1. Introduction

Subwavelength metal nanostructures enhance light absorption via localized surface plasmon resonance [1]. This phenomena can be used for a wide range of applications such as biosensing [2], solar optical energy harvesting [3], and enhanced photodetection [4]. One widely investigated subwavelength metal nanostructure is the gap plasmon structure that consists of a patterned array of metal elements separated from a thick metal film by a nanoscale thickness dielectric gap layer. In the dielectric gap layer, the electromagnetic field is strongly enhanced at resonance, leading to perfect or near-perfect light absorption at the resonance wavelength [5,6]. Gap plasmon structure perfect and near-perfect light absorbers have been investigated in visible [7,8], infrared [9–15], microwave [16–19], and terahertz [20–24] frequencies. Simple periodic gap plasmon light absorbers only work in a narrow spectral band. Since wideband perfect absorption is desired for many applications, various approaches have been proposed to broaden the absorption bandwidth with complex gap plasmon structures [8,11,12] or intentionally randomized nanostructure element distributions [25,26]. Indeed, these approaches result in broadened absorption band, however, the improvement comes at the expense of increased region to region gap element density variations, which limit the uniformity of large-area device performance.

In metal-insulator-metal (MIM) gap plasmon metasurfaces, enhanced light absorption arises from coupling of incident light to the localized and non-localized resonance modes that are dependent on patterned metal particle size and periodicity [27]. Periodic MIM structures support a localized plasmon resonance mode and a non-localized guided optical resonance mode. If periodicity is disturbed and inter-element distances vary from one area to another area, both the localized plasmon resonance mode and non-localized guided optical resonance mode become non-uniformly distributed. The extreme case is the completely random structure where the positions of all elements have a broad distribution of inter-particle distances, correspondingly a broader distribution of resonance modes. The approach of using random structures has been applied to metallic apertures [28,29] and metallic elements on dielectrics [30–34] through lithographic patterning or thermal annealing. However, an important problem of the complete randomness of element locations is the increased variation of density of elements as the device area increases. Specifically, as the radius R of a sampling circle in a planar system increases, the area to area variance of the density of elements increases with ${R^2}$. Therefore, as the device size becomes large, the density of elements varies wildly from area to area, rendering that some areas of the random structure have no elements at all and become useless while other areas may have a heavy cluster of elements. Different from the random pattern, a hyperuniform disordered pattern is a limited disorder pattern that consists of an ensemble of seemingly randomly positioned elements, but the randomness of the element positions is limited [35,36]. It has been discovered that hyperuniform disordered patterns widely exist in nature. In a hyperuniform pattern, the positions of elements have a limited displacement from their corresponding periodic locations. Furthermore, the density of elements has a smaller variation from one region to another region than the density of elements of the random pattern does. Mathematical definition of a two-dimensional hyperuniform pattern is that the variance of density of elements, i. e., the variance of number of elements in a circle area of a fixed radius R, increases proportionally with ${R^1}$, as opposed to ${R^2}\; $ in random distribution patterns. Therefore, a hyperuniform pattern results in drastically reduced fluctuation of device performance over a large area. Hyperuniform patterns were originally found in nature [35,37]. Previously, the concept of hyperuniformity has been applied to engineer optical transparency [38] and photonic bandgap materials [39,40]. Recently, wide spectral band and wide angle absorption have been reported in hyperuniform disordered surface structures [41,42]. Hyperuniform disordered pattern metasurfaces have also been investigated for reducing directional scattering from structured metasurface [43]. In this work, we report the first investigation on hyperuniform disordered metal-insulator-metal gap plasmon metasurfaces, and demonstrate wideband near-perfect absorption in the visible and near infra-red range.

2. Design of a hyperuniform disordered gap plasmon metasurface

Hyperuniform disordered patterns are different from periodic patterns and random patterns. To illustrate the difference between them, a periodic pattern, a hyperuniform disordered pattern, and a random distribution pattern are shown in Figs. 1(a)-(c), respectively. In the periodic pattern in Fig. 1(a), particle elements are arranged in a periodic square lattice. In the hyperuniform disordered pattern in Fig. 1(b), locations of elements are randomly distributed within a limited displacement range d from their lattice centers, where the d is the maximal range of shift of x and y coordinates away from the lattice centers. In the hyperuniform disordered pattern, only one element can be found in a unit cell within a limited displacement range d. In the random pattern shown in Fig. 1(c), multiple elements and clusters of elements can exist in a unit cell. The property of hyperuniformity prevents forming particle clusters and overlapping which normally exist in random patterns.

 

Fig. 1. (a) A periodic pattern, (b) a hyperuniform disordered pattern where the center of each element has a limited range of random displacement from its periodic lattice centers, (c) the random pattern where particle overlapping and clusters are found. (d) Mean of number of elements for periodic pattern and hyperuniform patterns with limited random displacement of d=100 nm, 150 nm, 200 nm, and 250 nm, and the completely random pattern. (e) Variance of number of elements with sampling circle radius R for the periodic pattern, hyperuniform patterns with displacement limit of 100 nm, 150 nm, 200 nm, and 250 nm, and the random pattern. The variance of number of elements of the random pattern scales up with radius R as R².

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Before fabrication, hyperuniform disordered patterns with different variances of element density are generated with a Matlab script implementing the following process. First, the size of the square elements is chosen at 180 nm and the coordinates of the element are saved. Next, points of square elements are placed in periodic arrays with period ranging from 450 nm to 550 nm, in 25 nm steps. Then, center coordinates of the square elements are randomly displaced from their original periodic lattice points. The distribution of displacement is uniform, and the maximal shift distance is defined by the maximal displacement ranging from 100 nm to 250 nm, with 50 nm step. The x and y coordinates of all points of hyperuniform patterns are written in a .dc2 file (DesignCad software format). Then, cad files of hyperuniform elements with different periods and different maximal displacements are loaded for electron beam lithography patterning. The sizes of the gold element squares in all patterns (periodic, hyperuniform, and random) are fixed at 180 nm.

To illustrate the difference between the hyperuniform disordered pattern and the random pattern, we calculated the mean and variance of the number of elements within a large sampling circle of radius R of computer-generated periodic pattern, hyperuniform pattern, and the random pattern, respectively. The variance of number of elements V_ar sampled within a circle with radius R is,

Because the sampling circle area increases as R², the means of number of elements of all three kinds of patterns increase with R² as shown in Fig. 1(d). However, the scaling of variance with radius R is quite different for periodic, hyperuniform disordered, and random patterns as shown in Fig. 1(e). For the periodic pattern, the variance of number of elements is always zero, because the locations of all elements in the periodic pattern are fixed in their lattice center locations. For hyperuniform patterns with displacement limit d=100, 150, 200, 250 nm, the variance increases with the radius R, conforming to the expectation for hyperuniform patterns [33]. For the random pattern, the variance of number of elements scales with R² as shown by the black line curve in Fig. 1(e). Variance of the random pattern grows faster than the variance of hyperuniform disordered patterns as the sampling circle radius R increases.

3. Hyperuniform disordered gap plasmon metasurface fabrication and measurement results

In the experiment, periodic pattern, hyperuniform disordered pattern, and complete random pattern gap plasmon metasurface devices were fabricated by using a standard e-beam lithography patterning and dry etching process. During the fabrication process, a titanium adhesion layer of 2 nm was first deposited on a silicon wafer using electron beam evaporation, then the process was followed by the deposition of a 300 nm gold film using a sputter machine. On top of the gold film, a 90 nm thick aluminum nitride film was grown using atomic layer deposition. Metal squares of different patterns were directly written in an e-beam resist layer spin-coated on the aluminum nitride film by using a standard e-beam lithography process. In the e-beam lithography process, a 190 nm thin layer of e-beam resist (495 PMMA A4) was first spin-coated at 2500 RPM and baked at 180° C for two minutes. Then, periodic, hyperuniform, and random patterns were written in the e-beam resist layer with the focused electron beam in an area of 220 × 220 µm each. The actual size of patterned e-beam resist elements is 210 nm, which is bigger than the intended size of 180 nm in the Designcad file due to the proximity effect. After development in IPA:MIBK 3:1 solution, an oxygen plasma descum process was carried out for 30 seconds to clean the e-beam resist residues from the e-beam exposed area. Then, an approximate 2 nm titanium layer and a 60 nm gold layer were deposited on the sample by thermal evaporation, followed by lift-off using acetone to dissolve the e-beam resist and cleaning in isopropyl alcohol. Figure 2(a) illustrates the hyperuniform disordered gap plasmon metasurface structure. The structure consists of a layer of patterned gold squares of 60 nm thickness, an aluminum nitride dielectric layer of 90 nm thickness, and an optically thick gold film of 300 nm thickness on a silicon wafer. When the displacement d is zero, the distribution of patterned gold elements has a periodic pattern. When d is infinitely large, the distribution of gold elements is a complete random pattern.

 

Fig. 2. (a) Schematic of the hyperuniform disordered gap plasmon resonance structure where the distribution of the metal squares deviates from the distribution of the periodic pattern, but is not random. Scanning electron micrograph of (b) periodically patterned gold nano-disk gap plasmon metasurface, hyperuniformly distributed gold squares with displacement limit of (c) 100 nm and (d) 250 nm, and (e) randomly patterned gold disks.

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Figure 2(b) shows a scanning electron micrograph (SEM) picture of a fabricated periodic gap plasmon metasurface device. The gold particle elements are squares with a size of 210 nm by 210 nm. When the maximal displacement d is not zero, the period becomes ill-defined and the structure becomes hyperuniform disordered as shown in Figs. 2(c) and (d). Because the periodicity is lost, hyperuniform disordered patterns can only be discussed in terms of the particle area density and the maximal displacement. The particle area densities are calculated by dividing the number of total gold squares by a large sample area of 220 µm × 220 µm. Figures 2(c) and (d) are SEM pictures of fabricated hyperuniform disordered patterns with maximal displacement of d=100 nm and 250 nm, respectively. Figure 2 (e) shows a SEM picture of a fabricated random distribution pattern (d=∞). In Fig. 2(b), the gold particle distribution is periodic with a period of 500 nm. As d is increased to 100 nm and 250 nm, the gold particle pattern appears disordered, as seen in Figs. 2(c) and (d). When d increases to 250 nm, some gold particles become connected to each other. When d is larger than 500 nm, some gold particles start to overlap with each other. When the maximal displacement d is infinite (much larger than $1/\sqrt {\; density} $), hyperuniform disordered patterns become random patterns as shown in Fig. 2(e). It can be seen in Fig. 2(e) that the particle density of random pattern varies significantly from one area to another area, resulting in overlaps of gold particles on the surface. In this work, we fabricated hyperuniform disordered gap plasmon structures with particle density of 4.9, 4.4, 4.0, 3.6, and 3.3 particles $/\mathrm{\mu}{\textrm{m}^2}$, respectively. These hyperuniform disordered patterns have the same particle densities as the corresponding periodic patterns of 450 nm, 475 nm, 500 nm, 525 nm, and 550 nm period, respectively.

Optical spectra of reflectance from fabricated devices were measured by using a fiber pigtailed broadband halogen light source and an optical spectrometer (StellarNet, Inc.). In the measurement setup, a broadband light from a multimode fiber was normally incident to the device surface. The multimode fiber has a core diameter of 62.5 µm. The same optical fiber was used to collect the reflected light and send it to the optical spectrometer by using a home-made broadband fiber optical beam splitter. The measurement setup was first calibrated by measuring the spectrum of reflection from a thick silver film as a mirror. Figure 3 shows measured optical reflectance spectra from fabricated devices with different distribution patterns and different densities of particle elements. The element density is 4.9 particles/µm² in Fig. 3 (a), 4.4 particles/µm² in Fig. 3 (b), 4.0 particles/µm² in Fig. 3 (c), and 3.6 particles/µm² in Fig. 3 (d). In each figure, optical reflectance spectra of six different particle distribution patterns are plotted. Reflectance spectrum is plotted in blue for the periodic pattern, in black for the complete random pattern. Reflectance spectral curves from hyperuniform devices with different limits of particle displacement d, are plotted in green for d = 100 nm, in red for d = 150 nm, in orange for d = 200 nm, and in purple for d = 250 nm.

 

Fig. 3. Reflectance of hyperuniform disordered gap-plasmon metasurface devices of gold square densities of (a) 4.9 particles/$\mathrm{\mu}{\textrm{m}^2}$, (b) 4.4 particles/$\mathrm{\mu}{\textrm{m}^2}$, (c) 4.0 particles/$\mathrm{\mu}{\textrm{m}^2}$, and (d) 3.6 particles/$\mathrm{\mu}{\textrm{m}^2}$. The blue line curves are reflectance spectra of periodic structures with same particle densities as the hyperuniform disordered patterns. The black line curves are reflectance spectra of random structures with same means of density of the hyperuniform patterns.

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For periodic patterns, reflectance spectra exhibit two sharp reflection dips corresponding to two strong absorption bands. The two absorption bands correspond to different resonance modes. The higher energy mode in the blue side of the absorption spectrum is caused by the optical guided resonance mode propagating in the direction orthogonal to the electric field (a TE wave). The absorption band in red-side of the spectrum is caused by the coupled localized gap plasmon resonance mode which propagates in the direction of electric field (a TM wave) [27]. For hyperuniform disordered patterns, as we start to allocate the particle elements with a small deviation from the periodic pattern with d = 100 nm, the guided mode resonance in the blue side of the spectrum disappears quickly, while the absorption band in the red side of spectrum stays in about the same wavelength. This indicates that the resonance mode in the blue side is a long range coupled optical guided mode that depends more on the periodicity of the structure than the localized gap plasmon resonance mode in the red side of the spectrum. As the displacement variation range is increased, the long-range optical resonance mode disappears and a broad reflectance grows in towards the red and near infrared regions. The resonant feature associated with the localized gap plasmon resonance remains unchanged although the absorption broadens to red side of the spectrum. These results indicate that the long-range coupled guided optical resonance weakens as the periodicity is broken and the broad absorption band in the red side of spectral region is due to the broadening of the gap-plasmon resonance modes in hyperuniform disordered structures. Measurement results of random pattern devices show strong absorption in the 1.0 - 1.2 μm spectral region at the expense of low absorptance in the visible region. The absorption of the random pattern device in the 1.0 - 1.2 μm is due to the overlapping and touching of gold particles. For MIM gap plasmon structure metasurfaces, perfect absorption associated with the localized gap plasmon resonance is due to critical coupling of incident optical wave to the localized gap plasmon resonance mode [44]. Because of the disorder of the gap plasmon resonator distribution, the gap plasmon resonance modes also have a distribution which enables broadening of the absorption spectrum.

Reflectance spectrum variation with different particle densities is more clearly seen in Fig. 4, which shows the absorption spectra of structures with the same limit of displacement ranges but different element densities. When the displacement range is zero, as shown in Fig. 4(a), the absorption bands due to localized plasmon resonance and non-localized optical resonance modes are clearly distinguishable from each other. Resonance wavelengths of both modes shifts with lattice period, as detailed in the inset of Fig. 4(a). The blue dot line in the inset shows the resonance wavelength of the guided resonance mode, which is sensitive to change of period. The red dot line in the inset presents the resonance wavelength of the gap plasmon mode which is less sensitive to the change of the period. When periodicity is broken, as shown in Fig. 4(b) with d = 100 nm, the reflectance spectra broadens because the non-localized optical resonance mode becomes weaker. This trend continues to the hyperuniform pattern of d = 250 nm shown in Fig. 4(c), where the absorption band due to localized surface plasmon resonance becomes significantly wider. For gold particle densities of 4.9 particles $/\mathrm{\mu}{\textrm{m}^2}$ and 4.4 particles $/\mathrm{\mu}{\textrm{m}^2}$, the lattice spacing is small enough that some of gold square elements touch each other as seen in Fig. 2(d). Touching of gold particles means that the size of some plasmon resonators is doubled, resulting in a much longer resonance wavelength. The single and double-sized resonators result in two resonance wavelengths. The onset of this behavior is clearly seen in the blue and green line curves of Fig. 4(c) for particles densities of 4.4 and 4.9 particles/μm². When gold particle densities are as small as 4.0, 3.6, and 3.3 particles $/\mathrm{\mu}{\textrm{m}^2}$, particles do not have overlap so only one wide absorption band exists. In the random structures, particle touching and overlapping happen more frequently than touching of two gold particles in hyperuniform patterns. This means that random structures have gold elements of multiple sizes and, as a result, reflectance spectrum of random structures is generally flatter than that of hyperuniform structure devices.

 

Fig. 4. (a) Reflectance spectra of fabricated periodic pattern metasurface devices with different periods of 450 nm, 475 nm, 500 nm, 525 nm, and 550 nm. (b) Reflectance spectra of fabricated hyperuniform disordered devices with different particle densities for a same particle displacement limited range d=100 nm from their periodic lattice points. (c) Reflectance spectra of fabricated hyperuniform disordered devices with different particle densities for a same particle displacement limited range of d=250 nm. (d) Reflectance spectra of fabricated completely random pattern devices for different means of particle element densities.

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As we reported previously [27], both the non-local optical resonance mode and localized gap plasmon resonance mode in the MIM structure depend on the period. Because the actual displacement varies from location to location, the resonance wavelengths of these modes also vary with location, resulting in a range of resonant wavelengths and broadened absorption in the reflectance spectrum. In measurements, we noticed the variation of reflectance spectrum with the measurement spot location for the random structure devices. Figure 4(d) shows the measured spectra of fabricated devices with best absorption performance in terms of absorption bandwidth.

4. Summary

In this work, we designed, fabricated, and characterized periodic, hyperuniform disordered, and random pattern gap plasmon metasurface devices. It is found that hyperuniform disordered gap plasmon metasurfaces exhibit broader absorption bands as the limit of the displacement range of disordered gap plasmon elements increases as expected. As the displacement limit increases to the boundary of the unit cell of the periodic lattice pattern, the absorption band approaches to the absorption band of the completely random gap plasmon resonance metasurface. Additionally, experimental results revealed two optical resonance modes that contribute to enhanced light absorption. The resonance mode in the short wavelength region vanishes quickly as the periodicity of the gap plasmon elements vanishes, indicating its nature of the long-range coupled optical resonance. The resonance mode in the long wavelength region is less sensitive to the reduction of the periodicity, indicating that the coherent coupling between gap plasmon resonators is weak for that mode and the nature of it is strong mode localization. Hyperuniform disordered gap plasmon patterns have controlled randomness of the gap plasmon element distributions, which has an advantage over completely random gap plasmon patterns in maintaining spatial uniformity of device performance.