1. Introduction

Metamaterials exhibit a variety of extraordinary and agile optical properties, which have attracted considerate interest for studying both fundamental electromagnetic phenomena and device applications [1,2]. One common metamaterial design is the so-called metal-insulator-metal (MIM) structure, which has been widely used in the demonstrations of metamaterial perfect absorbers [3,4], molecular sensors [5,6] and polarization converters [7,8] etc. The exotic properties of metamaterials originate from their localized plasmonic resonances with enhanced light-matter interactions, which are often characterized with reflection spectroscopy especially for the MIM metamaterials with zero transmittance [9,10]. In reflection spectrum analysis of metamaterials, diffuse scattering is an important factor, which affects the analysis on metamaterial resonant properties such as absorption efficiency, line shape and hybridization behavior, etc. In most cases, diffuse scattering is ignored and specular reflection completely captures the resonant properties of metamaterials [11,12]. The ignorance of diffuse scattering is well justified in such case that unit-cell of the metamaterial structure is much less than a quarter-wavelength and the metamaterial can be considered as a homogeneous medium [13–15]. However, there are other cases in which the wavelength of metamaterial resonance approaches the unit-cell size or even smaller values [16–18]. For these metamaterial structures not satisfying deep-subwavelength requirement, diffuse scattering is likely to occur and needs to be considered. Indeed, a number of studies have revealed that diffraction from the periodic unit-cells in metamaterials plays an important role and often results in anti-crossing behavior with the metamaterial resonance [19–21]. In order to avoid the disturbance of diffraction on intrinsic metamaterial resonant properties, P. Chevalier and H. Bertin et al. introduced randomness into the metamaterial structures [22,23], and suppressed the diffractive Rayleigh anomalies, although the disorders often add more complexity in metamaterial design and fabrication. Recently, E. EI Shamy et al. further revealed that besides suppressing the diffractions, disorders could also lead to diffuse scattering of light [24]. Although diffraction orders have been shown to be important in diffuse reflection in above literature work, their full spectral response and their influence on reflection spectrum analysis of metamaterial modes are not yet complete.

In this paper, we characterize diffuse reflection behaviors in metasurfaces consisted of gold disk arrays in the MIM structure. An integrating sphere is used with Fourier transform infrared spectrometer (FTIR) to measure hemispherical diffuse reflection spectra of the disk array samples with different periods and diameter sizes. Our measurements and analysis indicate that diffuse reflection is governed by grating diffractions and occurs in a regime whose wavelengths are smaller than that of the first order Rayleigh anomaly. Meanwhile, intensity of the diffuse reflection is greatly enhanced by metasurface resonance modes, and exhibits an overall increasing trend as the wavelength decreases. The diffuse reflection is revealed to cause an obvious difference in analyzing the metamaterial resonant absorption efficiency and a slight shift of the resonance frequency. These results provide new insights in understanding the interaction between light and MIM metamaterials with periodic unit-cells, and are helpful for analyzing metamaterial properties by using reflection spectroscopy.

2. Design and fabrication

The structure of our designed metasurface and its unit-cell are sketched in Figs. 1(a) and 1(b). The metasurface consists of a copper film, a magnesium fluoride (MgF₂) spacing layer, and a top array of gold disks. Such MIM metasurface typically exhibits magnetic resonances with excited anti-parallel surface currents in the disks and the copper ground plane [25]. To study effects of diffuse reflection on the metamaterial magnetic resonances, we designed disk arrays with different diameters and periods. In one series of samples, the disk diameter increases from 3 µm to 6 µm with a fixed period of 10 µm. For the second series, the disk diameter is fixed at 3 µm, and the period increases from 6 µm to 10 µm.

 

Fig. 1. (a) Schematic of designed metal-insulator-metal (MIM) disk array metasurface and (b) its unit-cell with relevant dimensions labeled. (c) and (d) are top-view optical image and SEM image of the fabricated MIM disk array sample with D=3 µm and P=6 µm, respectively.

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Our designed sample structures were fabricated with standard thin-film deposition and photolithographic patterning. First, a 300 nm thick copper film was deposited on a 4-inch silicon wafer, and then a 270 nm thick MgF₂ spacing layer was deposited on top of the copper film by using electron beam evaporation technique. Next, a 100 nm thick gold disk array was fabricated on top of the MgF₂ using contact photolithography, metal deposition and lift-off processes. Top-view optical image and scanning electron microscope (SEM) image of a representative sample with D=3 µm and P=6 µm are shown in Figs. 1(c) and 1(d), respectively. The area size of the disk array is 1 cm×1 cm. Diameters and periods of the fabricated disks are very close to the designed values with small deviations of less than 5%.

3. Measurement results and analysis

Our disk array metasurface samples were characterized with a FTIR equipped with a PIKE upward integrating sphere detector, as shown in Fig. 2. Collimated infrared light from a globar in FTIR is incident on the sample at an angle of θ=12°. The reflected light in all directions is collected with the integrating sphere and is detected with a mercury cadmium telluride (MCT) detector. A switchable specular exclusion port is used to include or exclude the specular reflection. Therefore, both total reflection (R_tot) and diffuse reflection (R_diff) can be measured. The difference between R_tot and R_diff gives the specular reflection (R_spec). In the spectral measurements, reflection from a reference diffuse gold mirror is used as the background spectrum.

 

Fig. 2. Schematic view of FTIR spectral measurement system using an integrating sphere.

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The measured reflection spectra of our gold disk array samples with four different diameters and 10 μm period are shown in Fig. 3. For the 3 µm diameter sample shown in Fig. 3(a), both total reflection R_tot and specular reflection R_spec exhibit a dip at around 9 µm, which is the first order metamaterial magnetic resonance. Its magnetic fields and surface currents are shown in Fig. 3(f). The excited currents in the disk and the metallic ground plane are antiparallel, which create a strong localized magnetic field within the MgF₂ spacing layer. In addition, as revealed in Fig. 3(a), there is an obvious difference between the R_tot and R_spec within the band with wavelengths less than about 10 µm. The resulted diffuse reflection R_diff, as shown in red, shows a peak at the magnetic resonance wavelength and spans over the entire wavelength region below 10 µm. Therefore, for this sample with overlapped metamaterial magnetic resonance and diffuse reflection, specular reflection is insufficient for analyzing the resonant properties. In particular, the diffuse reflection causes a significant difference in resonance amplitudes of the magnetic mode as observed in R_tot and R_spec, which affects the evaluation on absolute absorption efficiency. Meanwhile, if one looks closer at the spectra in Fig. 3(a), a small wavelength difference of the magnetic resonances as revealed in R_tot and R_spec is observable. Table 1 lists the detailed resonance wavelength differences of the fabricated samples with different diameters. For the D=3 µm sample, its magnetic resonance obtained in R_spec is blue-shifted by 31 nm, as relative to that observed in R_tot. As the disk diameter increases, the metamaterial magnetic resonance gradually moves to longer wavelength as shown in Figs. 3(b)–3(d). Meanwhile, the total reflection R_tot and specular reflection R_spec are approaching identical at the metamaterial resonance. The diffuse reflection nearly doesn’t affect the metamaterial resonance for the sample with larger disk diameter of D=6 µm as shown in Fig. 3(d). The resonance wavelength difference drops to 9 nm as listed in Table 1, approaching the 0.4 cm^-1 resolution limit of our spectral measurements. The diffuse reflection spectra for these four samples are shown in Fig. 3(e). As the disk diameter increases from 3 µm to 6 µm, the diffuse reflection exhibits intensity variations in addition to the enhanced peaks at metamaterial magnetic resonances. More importantly, these diffuse reflection spectra are characterized with a truncation wavelength at about 12.1 µm, which corresponds to the first order Rayleigh anomaly, i.e. $\lambda _{RA}^{(1,0)} = P\left( {{\textrm{Re}} \left[ {\sqrt {{{{\varepsilon_m}{\varepsilon_d}} / {{\varepsilon_m} + {\varepsilon_d}}}} } \right] + \sin\theta } \right)$[26], where θ is the incident angle, ε_m and ε_d are the permittivity of gold and air, respectively. It is also noticeable that there are two tiny reflection dips at 3 µm and 10 µm wavelengths in our measured reflection spectra. The latter is in overlap with the metamaterial magnetic resonance of the sample shown in Fig. 3(b). To find out origins of these dip features, we measured specular reflection spectra of MgF₂ films on top of copper as shown in Fig. 4. It is seen that the two dips features observed in the metasurface sample also exist in the MgF₂ films without top disk arrays. This suggests that the two dips are from impurity defect absorption in MgF₂ spacing layer [27].

 

Fig. 3. Measured reflection spectra of metasurface samples with disk diameter of (a) 3 µm, (b) 3.5 µm, (c) 5 µm, and (d) 6 µm. The disk period is taken as 10 µm. Diffuse reflection spectra of these four samples are shown in (e). The black arrow indicates wavelength of the first order Rayleigh anomaly. (f) Magnetic field and surface current distributions of the resonance mode at around 9 µm wavelength for the metasurface sample with 3 µm disk diameter and 10 µm period. The white arrows represent directions of surface currents.

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Fig. 4. Measured specular reflection spectra of MgF₂ films of different thicknesses on top of copper. The black curve is total reflection spectrum of the metasurface sample with D=3 µm and P=10 µm for comparison.

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Table 1. Wavelength differences of the magnetic resonances as observed in total reflection spectrum R_tot and specular reflection spectrum R_spec.

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We next examined the disk array samples with different periods. Figure 5 shows the reflection spectra of four samples with 3 μm diameter and different periods of 6 µm, 7 µm, 9 µm and 10 µm, respectively. For the sample with small period of 6 µm shown in Fig. 5(a), the metamaterial magnetic resonance is at about 9 µm, around which the total reflection spectrum R_tot and the specular reflection spectrum R_spec are identical. The diffuse reflection R_diff is limited to wavelengths of less than 8 µm without disturbing the metasurface resonance in this case. As the disk period increases, the metamaterial resonance remains at about 9 µm, and meanwhile diffuse reflection R_diff spans toward longer wavelengths and eventually covers the metasurface resonance as shown in Figs. 5(b)–5(d). In these cases, the diffuse reflection causes an obvious amplitude difference and a small wavelength shift for the resonance dips revealed in R_tot and R_spec, similar to the properties observed in Fig. 3. Figure 5(e) shows the diffuse reflection spectra for the four samples. It is seen that as the period increases from 6 µm to 10 µm, the diffuse reflection gradually extends towards longer wavelength region. Moreover, diffuse reflection spectra of these four samples are all limited to wavelengths less than those of first order Rayleigh anomalies as indicated by the arrows. In addition, similar to the measured samples with different disk diameters in Fig. 3, the diffuse reflection spectra exhibit enhanced intensity at the metamaterial magnetic resonances in addition to a general increasing trend toward shorter wavelengths. From above measured results for disk arrays with different diameters and periods, it can be concluded that the spectral range of diffuse reflection is primarily determined by the period rather than the disk diameter. The diffuse reflection occurs in the region with wavelengths less than that of the first order Rayleigh anomaly.

 

Fig. 5. Measured reflection spectra of metasurface samples with period of (a) 6 µm, (b) 7 µm, (c) 9 µm, and (d) 10 µm. The disk diameter is fixed as 3 µm. Diffuse reflection spectra of these four sample are shown in (e). The arrows in (e) indicate wavelengths of the first order Rayleigh anomalies.

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To gain better understanding on physical origins of the measured diffuse reflection, we next calculated diffuse reflection spectra of the samples using a numerical finite-difference time domain (FDTD) model. The gold and copper are described with Drude model with carrier parameters given in Ref. [28]. The refractive index of MgF₂ is taken from Ref. [29]. Under periodic boundary conditions and plane wave excitation at an angle of 12°, near-field within one unit-cell is first calculated, and then the far-field is obtained by summing up radiative diffraction orders, which take the form of

The above numerical far-field extrapolation method enables the calculation of diffusely reflected light and the contributions of each radiative diffraction order [30–32]. Figure 6 shows our calculated diffuse reflection spectra for a representative sample with D=3 µm and P=6 µm. It is seen that the simulated spectrum is in general agreement with the experiment. The calculated spectrum shows more sharp peaks while the experimental spectrum is smoother. These discrepancies are likely caused by beam divergence of incident light, which was not accounted in our calculation model. More importantly, the simulated spectrum can be decomposed into diffraction orders of (-1,0), (1,0), (0,±1), (-1,±1) and (1,±1), which suggests that diffuse reflection is mainly accounted for by summing up grating diffractions from the periodicity of the metasurface structure. Similar properties are also observed for the sample with larger period of 10 µm as shown in Fig. 7. In this case, the diffuse reflection covers the metamaterial resonance, and more diffraction orders of (2,0), (0,±2), (1,±2) and (2,±1) are included. These simulated results indicate that grating diffractions are the main origins of diffuse reflection, which are very different from those observed in nano-porous silicon [33], where the Rayleigh-like scattering resulted in diffuse reflection at wavelengths significantly larger than the scatter size. Thus for analyzing metamaterial resonance below wavelength of the first order Rayleigh anomaly, diffraction-caused diffuse reflection needs to be considered for obtaining accurate metamaterial resonant properties. It is noted that, although our measured increasing trend of diffuse reflection towards shorter wavelengths is consistent with numerical FDTD simulations, it will be more informative if an analytical model could be developed.

 

Fig. 6. Simulated diffuse reflection spectrum and diffraction orders of the metasuface sample with D=3 µm and P=6 µm. The black curve is experimental spectrum for comparison.

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Fig. 7. Simulated diffuse reflection spectrum and diffraction orders of the metasuface sample with D=3 µm and P=10 µm. The black curve is experimental spectrum for comparison.

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Finally, since the diffraction orders depend on incident angle, it would be interesting to see how the diffuse reflection changes with incident angle. As the angle is fixed at 12° in our used integrating sphere, we examined properties of this angle-dependence with FDTD simulations. Figure 8 shows the calculated diffuse reflection spectra of the sample with D=3 µm and P=6 µm at different incident angles. It is seen that, as the angle increases from 12° to 45° the diffuse reflection expands to longer wavelengths, which covers the magnetic metasurface resonance and exhibits pronounced diffuse reflection peaks at the metasurface magnetic resonance. This expanding of diffuse reflection spectrum is consistent with the behavior of first order Rayleigh anomaly, whose wavelength increases with incident angle.

 

Fig. 8. Simulated diffuse reflection spectrum the sample with D=3 µm and P=6 µm at different incident angles. The arrows indicate wavelengths of the first order Rayleigh anomalies.

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4. Conclusions

We have characterized diffuse reflection features in MIM disk array metasurfaces by using an integrating sphere. Our spectral measurements revealed that diffuse reflection occurs in the regime with wavelengths smaller than that of the first order Rayleigh anomaly. The diffuse reflection exhibits enhanced intensity at metasurface resonance in addition to an increasing trend towards shorter wavelengths. In addition, the diffuse reflection was shown to cause a significant difference in characterizing the absorption efficiency of metasurface mode as well as a small shift of the resonance frequency. Our numerical analysis further suggested that diffuse reflection originates from diffraction orders from the periodicity of the metamaterial structure. Our obtained results shed lights on further understanding the interaction between light and periodic MIM metasurface, and are helpful for designing and analyzing metamaterials especially when their resonance wavelengths are comparable to or smaller than the structure period.