonances with quality factors much higher than those typically achieved in conventional metallic metamaterials or plasmonic systems may be realized in dielectric structures, even in the presence of non-trivial losses.

As a point of interest, while the metamaterial considered here is not designed for the purpose of providing a strong magnetic response, i.e. a magnetic dipolar moment aligned with the incident magnetic field, the effective relative permittivity ϵ and permeability μ of such periodic arrays are intrinsically connected [32, 33] and a permittivity resonance is necessarily accompanied by a permeability anti-resonance as shown in Fig. 6.

 

Fig. 6 Silicon metamaterial near-IR magnetic response. (a) Spectral dispersion of effective permittivity ϵ and permeability μ derived from simulated scattering data for the zero-loss asymmetric metamaterial model structure of Fig. 2(a) under normally incident x-polarized illumination [N.B. the amplitude of permeability is multiplied here by a factor of ten for visibility on the same scale as permittivity].

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In summary, we have experimentally demonstrated a novel form of dielectric metamaterial composed of asymmetric silicon nano-bar pairs, which exhibits a sharp resonance in the near-IR wavelength range. The magnetic, trapped-mode nature of the resonance is illustrated in numerical simulations of electromagnetic response: The resonance is seen to depend critically on the existence of asymmetry between the two dielectric bars within the metamaterial unit cell and, while manufacturing imperfections (losses and inhomogeneous broadening) limit the resonance quality factor achieved in current experiential samples to values of order 15, simulations illustrate the potential for realization of VIS/NIR metamaterial resonances with Q-factors of several hundred using the silicon platform. Such structures open alternative paths to low-loss magnetism at optical frequencies and present new opportunities for controlling the output of quantum emitters [34, 35], realizing lasing spasers [36], and developing new kinds of opto-mechanically driven active metamaterials [37].