1. INTRODUCTION

Anomalous light absorption in metallic gratings was first discovered by Wood in 1902 [1]. It was explained later that the strong light absorption in metal gratings was because of the excitation of surface plasmon polaritons [2]. In recent years, interest in strong light absorption in metal nanostructures has resurfaced because of potential applications for optical energy harvesting and enhanced photodetection. Various metallic structures have been proposed and investigated with the intent to absorb electromagnetic optical radiation completely over broad or tailored spectral bands [3–28]. Among these structures, subwavelength-scale patterned metal-insulator-metal (MIM) structures have been investigated extensively over the visible to infrared [6–20], terahertz [21–27], and microwave [29] frequency ranges. Patterned MIM structures can trap energy efficiently in the dielectric gap between the patterned thin metal film and the thick metal film. In long wavelength regimes, such as mid-wave and long-wave infrared and terahertz frequencies, stratagems rely primarily on absorption by a localized electromagnetic resonant mode caused by antiparallel electric dipole currents in the top and the bottom metal layers [7,9–14]. At visible and near-infrared (near-IR) frequencies, where lossy nonlocalized surface plasmon polaritons (SPPs) can be excited in the metal layers, nearly complete absorption of light can also be achieved by grating coupling to the SPPs with periodic MIM arrays, even at frequencies far from localized plasmon resonances. In this case, the energy of the resonance modes concentrates mainly in the lateral gaps between the patterned metal nano-squares. It is also possible for grating-coupled modes to coexist with localized plasmon modes, in which case interactions leading to avoided crossings may occur if mode symmetries are suitable [20,30]. Coupling between the localized plasmon modes and the nonlocalized plasmons was also reported [31].

In this work, we systematically investigate optical resonance modes in MIM structures consisting of two-dimensional square arrays of thin gold squares patterned on top of a 90 nm thick aluminum nitride dielectric layer deposited on a 300 nm thick gold film. Although a one-dimensional MIM structure is useful for light absorption [19] and plasmonic waveguides [32], the surface plasmon resonance can only be excited for TM-polarized light in a one-dimensional structure where the direction of TM polarization is perpendicular to the metal grating lines. Two-dimensional MIM structures allow excitation of plasmon resonance modes for both TE and TM polarizations. Here, we focus on the optical modal structure of the MIM metamaterial through measurements of reflectance spectra from arrays in which both the array period and patterned metal square size were varied systematically. While one-dimensional MIM structures exhibit absorption bands by localized surface plasmon resonance only [19], the two-dimensional MIM structures also exhibit multiple absorption bands in the visible and near-IR spectral range. Full-wave simulations for an extensive range of square sizes and array periods reproduce the experiments, and provide insights into the local fields, origin of the absorption bands, and dependence on structural dimensions. We find that the absorption bands are correlated with the grating-coupled transverse-electric (TE) mode and transverse-magnetic (TM) mode. The coupling to the two types of modes broadens the overall spectral absorption of the structure. We also find that the measured and computed dispersions, and the computed field patterns, suggest that TM modes can borrow energy from a localized magnetic resonance mode associated with isolated gold squares, leading to intense localized fields. The findings in this work provide physical insight for designing metal-dielectric metamaterial surfaces in the visible and near-IR spectral range for a variety of applications.

2. EXPERIMENTAL RESULTS

The schematic of MIM structure is shown in Fig. 1(a), which consists of an array of patterned gold squares of 60 nm thick on a 90 nm thick AlN dielectric spacing layer deposited on a 300 nm thick gold film on a silicon wafer substrate. We fabricated two sets of devices using e-beam lithography as described in the next paragraph. Set (i) has a nominally constant gold-square side length of 172 nm ($\pm 11\mathrm{nm}$ uncertainty range) and different periods from 360 to 540 nm stepped in 20 nm increments. (Throughout, we refer to the gold square size by its side length.) Set (ii) has a constant array period of 460 nm, but different gold square sizes from 160 to 373 nm. Figure 1(b) shows a scanning electron microscope image of one of these 460 nm pitch arrays with a gold square size of 220 nm.

 

Fig. 1. (a) Schematics of the MIM structure. Incident light is polarized in the x-direction and propagates in the z-direction. (b) Scanning electron micrograph of a fabricated device consisting of a gold square array of a period of 460 nm and square size of 220 nm.

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Samples were fabricated by the following process. First, 5 nm titanium and 300 nm of Au were deposited by thermal evaporation on a silicon wafer, respectively. Then, 90 nm of AlN were grown via atomic layer deposition on the thick gold film surface. Square arrays were patterned via electron beam lithography. In the e-beam lithography process, the e-beam resist (495 PMMA A4) was first spin-coated on top of the AlN layer at 2500 RPM and baked at 180°C for two minutes. Square arrays were written in the e-beam resist layer with the electron beam and developed in an IPA:MIBK $3:1$ solution. After the development, an oxygen plasma de-scum process was carried out for 30 seconds to clean the e-beam resist residues on the device surface. Then, 2 nm titanium and 60 nm of Au were deposited by thermal evaporation, followed by lift-off using acetone to dissolve the e-beam resist, and cleaning in isopropyl alcohol. The patterned area of each device is 250 by 250 micron, which is large enough for measurement. Optical reflectance spectra were measured with a microscope coupled spectrometer (Craic Technologies, Inc.) that allowed illumination and collecting at near normal incidence. Measurements were taken through a 0.2 NA ($10\times$) objective, with the aperture set to further restrict the incident and collection angle to $\sim 10°$ from the surface normal, and were normalized to background spectra recorded off the patterned device area.

First, measurements of set (i) were carried out (devices with a constant gold square size of 172 nm and varying array period). Figure 2(a) displays the data as a two-dimensional contour plot of measured reflectance spectra and shows the dispersion of the absorption resonances with a varying array period. Figure 2(b) shows a subset of the experimental reflectance spectra used to generate the contour plot of Fig. 2(a). In Figs. 2(a) and 2(b), two absorption bands are clearly seen as strong resonant dips in reflectance. The bluer mode disperses from 656 to 767 nm and the minimum reflectance reduces from 34% to 13% as the array pitch increases from 360 to 520 nm. The redder mode shifts from 760 to 981 nm, and its reflectivity increases from 22% to 49% over this same pitch range. The nearly linear dispersion with an array period for the two modes suggests that the absorptions are caused by grating coupling to propagating (nonlocalized) surface modes that trap the incident energy, as discussed in Section 3.

 

Fig. 2. (a) Two-dimensional plot of reflectance spectra measured from MIM devices fabricated with a nominally equal gold square size of 172 nm, but different array periods. (b) Selected reflectivity spectra from several fabricated devices with periods of 360, 400, 440, 480, and 520 nm.

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Figure 3(a) shows the two-dimensional plot of measured reflectance from arrays with a constant period of 460 nm, but with varying square sizes from 160 to 373 nm. Again, two absorption bands are observed. The shorter wavelength absorption band blueshifts from 726 to 650 nm, as the size of the metal square is increased. The longer-wavelength absorption band first becomes broken as the metal square size increases, and then becomes stronger and shifts to the red as the metal square size continues to increase. The minimum reflectance of this set reaches 5.3% and 6.3%, for the shorter and longer wavelength absorption bands, respectively.

 

Fig. 3. (a) Two-dimensional plot of measured reflectivity spectra from fabricated devices with a constant period of 460 nm, but different gold square sizes. (b) Measured reflectivity spectral curves from four devices with square sizes of 213, 242, 286, and 354 nm, respectively.

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3. NUMERICAL SIMULATION AND DISCUSSIONS

To understand the experimental results, we conducted extensive finite-difference time-domain (FDTD) numerical simulations by using an FDTD code developed by Lumerical Solutions, Inc. [33], which permit investigation of a broader range of array periods and square sizes than was available experimentally. In FDTD simulations, periodic boundary conditions are assigned in the x- and y-directions, and a perfectly matching layer condition is assigned in the z-direction. The incident wave is a plane wave, polarized in the x-direction and propagating in the z-direction. Rectangular mesh of 2.5 nm is used. The refractive index of gold was obtained from [34], while the refractive index of the AlN was measured with a reflectance-based metrology tool made by n&k Technology, Inc.

To examine the modal dispersion with an array period, we calculated the reflectance of arrays as a function of a period from 300 to 550 nm for four gold square sizes. The thickness of the gold squares was 60 nm. Figure 4 shows the results as a two-dimensional plot for devices with fixed square sizes of (a) 140, (b) 180, (c) 220, and (d) 260 nm. Three absorption bands can be seen clearly at larger pitches in Figs. 4(a)–4(c). (The nondispersive absorption band at the smallest wavelength, around 500 nm, marks the onset of the interband absorption in gold.) To facilitate further discussion, the maxima of the absorption bands are marked with lines (white dashed, white solid, and black solid) which connect the reflection minima in the two-dimensional plots. As the period increases, all three absorption bands shift approximately linearly to longer wavelengths and exhibit variable strengths that change as the array period changes.

 

Fig. 4. Calculated reflectivity versus the wavelength and the array period for different gold square sizes of (a) 140, (b) 180, (c) 220, and (d) 260 nm. Black dashed curves plot the dispersion of a propagating TM mode modeled analytically in Section 3. All other superposed curves are guides to the eye.

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The pitch-dependent simulation shown in Fig. 4(b) for 180 nm squares can be compared to the experimental dispersion of Fig. 2(a) measured for 172 nm squares. To facilitate comparison, we delineate with horizontal black dotted lines in Fig. 4(b) the range of periods examined experimentally. The simulations agree well with respect to the rate of dispersion with pitch and the intensity trends, thereby lending confidence in the simulations. The additional absorption band marked with white dashed lines in the simulation starts to become visible in the experimental data with the largest pitch [purple curve in Fig. 2(b)] as a high-energy shoulder.

As Fig. 4 illustrates, the size of the gold squares forming the array has a strong influence on the modal dispersions with pitch. To examine these effects in more detail, we fixed the array period and calculated the reflectance spectra as a function of gold square size. The simulated spectra are plotted in Fig. 5 for the four different periods of (a) 280, (b) 340, (c) 400, and (d) 460 nm. For the small array period of 280 nm, Fig. 5(a), the absorption band at a longer wavelength, denoted by the solid black line, is insensitive to square size as long as the size falls within the range of 80 to 200 nm. For devices with a large array period, the absorption band characteristics depend on square size dramatically. Thus, an important finding is that the dispersion of the absorption band with metal square size is very weak when the period is small, but increases significantly as the array period becomes large. For example, the wavelength separation between the strong reddest absorption band (marked with a black line) and the bluer band marked with a white line increase as the array period increases, with the separation accelerating for larger square sizes in Figs. 5(c) and 5(d), as the redder band shifts more red, while the bluer band shifts more blue with increasing square size. At the largest array period of 460 nm, Fig. 5(d), the bluer absorption band also splits into two branches at both small and large square sizes, and the reddest absorption band weakens noticeably for intermediate-sized squares from $\sim 200$ to $\sim 250\mathrm{nm}$. This largest period of 460 nm corresponds to the experimental results in Fig. 3(a), which were measured over a restricted range of square sizes denoted by horizontal dashed lines in Fig. 5(d). The absorption bands match well with the experimental results, as indicated by the white and black solid lines in Fig. 5(d).

 

Fig. 5. Two-dimensional plots of reflectivity spectra as a function of square size for a fixed period of (a) 280, (b) 340, (c) 400, and (d) 460 nm. Black dashed curves plot the dispersion of a propagating TM mode modeled analytically in Section 3. All other superposed curves are guides to the eye.

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In Fig. 4, absorption bands disperse approximately linearly with the array period, which suggests that the bands are caused by grating coupling of incident light into lossy in-plane propagating modes that trap the optical power and dissipate it in the metal components [30,35,36]. The dispersion is most linear in Fig. 4(a), where the small 140 nm square size affords the smallest perturbation to the propagating modes. For illumination at normal incidence, the condition for coupling into in-plane modes is given by the following equation:

To further assist with mode identification, we also computed electric field and magnetic field intensity distributions at mid-plane in the AlN dielectric layer at the peak absorption wavelength of different resonance modes. These are displayed in Figs. 6–9 for arrays with a 460 nm period, but different square sizes of 100, 180, 260, and 340 nm, respectively. The first and second columns show a single unit cell of the array with the patterned Au-square outlined in white. The third column shows a vertical profile of a magnetic field at $y=0\mathrm{nm}$, with a white line dividing the Au/AlN/Au regions. The incident plane wave is at normal incidence and has an electric field amplitude $E=1\mathrm{V}/\mathrm{m}$ and a magnetic field amplitude $H=E/Z_0=0.00265\mathrm{A}/\mathrm{m}$ ($Z_0$ is the free-space impedance).

 

Fig. 6. Calculated electric and magnetic field intensities as labeled at the three peak absorption wavelengths of 643 (a)–(c), 693 (d)–(f), and 811 nm (g)–(i). The gold square size is 100 nm, and the period of gold square array is 460 nm.

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Fig. 7. Simulations for an array of 180 nm Au squares with a 460 nm period. Simulated electric and magnetic field intensities at the two peak absorption wavelengths of 689 (a)–(c) and 841 nm (d)–(f).

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Fig. 8. Simulations for an array of 260 nm Au squares with a 460 nm period. Simulated electric field and magnetic field intensity distributions at the absorption wavelengths of 647 (a)–(c) and 835 nm (d)–(f).

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Fig. 9. Simulations for an array of 340 nm Au squares with a 460 nm period. Simulated electric field and magnetic field intensity distributions at the peak absorption wavelengths of 611 (a)–(c) and 881 nm (d)–(f).

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The transfer–matrix calculation found that the inter-square areas (i.e., uniform AlN layers on Au) support two modes within the simulated space, namely a surface plasmon polariton (SPP) and a TE slab-waveguide mode. After comparing the wavelength ordering of these modes and their rates of dispersion to the simulations, we attribute the reddest mode in Fig. 4(a) (which displays the dispersion with an array period for small 140 nm squares) to a grating-coupled SPP. This assignment is also consistent with the field intensity patterns of Figs. 6(g)–6(i) that were simulated for a wavelength of 811 nm, at which an array of 100 nm squares absorbs maximally in the reddest mode. The field patterns show a strong magnetic response with maximum magnetic field intensities ${|H|}^2\sim 500{\mathrm{mA}}^2/{\mathrm{m}}^2$ beneath the square, and at the zone edges parallel to the y-axis in Fig. 6(h), as expected for an SPP standing wave. This represents an enhancement over the incident magnetic field intensity of $\sim 69$, which dominates the $\sim 30$ enhancement of the electric field in Fig. 6(g). These theoretical results show that SPPs are coupled resonantly at the [10] diffraction condition (i.e., $l=1$, $m=0$), with SPPs launched primarily in the x-direction, consistent with the incident polarization.

Figures 6(g)–6(i) show that, when SPPs are resonantly coupled, the strongly enhanced electric and magnetic field patterns in the vicinity of the Au square resemble a well-known localized mode reported for similar MIM structures comprising a metal structure separated from a thick metal film with a dielectric spacing layer [7,10,12,13]. This mode has been described variously as (1) a magnetic resonance mode [10] (an in-plane magnetic dipole field is encircled by conduction currents in the metal and displacement currents in the dielectric); (2) a quadrupole-like mode [12], named to reflect the oppositely directed conduction currents in the metal square and metal substrate; and (3) a lateral Fabry-Perot mode [7,13], wherein an MIM SPP passes back and forth beneath the metal nanostructure. Similarly, field plots in the second row in Figs. 7–9 indicate the magnetic resonance mode [10]. Figure 10 shows calculated scattering cross-section spectra for two single isolated Au squares lying on a 90 nm thick AlN layer on a thick Au film substrate. The single gold square has a square size of 100 and 140 nm. The peaks of the scattering cross-section spectra correspond to the localized magnetic resonance modes at the two wavelengths in the near IR. For the 100 nm single Au square, the localized resonance wavelength is at 0.98 μm, as indicated as the red arrow in Fig. 10. The electric and magnetic field profiles for this localized resonance mode, excited at normal incidence, are shown in the inset of Fig. 10. The patterns closely resemble the field patterns for a 100 nm Au square in an array, plotted in Figs. 6(g) and 6(h).

 

Fig. 10. Computed scattering cross-section spectra for two single isolated Au squares lying on a 90 nm thick film of AlN deposited on an Au substrate. The two squares have side lengths of 100 and 140 nm. Note the rapid dispersion with the size of the mode in the near IR. Inset: electric and magnetic field intensities at the resonance wavelength of 0.98 micron for the 100 nm metal square, plotted in a plane parallel to the substrate and bisecting the AlN film. Compare the patterns in Figs. 6(e) and 6(f) for a 100 nm square in an array at the bluer grating-coupled wavelength.

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To find the resonance spectrum of the single metal square MIM element, we calculated the scattering cross section of a 140 nm single square. The calculation is carried out by an FDTD method with a PML boundary condition in all simulation boundaries. It is important to note that, for our array geometries, the resonant frequency computed with an FDTD for the localized resonance mode of a single metal square lies too far to the red to interact directly with the grating-coupled SPP mode. A strong direct interaction has been predicted for a similar metamaterial when the localized mode is energetically degenerate with the grating-coupled SPP mode, leading to an avoided crossing [20,30]. In our case, as shown in Fig. 10, the scattering cross section of a 140 nm single square is computed to exhibit a magnetic resonance mode at $\sim 1140\mathrm{nm}$, which is spectrally off scale in the period-dependent dispersion plot for 140 nm squares in Fig. 4(a). In addition, the single-square resonance is spectrally very broad. The breadth of this localized resonance mode is such that its spectral wings overlap with the propagating SPP. This overlap enhances the relatively strong localized magnetic mode observed for the field intensity distribution in Figs. 6(g) and 6(h), and strengthens the traveling SPP through “borrowed intensity.”

In addition to the SPPs that propagate at the Au-AlN interface between squares, we also find that the AlN dielectric layer between the Au square and the Au substrate supports both TM and very lossy TE MIM modes. The two modes do not exist in the one-dimensional MIM structure. These modes can also be expected to couple diffractively and play a role, especially once the Au square size increases to cover a large fraction of the array area. Focusing again on the reddest (TM) mode, we can roughly approximate the coupling condition when two types of in-plane TM modes participate with the expression $k_{\text{mim}}s+k_{\text{spp}}(p-s)=2\pi m$, where $k_{\text{mim}}$ is the wavevector of the SPP supported in the gap between square and substrate, $k_{\text{spp}}$ is the wavevector of the AlN/Au SPP between squares, $s$ is the square side length, $p$ is the array period, and $m$ is a diffraction order that here we take to be unity. The formula simply states that, at a diffractive resonance, a total phase of $2\pi$ accumulates as a wave propagates across a unit cell. That is, an SPP wave travels from the edge of one square to the edge of an adjacent square over a distance ($p-s$), where it end-couples to an MIM SPP, which then propagates the length $s$ of the square. Expressed in terms of modal indices and the free-space wavelength ${\lambda }_0$, the coupling condition becomes

As described above, the TM character of the reddest mode implicit in Eq. (2) leads to field intensity patterns consistent with a grating-coupled SPP traveling in the x-direction for an array with 100 nm squares and a large 460 nm period, Figs. 6(d)–6(f). The TM character of the reddest mode is also evident as square size increases, as seen in the computed intensity patterns of Figs. 7(d)–7(f) for 180 nm squares, Figs. 8(d)–8(f) for 260 nm squares, and Figs. 9(d)–9(f) for 340 nm squares. The strength of the localized fields follows the strength of the far-field reflectance dips, becoming weaker and then stronger as square size increases. By the largest square size, the TM wave traveling in the x-direction encounters mostly the MIM configuration. The weaker absorption occurs for square sizes where the in-plane wave propagates roughly equally in slab and MIM configurations. The simulations thus show that one can achieve a desired absorption wavelength by controlling pitch, but also can control independently the strength of the absorption with square size.

In addition to the reddest mode considered so far, two closely spaced grating-coupled bands appear in Fig. 4 at bluer wavelengths. The dispersions given by Eq. (2) for modal indices computed with transfer–matrix methods do not overlap these modes as well as they do for the TM reddest mode. The spectral ordering computed with transfer matrices implies that the bluest mode in Fig. 4(a) is a TE [01] slab-waveguide mode, and the intermediate (next reddest) mode is the SPP [11] mode [30]. However, computed field intensity distributions do not permit an unambiguous assignment, for example, as displayed at the resonant wavelength of arrays comprising 100 nm squares in Figs. 6(a)–6(f). In these distributions, a TE-standing wave appears to be propagating in the y-direction in Fig. 6(d), which pertains to the intermediate mode at 693 nm [solid white line in Fig. 4(d)], because the intensity of ${|E|}^2$ is strong at the unit cell edges that are parallel to the x-axis. A y-propagating TE mode is consistent with the x-polarized incident radiation. However, a close inspection of ${|H|}^2$ in the accompanying Fig. 6(e) shows interference with a mode of [11] character (i.e., intensity modulation along lines at 45° to the x-axis). Similarly, the field intensity distributions of Figs. 6(a)–6(c), which pertain to the bluest grating-coupled mode [643 nm, white dashed line in Fig. 5(d)], display a mixed character. It may not be surprising that the field intensity distributions are ambiguous, given the near degeneracy of the bluest and intermediate grating-coupled modes. In fact, these modes for a 460 nm array period appear to merge spectrally and overlap for square sizes between $\sim 175$ and $\sim 350\mathrm{nm}$ as per Fig. 5(d), and are not resolved for smaller periods [Figs. 5(a)–5(c)]. Inspection of the field intensity distributions for these modes as square size increases show that they are increasingly consistent with a TE mode propagating in the y-direction, i.e., with a strong E-field at the unit cell boundary parallel to the x-axis. Hence, we identify the presence of both TM and TE modes, which enable absorption to occur over at least two bands spanning the visible and near IR.

4. SUMMARY

We carried out comprehensive experimental and numerical investigations for the plasmon resonance modes of the MIM plasmon resonance structure in the visible and near-IR spectral range. Numerical simulations reproduced well the absorption bands measured in reflectance spectra. The linear dispersions of the absorption modes with an array period, and the computed electric and magnetic field intensity patterns establish that the modes are primarily because of the grating coupling of the normally incident light into attenuating in-plane traveling waves. Both the TE slab-waveguide mode and the TM SPP waves are excited simultaneously, which provides a means of creating strong absorption bands in both the visible and near-IR spectral ranges. It is also found that a localized mode associated with the well-known plasmon magnetic resonance of a single square strengthens the near-IR SPP band for small square sizes. For larger square sizes, this near-IR band is further influenced by square size as the SPP assumes increasing MIM character, and, consequently, weakly shifts to the red. Reflectance as small as 5.3% has been observed, and numerical simulations indicate that even stronger absorption is possible. The results in this paper can help in the design of perfect light absorbers in the visible and near-IR spectral range for a variety of applications.