A novel plasmonic metamaterial consisting of the solid (bar) and the inverse (slot) compound metallic nanostructure for electromagnetically induced absorption (EIA) is proposed in this paper, which is demonstrated to achieve an ultra-narrow absorption peak with the linewidth less than 8 nm and the absorptivity exceeding 97% at optical frequencies. This is attributed to the plasmonic EIA resonance arising from the efficient coupling between the magnetic response of the slot (dark mode) and the electric resonance of the bar (bright mode). To the best of our knowledge, this is the first time that the plasmonic EIA is used to realize the narrow-band perfect absorbers. The underlying physics are revealed by applying the two-coupled-oscillator model. The near-perfect-absorption resonance also causes an enhancement of about 50 times in H-field and about 130 times in E-field within the slots. Such absorber possesses potential for applications in filter, thermal emitter, surface enhanced Raman scattering, sensing and nonlinear optics.
© 2015 Optical Society of America
Resonant plasmonic or metamaterial absorbers have attracted enormous attention due to their importance in science and practical applications including absorption filters, thermal emitters, thermophotovoltaics and biosensors. In the past decade, many metamaterial absorbers based on different physical mechanisms have been demonstrated theoretically and experimentally [1–8]. For example, by manipulating the magnetic and the electric resonance independently, it is possible to match the effective impedance of the metamaterials to that of incident medium, thus minimizing the reflection to zero . Besides, the triple-layer metal-insulator-metal film stack is another common and standard design in metamaterial absorbers, in which by tailoring the size and the periodicity of the top metal nanostructures and the dielectric spacer thickness, incident light gets absorbed at the resonant wavelengths due to the strong interaction between localized and delocalized surface plasmons [5, 6]. However, owing to the strongly radiative damping and the intrinsic metal loss, the bandwidths of absorption resonance in the plasmonic metamaterials are always broad (> 40 nm). This severely hampers its applications in filters, sensors and thermal radiation tailoring, where a sharp and pronounced narrow-band spectral response is highly desired.
In a different context, based on the constructive interference between a bright and a dark oscillator, a classical electromagnetically induced absorption (EIA) analog was demonstrated . Recently, Giessen et al. provided the first experimental demonstration  and then gave a systemically theoretical discussion  of the plasmonic analog of EIA in metamaterials by employing near- and far-field effects simultaneously. Subsequently, Tassin et al. developed a theoretical model of the two radiating oscillators for the plasmonic EIA effect . The EIA-like resonance in plasmonic metamaterials usually has a narrow linewidth accompanied with the enhanced absorbance. Narrow linewidth is attributed to the reduced radiative loss in dark resonator, and enhanced absorbance is due to constructive interference between the resonators. Thus, as far as its spectral feature, the plasmonic EIA resonance has the potential of realizing narrow-band absorbers if the absorbance can be enhanced to the value approximating unity by elaborately designing the nanostructures. However, up to now, only few studies are related to the plasmonic EIA [13, 14]. Moreover, the resonant absorbance is generally greater than 50% in previous work by utilizing the coupling of the purely electric resonances.
In this work, by utilizing the plasmonic EIA effect, an ultra-narrow absorption resonance with the linewidth less than 8 nm and the absorptivity exceeding 97% was demonstrated in a solid-inverse compound metamaterial. Both the simulations and the theoretical model of two-coupled-oscillator reveal that the EIA resonance arises from the efficient coupling between an electric dipole (bright mode) and a magnetic quadrupole (dark mode). Our finding provides a promising scheme for the realization of ultra-narrow perfect absorbers. Moreover, at the EIA resonance, the strong electromagnetic field “hot spots” are also obtained inside the slots. The proposed metamaterial thus suggests remarkable promising for applications in filters, thermal emitters, sensors, surface enhanced Raman scattering (SERS) and nonlinear optics.
2. Structure and simulation method
The electric and the magnetic field of an electromagnetic structure and its complement can be related intuitively by Babinet’s principle [15–17]. For example, it is well known that a metal bar supports an electric quadrupole mode with the electric and the magnetic field depicted in Fig. 1(a) (left) [18, 19]. According to Babinet’s principle, a magnetic quadrupole should be excited in its complement - a slot in a continuous metal film - by exchanging the role of the electric and the magnetic field, as depicted in Fig. 1(a) (right).
Inverse nanostructures are particularly interesting as they offer magnetic resonant modes not obtained easily in the solid nanostructures . Considering this point, we design a novel plasmonic EIA structure: a metal bar stacked above a metal film with a long slot (Figs. 1(b) and 1(c)). The bar and the slot in two function layers are oriented perpendicular to each other for efficient near-field coupling. Specifically, the top bar serves as a broad-linewidth dipole antenna (bright mode), which can be strongly coupled to free space. The bottom slot acts as a non-radiative magnetic quadrupole antenna (dark mode), which is only excited by the dipole antenna via both near- and far-field interactions. The lateral displacement of the top bar with respect to the symmetry axis of the slot is defined as S. The vertical spacing between the two layers is defined as D. The periodic array of the structure is schematically given in Fig. 1(d). Such stacked metamaterial can be fabricated by a two-step electron-beam lithography process  or layer-by-layer stacking nanofabrication techniques [20, 21].
Numerical calculations were performed by finite element method (FEM) with commercial software (COMSOL Multiphysics). The computational domain contained a single unit cell, in which periodic boundaries were employed for four lateral boundaries, and perfectly matched layers were applied in propagation directions to eliminate nonphysical boundary reflections. The unit cell was meshed with tetrahedral elements and local mesh refinement with extremely fine was applied around the metal and slot regions. The frequency-dependent permittivity of Silver was described by Drude model with the plasma frequency ωp = 1.366 × 1016 rad/s, and the damping constant ωγ = 3.07 × 1013 1/s [22, 23]. The surrounding material was assumed to be air for simplification of the calculations. A plane wave with the polarization along the X-axis normally irradiated the stacked metamaterial (Z-axis).
3. Results and discussions
3.1 Ultra-narrow-band perfect absorption based on EIA-like effects
As discussed in previous work [10, 11], a significant difference in absorption between a bright and a dark mode is beneficial for producing a pronounced plasmonic EIA resonance. Thus, to improve the spectral observability of the effect, it is advisable to reduce the absorption of the bar with respect to that of the slot. This can be accomplished by increasing the bar’s width (W1) and height (h1), because the optical response of small nanoparticles is usually dominated by the absorption, whereas the response of larger nanoparticles is mostly determined by the scattering . Similarly, the absorption of the slot can be increased by reducing the slot cross section, while preserving its spectral position by adjusting its length (L2). Therefore, the geometrical parameters of the two antennas have been optimized to be L1 × W1 × h1 = 168 × 60 × 30 nm3, and L2 × W2 × h2 = 360 × 40 × 20 nm3. It is found in Fig. 2 that the bar array exhibits a broad-linewidth dipole resonance with a relatively low absorbance (less than 20%) as the plane wave is at normal incidence (black). For the slot array, there is no response in the considered spectral range at normal incidence of plane wave (red). But, for 20° off-normal incidence, a sharp peak with a relatively high absorbance (50%) appears at the centre of the dipole resonance corresponding to the frequency of 420 THz (blue). This is attributed to the excitation of magnetic quadrupole of the slot by phase retardation, which is inaccessible for normally incident plane wave (dark mode). Thus, a narrow linewidth is observed due to the nearly suppression of radiative loss.
When arranged in close proximity to each other, the two antennas are coupled strongly. The lateral displacement S, indicating the structural asymmetry relative to the polarization of excitation light, determines the near-field coupling between the two antennas [25, 26]. The simulated spectra of the compound structure for different S are given in Fig. 3. The vertical spacing is fixed at D = 175 nm. At S = 0, only a broad dipolar absorption arising from the bar is observed at 420 THz and the underlying slot does not contribute since the two elements are not coupled to each other at the absence of asymmetry (See Fig. 3(b)). When the symmetry is broken, a sharp EIA-like absorption peak, arising from the coupling between the bar and the slot, emerges on top of the center of the broad dipolar absorption at S = 15 nm. As increasing S, the peak grows in strength gradually and becomes more and more prominent owing to the increased near-field coupling. When S reaches 70 nm, the peak absorbance is improved to a nearly perfect value (exceeding 97%), corresponding to an enhancement of about 4.85-fold as compared to 20% of the uncoupled case (S = 0). The peak linewidth is approximately 7.5 nm by calculating the full width at its half-maximum height. With a further increase of S, however, the absorbance is decreased to about 93% at S = 90 nm, and meanwhile the peak linewidth is broadened obviously.
To reveal the physics of the near-unity absorption achieved in the proposed structure, we calculated the absorption of other similar structure by replacing the bottom slot with a flat metallic film and keeping D = 175 nm. It is found that there exists only a dipolar absorption with the maximum absorptivity of about 19.5%, much smaller than 97.8% of the proposed EIA-like structure (not shown). We also calculated the absorption of other similar structure by replacing the bottom slot with a long metal bar (See the inset of Fig. 3(c)), in which the plasmonic EIA occurs via the coupling of the electric dipole (bright mode) and the electric quadrupole (dark mode), instead of the coupling of the electric and the magnetic mode. The vertical spacing and parameters of the long metal bar have been optimized to be D' = 150 nm and L2' × W2' × h2' = 330 × 40 × 20 nm3, and other parameters and the excitation ways are not changed. It is found in Fig. 3(c) that the maximum absorbance of the EIA-like resonance in the structure, being only about 49%, appears at S' = 60 nm. These indicate that the metal film with slots supporting the magnetic mode in our proposed metamaterial plays a key element for the near- perfect-absorption resonance.
It can be explained qualitatively from two aspects in the following. First, the bottom metal film with slots may contribute significantly to the absorption as considering the blocking of the transmission channel. As shown in Fig. 3(a), the transmittance is always very small in the considered spectral range. A little rise at high frequencies is attributed to stronger penetration capability of the shorter-wavelength wave . On the other hand, the efficient coupling (including both near- and far-field interactions) between the electric (bright) and the magnetic (dark) mode suppresses the reflection into the absorption. It can be seen in Fig. 3(a) that the shallow dip of the reflectance becomes deeper and deeper with enlarging S owing to increased near-field coupling. When S is increased to 70 nm, the dip reflectance is reduced to a value approaching zero. As a result, the absorption of the system is increased dramatically to a near-unity value.
3.2 Theoretical model: two coupled oscillators
To provide more insights into the plasmonic EIA behavior, we utilize the model of two coupled oscillators (TCO) to reproduce our simulation results . The bright antenna (bar) is represented by oscillator 1, which is driven by an applied field E(t) = E0exp(-iωt). The dark antenna (slot) is represented by oscillator 2, which is coupled to oscillator 1 via both near- and far-field interactions. So a complex coupling coefficient κexp(iφ) instead of a real quantity is used, where φ is the phase shift between two oscillators induced by the retardation effect due to the coupling distance in propagation direction. The amplitudes x1(t) and x2(t) of oscillator 1 and 2 satisfy the coupled differential equation:Eq. (1), the system absorption is obtained by calculating the dissipated energy as follows:
If assuming both oscillators have zero detuning frequencies (ω1 = ω2 = ω0), we can rewrite Eq. (2) to the second-order approximation around the resonant frequency ω0:
From Eq. (3), it is concluded that the interference term of exp(i2φ) plays an important role for the absorbance at the frequency of ω = ω0. Specifically, as the real part of the interference term has a positive value at 0 ≤ φ ≤ π/4, the absorbance at ω = ω0 is reduced as compared to the case of no coupling (κ = 0). On the contrary, the enhanced absorbance appears when the interference term produces a negative real part for π/4 ≤ φ ≤ π/2. The former corresponds to plasmonic electromagnetically induced transparency (EIT) , while the latter corresponds to the plasmonic EIA. Thus, depending on the coupling phase φ, the EIT- as well as the EIA-like behavior is achieved. Notice that the EIA-like resonance should be the most prominent at exactly φ = π/2.
We fit the simulated absorption spectra of Fig. 3(b) using Eq. (2) and present the results with solid circles in the same figure for a direct comparison. It is evident that the simulated curves are reproduced nearly perfectly by the fitted results. These parameters retrieved from the fits are selectively shown as a function of S in Fig. 4. As expected, the coupling amplitude k representing the near-field coupling is always increased with more structural asymmetry. However, when S is increased greater than 70 nm, k begins to decrease, resulting in the shrink of the absorbance at EIA-like resonance. As for the phase shift φ, it almost remains constant during this process because the coupling distance (D) is always unchanged. Importantly, φ is just around π/2, indicating the coupling distance is suitable for producing the most prominent EIA-like resonance according to Eq. (3). In addition, the fitted parameter γ2 is smaller than the γ1. This is already obvious from the simulated spectra in Fig. 2. Moreover, with the increase of S, γ2 increases successively, which s leads to the broadening of the EIA-like resonance. These quantitative results from TCO model further substantiate our expectations on the simulations.
3.3 Influence of the vertical spacing (D) on the spectral response
According to Eq. (3), the phase shift φ is a key role in determining the type of the interference between the two resonators. We thus calculate the absorption spectra of the system with different value of D in Fig. 5(a), by which one tune the coupling phase φ. The displacement S is fixed at 70 nm. For small D, a prominent dip emerges within a broad absorption background, carrying a typical feature of the plasmonic EIT. With the increase of D, the dip grows in strength successively and the symmetric plasmonic EIT spectral feature is reduced: the absorbance at the high-energy peak increases with respect to at the low-energy peak and both shift towards the central position. When D is increased to 175 nm, a sharp peak with high absorbance replaces the original dip and the spectral symmetry recovers again, indicating the characteristic of plasmonic EIA.
We fit the absorption spectra using Eq. (2) and present the results with solid circles in the same figure (Fig. 5(a)). The extracted phase φ from the fits is given in Fig. 5(b). Obviously, φ is increased with enlarging D, starting from 0 at D = 55 nm to approximately π/2 at D = 175 nm. At φ = 0, there is only near-field coupling and the real coupling coefficient yields an EIT-like resonance. With the increase of D, the far-field effect is introduced by the phase shift φ, resulting in the transition of spectrum from the plasmonic EIT to EIA. When φ is increased to π/2, the most pronounced plasmonic EIA resonance is achieved. Notice that a further increase of D, which not only breaks the condition of φ = π/2 but also weakens the near-field coupling (k), will lead to the decrease of the absorbance (not shown).
3.4 Giant electromagnetic field enhancements inside the slots
Plasmonic nanostructures that support narrow and strong absorption peaks generally have the ability to create dramatically enhanced electromagnetic fields . It is also demonstrated that the complementary structure of the solid nanoparticles with the developed magnetic moments offers the access to highly confined magnetic fields [30, 31]. Usually, the magnetic response of natural materials is quite weak due to the fact that the magnetic dipole transition probability is far smaller than the electric dipole transition at the optical frequencies . As a result, it is highly desirable to achieve a giant magnetic field enhancement in artificial metamaterials for developing the magnetic-based devices and improving magnetic nonlinearities. It is expected that the proposed metamaterial supporting a narrow resonance of near-perfect-absorption will produce highly confined magnetic fields inside the slots.
Before examining the field enhancements, let us at first calculate the z-component of E- and H-field to visualize the resonant nature of the two plasmon modes. The metamaterial with S = 70 nm and D = 175 nm is chosen. The fields are calculated at the frequency of 420 THz corresponding to the EIA-like resonance. Figure 6(a) shows that the metal bar exhibits a clear electric dipolar field distribution with the induced charges located at its two ends. Figure 6(b) indicates that the Hz distribution in the middle of the slot, with three nodes along the slot, is in accordance with the Ez distribution of the quadrupolar eigenmode of a metal bar , demonstrating the excitations of magnetic quadrupole. These near-field distributions provide an intuitive picture of the nature of original resonant modes.
Figures 6(c)-6(f) display the distributions of field enhancements of the metamaterial with S = 70 nm and D = 175 nm at 420THz in the Y-Z (Figs. 6(c) and 6(e)) and X-Y (Figs. 6(d) and 6(f)) planes. From Figs. 6(c) and 6(d), it can be seen clearly that the enhanced H-fields are spread over the middle region of the slot, becoming higher than 50 as close to the ends of the slot. Besides, the H-field enhancements within the bottom slot are far larger than that around the top bar. Likewise, the enhancements of the E-fields are mainly concentrated in the bottom slot, as indicated in Figs. 6(e) and 6(f), where the enhancement factor of E-fields can reach up to 134 near the edges of the slot. The H- and E-field enhancement factor in the slot are comparable with or even higher than those achieved in the circular cluster of plasmonic nanoparticles  and the diabolo nanoantenna , which are designed specifically for obtaining giant H-field enhancements. More importantly, the enhanced H- and E-fields in the proposed system are localized inside the slot with a relatively large region, contrast to the case of solid nanostructures such as a metal rod usually generating field localizations at its four tips due to the “lighting rod” effect.
These results suggest a powerful approach for boosting electromagnetic fields by utilizing the constructive interference between a solid and an inverse nanostructure, which can find applications in SERS, biosensing and nonlinear optics. However, in practical applications, the effects of the dielectric substrate and spacer on the optical properties of the stacked EIA-like metamaterial need to be considered. A redshift of the resonant frequency and a slight increase of the resonant linewidth are expected since surface plasmon resonance will shift to the longer wavelength and become broad in linewidth due to the dielectric screening from the substrate or spacer [34, 35]. This also indicates a slightly reduced field enhancement factor associated with the EIA-like resonance due to its decreased quality factor.
In summary, we have theoretically investigated the plasmonic EIA effect and demonstrated an ultra-narrow-band perfect absorption in a stacked metamaterial. The calculated absorption peak has a linewidth less than 8 nm and the absorptivity exceeding 97%. The two-coupled-oscillator model is used to quantitatively analyze the underlying physics. The findings provide a promising scheme for achieving ultra-sharp perfect absorption. Moreover, the stacked EIA-like metamaterial exhibits large electromagnetic field enhancements at the optical frequencies, which is beneficial for improving the sensitivity of spectroscopic techniques, such as SERS and sensing. We believe the plasmonic EIA absorber may find applications in optical filters, thermophotovoltaics, nonlinear optics and biosensors.
This work was supported by National Natural Science Foundations of China (Nos. 11404291 and 11104252), and by the Ministry of Education of China (No. 20114101110003), and by the fund for Science & Technology innovation team of Zhengzhou (No.112PCXTD337), and by the Key science and technology research project of Henan Province (142102210489), the Foundation of Henan Educational Committee (14A140004).
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