1. Introduction

Metamaterials have attracted extensive attention in recent years due to their ability to display exotic properties that are unavailable in nature [1], such as negative refraction [2], invisible cloak [3], superlens [4], etc. Complex electric permittivity (ε) and magnetic permeability (μ) are two fundamental parameters characterizing the electromagnetic properties of metamaterials. With fair adjustment of the electric resonance and magnetic resonance independently, it is possible to match the impedance in free space (i.e.$z=\sqrt{\mu /\epsilon }=1$), minimizing the reflectance to zero [5]. Particularly, perfect absorption with zero reflection and transmission has potential applications in photovoltaic cells [6], sensors [7,8], filters [9], imaging [10], and thermal emitters and detectors [11].

The first successful experimental realization of perfect absorber with metamaterials was done by Landy et al. [1]. Their structures consisted of a metallic split ring and a cut wire, which could couple separately to electric and magnetic fields and give rise to an absorbance of about 88% at 11.5 GHz within a single unit cell layer. Subsequently, other structures such as electric ring resonators [12,13], periodical metallic nanoparticles [5,14], sub-wavelength hole arrays [15] were designed for perfect or near-perfect absorbers in different spectral ranges (microwave, THz, infrared and visible frequencies [16,17]). Such structures were characterized by narrow-band response. Sub-wavelength square hole array [18], multiplexed plasmonic nanostructures [19], and cut-wire metamaterials [20] were proposed for wide-band perfect absorbers in visible and infrared frequencies. Careful design of metamaterials with multiple resonances is generally required for wide-band perfect absorber [21] though it is possible to broaden absorption peaks using high intrinsic damping of metals in a perfect plasmonic absorber [22]. By combining all distinct narrow-band resonant frequencies together and packing them closely through varying the geometric parameters of different component in the unit cell, broadband resonance metamaterials can be obtained [23]. Following this design strategy, broad- or multiple-band metamaterial absorbers have been demonstrated in microwave [24,25], THz [26], infrared [19,23,27], respectively. For example, Guo et al. [19] and Hendrickson et al. [27] theoretically and experimentally demonstrated wide-band perfect absorbers with multiplexed plasmonic nanostructures in midwave infrared frequencies. This multiplexed structure comprising two gold metal squares of different sizes in the unit cell exhibits absorption of above 98% over a bandwidth of 0.5 μm centered at 3.45 μm wavelength. Broadband metamaterials absorber in higher frequencies has been challenging. Though Hu et al. [18] observed near-perfect absorption (about 90%) by combing mix-sized sub-wavelength square hole arrays with thick metal layer; the bandwidth is about 17 nm. Besides, the combination of different sized or shaped subunits needs accurate control and leads to the complexity in manufacturing.

In this paper, we design a broadband metamaterial absorber at visible frequencies, which consists of a single-sized square metal-dielectric-metal (MDM) sandwich structures on dielectric/metal substrate. Our simulation results demonstrate that an extremely high absorbance (no less than 99%) in a contiguous range of frequencies with a bandwidth of about 50 nm can be achieved. To our knowledge, this present a new record for plasmonic thin-film absorption bandwidth determined at the 99% absorption level. Different from previous reports by combing various sized subunits into a unit cell to obtain board-band response [18–20,23–27], the proposed structure utilizes the resonance overlapping of the inter-units interactions and the intra-units interactions. Therefore, this metamaterial absorber is easier to be fabricated by electron-beam lithography [28–30] than above mentioned structures.

2. Structures and design

A unit cell of the compact structure is shown in Fig. 1(a) . The sandwiched layers have a square planar structure with side length a_x = a_y = a = 346 nm. The thicknesses of each metal slab and dielectric layer are set to t₁ = 30 nm and t₂ = 35 nm, respectively. The thickness of the metal substrate is t₃ = 100 nm. The unit cells are periodically arranged along x and y directions with P_x = P_y = P = 480 nm. A plane wave propagates along the z direction with the electric and magnetic fields polarized along the x and y directions, respectively. The simulation is performed by the frequency domain solver of commercial software (CST Micro Studio), where the periodic boundary conditions are used for a unit cell in the x-y plane and perfectly matched layers (PML) are applied in the z axis. The metal layers are chosen to be Au and its dielectric properties are derived from ref [31]. The dielectric layer is SiO₂ with the dielectric constant of${\epsilon }_d=2.07$.

 

Fig. 1 (a) Unit structure of the proposed wide-band perfect absorber; (b) simulated absorption spectra of the wide-band perfect absorber and the components of this system. The green curve: MDM sandwich alone; red curve: Au square on dielectric/metal substrate; blue curve: MDM sandwich structures on dielectric/metal substrate. The insert in (b) is the effective impedance Z of designed metamaterials absorber, where the dashed line denotes Z = 1.

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The simulated absorption spectrum of the designed structure is presented by the blue curve in Fig. 1(b). It is obvious that a wide band near-perfect absorption around 770 nm is obtained (absorption coefficients of 99.98% at λ_m = 745 nm and 99.96% at λ_e = 795 nm). Two resonances are expected to account for this wide band near-perfect absorption. Generally, absorption close to 100% requires more than just one or more resonant absorption bands and impedance matching [32]. In order to see whether the broad band absorber has two impedance-matching frequencies close to 745 and 795nm, or just one somewhere in the middle of the absorption band, we calculated the effective impedances as a function of wavelength (see the insert in Fig. 1(b)) that are retrieved from the reflection and transmission coefficients [33,34]. It shows that the impedance matching conditions are reached around 745 nm (Z = 1.002 + i*0.033) and 795nm (Z = 0.982 + i*0.217).

In order to see structure’s inner workings of different parts and their contributions to the broadband absorption, we present the absorption spectra of the MDM sandwich alone (green curve in Fig. 1(b)) and an Au square on dielectric/metal substrate (red curve in Fig. 1(b)), respectively. The MDM sandwich structure alone gives rise to two relatively weak absorption peaks (P1 and P2) resulting from the interaction between top and down Au squares and the magnetic plasmon resonance, respectively, while the Au square on dielectric/metal substrate exhibits two strong absorption peaks (P3 and P4) arising from the propagating surface plasmon polaritons (SPP) and the coupling between adjacent Au squares, respectively. The assignments of these resonance peaks are based on an investigation of the E-field distributions (not shown here). It is evident that the thick Au substrate plays an important role in achieving near perfect absorption while the sandwich structure mainly contributes to the electric and magnetic plasmon resonances.

In order to understand the physical origins of this broad-band perfect absorption of the designed structure, we give the patterns of the electric and magnetic field components and the current distributions at the two absorption maxima (λ_m and λ_e) in Fig. 2 . Different field and current distributions are observed for the resonances excited at 745 nm and 795 nm. At 745 nm, two intense electric hot spots locate at the ends and two weak ones are approaching the middle in the dielectric layer of MDM while they are just oppositely distributed in the dielectric layer of the substrate (Fig. 2(b₁)). Corresponding to the four field hot spots in the dielectric layer of the MDM, the positive and negative charges are alternatively distributed as “+”, “-”, “+”, “-” along the x direction in top metal layer or vice versa in bottom metal layer. The charge distribution at the metal substrate is the same as that at the top metal layer. Consequently, the total electric dipole moment of the whole structure nearly equals to zero. Nevertheless, the magnetic field (Fig. 2(c₁)) has three hot spots in the dielectric layer of each MDM unit, two at the ends and one in the center, corresponding to the three anti-parallel current regions in the two adjacent metal layers (Fig. 2(d₁)). The magnetic dipole moments in the dielectric layer of MDM are hence coherently strengthened by the circulating loops or anti-parallel currents. Because the two magnetic-field hot spots arise from the two strong magnetic dipoles oscillating in-phase, the whole structure behaves as a big net magnetic moment. Therefore, the resonance at λ_m = 745 nm can be attributed to multiple magnetic dipole plasmon resonances (referred to M1 mode) induced within a single unit cell.

 

Fig. 2 The electric field E (a₁, a₂, b₁, b₂), magnetic field H (c₁, c₂) and current density C (d1, d2) distributions for the designed structure at the resonance wavelength λ_m = 745 nm (a1-d1) and λ_e = 795 nm (a2-d2), respectively. Picture (a₁)-(d₁) and (a₂)-(c₂) are plotted in x-z plane, and (d₂) in y-z plane.

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Figures 2(a₂), 2(b₂), 2(c₂) and 2(d₂) plot the electric and magnetic field components and the current distributions at the resonance wavelength λ_e = 795 nm, respectively. The electric field hot spots appear at the ends of the top metal layer, corresponding to positive charges at one end and negative charges at the other end. Strong electric bonding interaction between adjacent unit cells occurs. All the inter-units interactions along the y direction are in-phase and strong, generating a huge net electric moment contributing to the resonance at λ_e = 795 nm. On the other hand, the magnetic fields are mainly confined in two regions: in the middle of the dielectric layers of a unit cell and the area between the units. Because the currents induced in the adjacent metal layers are anti-parallel, the magnetic dipole moments produced in the two dielectric layers (also the area between the MDMs) are opposite. The net magnetic moment of the whole structure approaches zero due to the cancellation effect. The resonance at 795 nm is therefore attributed to the inter-units electric plasmon resonance (E1 mode).

3. Geometrical effects on the resonance frequencies

The dimension of the MDM is critical in obtaining the near perfect absorption because the changes in the length a of the squares can significantly influence the inter-units interactions as well as the intra-units interactions and consequently tune the electric and magnetic resonances. In Fig. 3 , we show the influence of the dimension of square plates on the resonance frequencies and absorption coefficients. It is clear that the optimal perfect absorption is found for a around 350 nm, at which the intensity of the two resonance absorption peaks are approximately 100% due to the largest overlap between the E1 and M1 modes. According to the LC circuit model, the variation of parameter a will mainly change the capacitance C_x and C_y (C_x is the capacitance between two adjacent unit cells, C_y is the capacitance between two adjacent metal layers). When a reduces, the capacitances C_x and C_y decrease as $C_x\propto \frac{a}{P-ma}$ and C_y ∝a² (here P is the period of the designed structures, m is a parameter related to the current distributions on the end faces of MDM paralleled to the y axis), and the resonance wavelengths (λ_e and λ_m) move towards lower values ${\lambda }_e\propto \sqrt{\frac{a}{P-ma}}$ and ${\lambda }_m\propto a$. However, due to the different moving speed of the two resonances with a, the width of the near perfect absorption band becoming narrower as a decreases. When a is equal to or smaller than 280 nm, the spectrum becomes a single-peak perfect absorption at $\lambda =680\text{nm}$(as shown by the red curve in Fig. 3(a)). We checked the electric field distribution at $\lambda =680\text{nm}$ for a = 280 nm, the electric fields greatly concentrate on the two adjacent ends of the top metal plates, presenting intense inter-units electric dipole bonding interaction property, and the magnetic plasmon resonance vanishes. On the contrary, the near perfect absorption moves towards a longer wavelength as the a increases (a>280 nm), and a broad-band strong absorption is obtained by the overlap of the two plasmon resonance modes E1 and M1. The whole intensity of the near perfect absorption band retains above 90% and its bandwidth changes from 32 nm to 60 nm when a varies from 300 nm to 390 nm. The dependence of the two maximum absorption peaks with a is given in Fig. 3(b). Due to the red-shift of the electric plasmon resonance at λ_e being faster than the magnetic one at λ_m with increase of a, the near perfect absorption becomes wider. From the above analysis, the size effect in the MDM structure can induce multiple magnetic-dipole plasmon resonance modes, contributing to the broad-band perfect absorption.

 

Fig. 3 Dependence of the absorption spectra (a) and the resonance peaks positions (b) on the length a of the squares in the MDM structure.

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In addition to the size effect of the metal squares in the MDM, the dielectric spacer and substrate are also expected to affect the near perfect absorption. Figure 4 shows the effect of the dielectric layer thickness t₂ on the near perfect absorption. It is clear that the dielectric layer thickness has an obvious effect on the positions of the magnetic resonance but little on the electric resonance. The absorption peak at λ_m shifts to lower wavelength while that at λ_e remains almost unchanged because the increase in t₂ reduces the capacitance in the MDM but not that between MDMs. We also inspected the electric field in the middle of the dielectric layer of the MDM with different t₂ at corresponding resonance wavelength λ_m. The electric field is largest when t₂ is about 35 nm, corresponding to the maximum overlap between the inter-units electric-dipole interaction and intra-unit multiple modes (E1 and M1), which is in coincidence with Fig. 4(a).

 

Fig. 4 The two maximum absorption peaks change with thickness of dielectric layer of MDM structure.

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Figure 5 shows the influence of the refractive index n of the dielectric spacer on the absorption. As the refractive index n increases, both resonances exhibit linear shifts towards longer wavelength (Fig. 5 (b)), resulting in a larger bandwidth (from 44 nm to 82 nm) of the near perfect absorption. This can be understood by the fact that the resonance wavelength is proportional to the square root of capacitance C_x (or C_y), which is proportional to the dielectric constants (i.e. C_x, C_y∝ε = n²).

 

Fig. 5 The changes of absorption properties of the metamaterials with different refractive index n of dielectric materials of MDM and substrate.

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The sharp absorption peak appearing in the short wavelength region (Fig. 5(a)) is due to the resonance of SPP excited in the periodic metallic structures [35]. The resonance wavelength of the SPP is also proportional to effective refractive index of the periodic structure. As shown by Fig. 5(a), although the SPP resonance can be excited, it is too far away from the broad-absorption band for our designed structure and hence the coupling between the SPP and localized surface plasmon resonances (E1 and M1 modes) cannot occur. The SPP mode has no contribution to the broad-band absorption.

Figure 6 shows the dependence of the spectral response of the designed absorber with incident angles. It shows that the broad-band perfect absorption (above 90%) does not limited to normal incidence but can be extended at least to θ~20°. The absorption of the E1 mode decreases gradually with further increasing θ and an additional resonance appears in the low-wavelength region at θ>0°.

 

Fig. 6 Absorption spectra of the designed structures with different incident angles. The insert shows the direction of the incident light.

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Finally, we give a comparison of broad-band perfect absorption with electromagnetically induced transparency (EIT) effect [36]. Though both are based on the interplay between two resonances with a different field structure, they have different physical origins. The “plasmonic EIT” arises from destructive interference of two different excitation modes, which gives rise to a sharp transmission peak within a broad transmittance dip. In Contrast, the near perfect broad-band absorption in our designed structure originates from the constructive overlap of the electric dipoles bounding interactions between adjacent unit cells and the intra-unit multiple magnetic dipole resonances induced by size effect.

4. Conclusions

By designing two-dimensional periodic MDM sandwich array structures on dielectric/metal substrate, the metamaterials with wide-band perfect absorption at visible frequencies have been successfully obtained and analyzed theoretically. The near perfect absorption originates from the overlap of two plasmon resonance modes. One originates from the electric dipoles oscillating between adjacent unit cells while the other corresponds to multiple magnetic dipole resonance induced by size effect. This kind of planar multilayer structure is easy to be fabricated by focus-ion-beam milling or electron-beam lithography and vacuum coating equipment, and can find practical applications in band-stop filters, solar cells, detection and imaging at visible frequencies.