Skip to content
BY 4.0 license Open Access Published by De Gruyter November 25, 2020

Epitaxial aluminum plasmonics covering full visible spectrum

  • Chang-Wei Cheng ORCID logo , Soniya S. Raja , Ching-Wen Chang , Xin-Quan Zhang , Po-Yen Liu , Yi-Hsien Lee , Chih-Kang Shih and Shangjr Gwo ORCID logo EMAIL logo
From the journal Nanophotonics

Abstract

Aluminum has attracted a great deal of attention as an alternative plasmonic material to silver and gold because of its natural abundance on Earth, material stability, unique spectral capability in the ultraviolet spectral region, and complementary metal-oxide-semiconductor compatibility. Surprisingly, in some recent studies, aluminum has been reported to outperform silver in the visible range due to its superior surface and interface properties. Here, we demonstrate excellent structural and optical properties measured for aluminum epitaxial films grown on sapphire substrates by molecular-beam epitaxy under ultrahigh vacuum growth conditions. Using the epitaxial growth technique, distinct advantages can be achieved for plasmonic applications, including high-fidelity nanofabrication and wafer-scale system integration. Moreover, the aluminum film thickness is controllable down to a few atomic monolayers, allowing for plasmonic ultrathin layer devices. Two kinds of aluminum plasmonic applications are reported here, including precisely engineered plasmonic substrates for surface-enhanced Raman spectroscopy and high-quality-factor plasmonic surface lattices based on standing localized surface plasmons and propagating surface plasmon polaritons, respectively, in the entire visible spectrum (400–700 nm).

1 Introduction

Plasmonics is a rapidly evolving field that takes advantage of strong light confinement and drastically enhanced light–matter interactions beyond the diffraction limit near the surfaces and interfaces of metal nanostructures. In the past few decades, remarkable advances based on plasmonic nanostructures, metamaterials, and metasurfaces have been made for surface-enhanced spectroscopies, sensors, photovoltaics, super-resolution microscopy and lithography, metalenses, biomedical therapeutics, nonlinear optics, and integrated nanophotonics [1], [2], [3]. However, there are still significant material issues to be resolved such that plasmonics can be elevated to a transformative technology for general applications.

One critical issue of plasmonics is related to the intrinsic properties of available plasmonic materials. Nearly all of the research results adopt noble metals (silver [Ag] and gold [Au] are the most popular choices) as the plasmonic materials because they exhibit negative real and small imaginary parts of dielectric function in the visible and near-infrared spectral regions. However, noble metals suffer from high material cost (Au), low material stability (Ag), and incompatibility with existing semiconducting technology (Ag, Au). Furthermore, owing to the interband transitions in noble metals, spectral responses of plasmonic devices are limited in some specific ranges. To overcome these difficulties, alternative plasmonic materials, such as aluminum (Al), copper (Cu), transition metal nitrides, conducting metal oxides, and graphene have been extensively pursued in recent years [4], [5], [6]. Among them, aluminum is particularly interesting because it acts as an ideal Drude metal except a narrow interband transition window in the near-infrared (at 800 nm) [7]. In particular, for the ultraviolet (UV) and deep-UV plasmonic applications, aluminum is the best plasmonic material due to the negative real and relatively small imaginary parts of aluminum dielectric function in the UV region.

Considering practical applications, aluminum is also a sustainable plasmonic material since it is naturally abundant in the Earth’s crust and has a native oxide protection layer (∼3–5 nm Al2O3) [8], [9]. However, aluminum was not previously considered as a good candidate for alternative plasmonic material [5] before the advent of high-quality aluminum nanocrystals [10], [11] and epitaxial films [9], [12], [13] with greatly improved material properties. During the past few years, the fast development of aluminum plasmonics has attract a great deal attention not only for the expected good performance of aluminum for UV plasmonics, such as UV surface-enhanced Raman spectroscopy (UV-SERS) [14], [15], plasmonic lasers [16], [17], [18], [19], [20], [21], [22], and deep-UV resonances [8], [23], but also for its unexpected excellent performance in the visible region, including complementary metal-oxide-semiconductor (CMOS)-compatible color filters [24], [25], [26], [27], [28], photocatalysis [29], nonlinear optics [30], [31], [32], and SERS [15], [33]. Very recently, aluminum has even been found to outperform silver in some important plasmonic applications [15], [34].

The key to understand these finding is that the performance of plasmonic materials depends not only on their intrinsic optical properties but also their material properties, such as crystallinity, surface and interface quality, as well as stability. In the literature, aluminum nanostructures and metasurface are typically fabricated by lithographic methods using thermally evaporated aluminum films. In such cases, amorphous or polycrystalline film growth, as well as residual oxygen in the growth chamber, will eventually affect the performance of aluminum-based plasmonic devices. Recently, epitaxial aluminum film growth on commercially available substrates (silicon [13], [35], [36], GaAs [12], [37], [38], sapphire [9], [39], [40]) has been developed by using the molecular-beam epitaxy (MBE) technique under ultrahigh vacuum conditions. The availability of high-quality aluminum epitaxial films opens the way to explore aluminum plasmonics for real-world applications [8], [41], [42].

Here, we report on aluminum epitaxial films grown on sapphire substrates by MBE. This heteroepitaxial system is possible since the hexagonal lattice of Al (111) plane is close to that of the c-plane sapphire substrate (lattice mismatch is about 3.9%). Using these aluminum epitaxial films, we can have some distinct advantages for plasmonic applications, including high-fidelity nanofabrication for precise control of surface plasmon resonances owing to the single-crystalline material structure and large-scale, highly uniform plasmonic structures required for SERS substrates and high-quality-factor (high-Q) plasmonic surface lattices. Moreover, the aluminum film thickness is controllable down to a few atomic monolayers, allowing for ultrathin metal layer plasmonic applications [43], [44], [45]. It is worth noting that, since aluminum is considered as the “silicon” of superconductivity [46], aluminum epitaxial films can also be used as the building material for quantum computers requiring high-performance superconducting qubits.

2 Epitaxial growth and structural properties

Previous works on silver epitaxial films and nanostructures have demonstrated that crystalline properties and surface morphologies play an important role in plasmonic applications [47], [48], [49], [50], [51], [52], [53]. Especially, uniform and controllable plasmonic hot spots can realized by high-fidelity top-down nanofabrication on ultrasmooth, single-crystalline Ag colloidal crystals [53], [54]. In this work, aluminum epitaxial growth was conducted by using a MBE system under ultrahigh vacuum conditions. Two-inch double-side-polished c-plane sapphire (0001) wafers were used as the substrates, and the base vacuum pressure was kept about 1 × 10−10 Torr during growth. Before growth, the c-plane sapphire substrate was thermally cleaned at 950 °C for 2 h. A streaky reflection high-energy electron diffraction (RHEED) pattern of the c-plane sapphire surface can be obtained after this cleaning step (Figure 1A). Then, aluminum was evaporated by using a Kundsen cell. The deposition rate (about 200 nm/h) was controlled by the cell temperature, and the substrate temperature was maintained at room temperature (∼300 K) during growth. A streaky RHEED pattern (Figure 1A) of aluminum film indicates a smooth film morphology during epitaxial growth.

Figure 1: Structural properties of epitaxial aluminum films on sapphire substrates. (A) In situ reflection high-energy electron diffraction (RHEED) patterns of c-plane sapphire and epitaxial aluminum film. (B) The X-ray diffraction patterns (2θ-scan) for 4.4 nm (∼19 ML), 10.8 nm (∼47 ML), 20.0 nm (∼ 87 ML) and 200 nm-thick films, showing clearly the Al (111) peak, X-ray inference fringes, and the c-plane sapphire peak. The experimental data and the fitting curve are shown by black and red line, respectively. (C) The in-plane X-ray diffraction patterns (ϕ-scan) of Al (220) and c-sapphire (11–26) planes. (D) Scanning electron microscope (SEM) image of a focused ion beam patterned epitaxial aluminum. (E) High-resolution transmission electron microscope (TEM) image of an epitaxial aluminum film showing an abrupt interface between the epitaxial aluminum film and the c-sapphire substrate. The inset shows the fast Fourier transform of Al lattice along the [02-2] zone axis. (F) Atomic force microscope (AFM) image (10 × 10 μm2) taken on the native oxide (∼3 nm)-covered aluminum film. The film roughness is about 0.2 nm.
Figure 1:

Structural properties of epitaxial aluminum films on sapphire substrates. (A) In situ reflection high-energy electron diffraction (RHEED) patterns of c-plane sapphire and epitaxial aluminum film. (B) The X-ray diffraction patterns (2θ-scan) for 4.4 nm (∼19 ML), 10.8 nm (∼47 ML), 20.0 nm (∼ 87 ML) and 200 nm-thick films, showing clearly the Al (111) peak, X-ray inference fringes, and the c-plane sapphire peak. The experimental data and the fitting curve are shown by black and red line, respectively. (C) The in-plane X-ray diffraction patterns (ϕ-scan) of Al (220) and c-sapphire (11–26) planes. (D) Scanning electron microscope (SEM) image of a focused ion beam patterned epitaxial aluminum. (E) High-resolution transmission electron microscope (TEM) image of an epitaxial aluminum film showing an abrupt interface between the epitaxial aluminum film and the c-sapphire substrate. The inset shows the fast Fourier transform of Al lattice along the [02-2] zone axis. (F) Atomic force microscope (AFM) image (10 × 10 μm2) taken on the native oxide (∼3 nm)-covered aluminum film. The film roughness is about 0.2 nm.

The crystal orientation of epitaxial aluminum film was measured by X-ray diffraction (XRD) using the copper Kα1 line at the wavelength of 0.15406 nm. The XRD pattern (Figure 1B) shows the aluminum film is single-crystalline and grown along the (111) direction. The Al (111) and c-sapphire (0006) diffraction peaks are at about 38.5° and 42°, respectively. Due to the abrupt aluminum/sapphire interface and smooth film surface morphology, clear X-ray interference fringes of ultrathin aluminum films can be observed by high-resolution XRD (Figure 1B). Thus, we can precisely determine the film thickness, ranging from a few nanometers, 4.4 nm (∼19 monolayers [ML]), 10.8 nm (∼47 ML), and 20.0 nm (∼87 ML) to bulk-like (∼200 nm). In Figure 1C, we show the in-plane X-ray diffraction scan performed for the Al (220) and c-sapphire (11–26) peaks, confirming the expected six-fold in-plane symmetry for epitaxial growth.

In Figure 1D, the scanning electron microscope image of a patterned aluminum epitaxial film (this pattern is adopted from an element periodic table) demonstrates that high-fidelity nanofabrication can be achieved via focused ion beam (FIB) lithography (FEI Helios NanoLab 600i) at an ion beam current of 7.7 pA due to the single-crystalline film properties. The high-resolution transmission electron microscope image (Figure 1E) shows the abrupt interface between the epitaxial aluminum film and the sapphire substrate. The root-mean-square (RMS) roughness of epitaxial aluminum film surface was measured by atomic force microscope (AFM), showing the RMS roughness of epitaxial aluminum film is atomically smooth (about 0.2 nm, Figure 1F).

3 Optical properties

The wafer scale epitaxial aluminum film is mirror-like (Figure 2A) due to a high optical reflectivity. We can compare the dielectric functions of literature data measured by spectroscopic ellipsometry (SE) for silver [51] and aluminum [9], [13] epitaxial films (Figure 2B and C). Previous studies have shown the Drude–Lorentz model can be used to fit dielectric functions of epitaxial silver and aluminum films [51], [55], which is expressed as

(1)ε(ω)=ε1(ω)+iε2(ω)=εbωp2ω(ω+iγp)+j=1Nfjω˜j2(ω˜j2ω2iωΓj),

where εb is the polarization response from the core electrons (background permittivity), ωp is the bulk plasmon frequency, γp is the relaxation rate (electron-electron scattering loss), fj and ω˜j are the strengths and resonant frequencies of interband transitions (N is the number of interband transitions used for modeling), and Γj is the damping rates of interband transitions. In Figure 2C (inset), aluminum is clearly a better plasmonic material in the UV region compared to silver. In the following sections, we will show that epitaxial aluminum plasmonics can even be extended to cover the full visible spectral region.

Figure 2: Optical properties of Al and Ag epitaxial films. (A) Optical image of Al epitaxial film on a 2-inch, c-plane sapphire substrate. (B) Real part of the dielectric function (ε1) extracted from the literature data as a function of wavelength (blue solid curve). (C) Imaginary part of the dielectric constant (ε2). For comparison, literature data of epitaxial Al (blue [9] and red line [13]) and Ag (black dash line [51]). The inset shows the wavelength from 287 to 380 nm. (D) The quality factor of SPP (QSPP=Re(kspp)/Im(kspp)≈2ε1+εdε1εd(ε1)2ε2)$\left({Q}_{\text{SPP}}=\mathrm{Re}\left({k}_{\text{spp}}\right)/\mathrm{Im}\left({k}_{\text{spp}}\right)\approx 2\frac{{\varepsilon }_{1}+{\varepsilon }_{d}}{{\varepsilon }_{1}{\varepsilon }_{d}}\frac{{\left({\varepsilon }_{1}\right)}^{2}}{{\varepsilon }_{2}}\right)$ comparison for Al and Ag epitaxial films. The inset shows the localized surface plasmons (LSP) quality factor (QLSP=ω(dε1dω)/2ε2)$\left({Q}_{\text{LSP}}=\omega \left(d{\varepsilon }_{1}}{d\omega }\right)/2{\varepsilon }_{2}\right)$ comparison for Al and Ag epitaxial films.
Figure 2:

Optical properties of Al and Ag epitaxial films. (A) Optical image of Al epitaxial film on a 2-inch, c-plane sapphire substrate. (B) Real part of the dielectric function (ε1) extracted from the literature data as a function of wavelength (blue solid curve). (C) Imaginary part of the dielectric constant (ε2). For comparison, literature data of epitaxial Al (blue [9] and red line [13]) and Ag (black dash line [51]). The inset shows the wavelength from 287 to 380 nm. (D) The quality factor of SPP (QSPP=Re(kspp)/Im(kspp)2ε1+εdε1εd(ε1)2ε2) comparison for Al and Ag epitaxial films. The inset shows the localized surface plasmons (LSP) quality factor (QLSP=ω(dε1dω)/2ε2) comparison for Al and Ag epitaxial films.

Silver [51] and aluminum [13] epitaxial films with the best material quality were previously reported using a refined two-step growth process that shows the lowest optical loss. However, although the two-step growth technique can lead to superior film quality, it is a time-consuming process and growth conditions at cryogenic temperatures are difficult to achieve. Instead, room temperature and near-zero-Celsius-degree growth conditions are widely used for aluminum epitaxial films grown on high-quality commercial substrates (silicon [35], [36], gallium arsenide [37], [38], and sapphire [9]). There are two types of surface plasmons on these films: propagating surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs). To compare the optical properties of epitaxial aluminum film between two different approaches [9], [13], we plot SPP (QSPP) and LSP (QLSP) quality factors in Figure 2D for both cases using the published data, where QSPP=Re(kSPP)Im(kSPP)2ε1+εdε1εd(ε1)2ε2 [5] can be derived from the plasmon dispersion relation kSPP=εdε(ω)εd+ε(ω)k0=neffk0=Re(kSPP)+iIm(kSPP)=2πRe(neff)λ+2πiIm(neff)λ (εd is the dielectric constant of surrounding medium, k0=2πλ is the vacuum wavenumber, and neff is the SPP effective index) and QLSP can be expressed as QLSP=ω(dε1dω)/2ε2 [56]. These comparison results indicate the optical properties of the room temperature–grown aluminum epitaxial films is indeed close to that grown by the two-step growth process.

4 Surface white light interface and plasmon propagation length

To demonstrate long SPP propagation length in the full visible spectral region, we fabricated surface double-groove structures by FIB milling. We measured SPP interference spectra using a white-light interference method [47], [48], [49], [52], [53] (WLI, Figure 3A). The incident SPPs are generated by a halogen light source with an oblique incident angle around 75–80° (see Supplementary material for experimental setup). The incident photons partially coupled to surface plasmons, which propagate along the aluminum surface covered with a 3-nm-thick native oxide (see Supplementary material for more details about the influence of oxide layer on optical properties). In order to reduce grain and surface scattering effects in the WLI measurements, single-crystalline and atomic-smooth aluminum surface are necessary, as reported in the previous works [47], [48], [49], [52], [53].

Figure 3: White-light surface plasmon interference. (A) Schematic of white-light interference method for measuring the surface plasmon polaritons (SPP) propagation length. (B) Scattering spectrum collected by the optical microscope objective. The inset is the optical scattering image from the double-groove structure. The groove separation (D) is 5 μm.
Figure 3:

White-light surface plasmon interference. (A) Schematic of white-light interference method for measuring the surface plasmon polaritons (SPP) propagation length. (B) Scattering spectrum collected by the optical microscope objective. The inset is the optical scattering image from the double-groove structure. The groove separation (D) is 5 μm.

Figure 3B shows a clearly interference spectrum, indicating that propagating SPPs can reflect back and forth multiple times between two grooves. After multiple reflections and decoupling into far-field radiation at the incident groove, a microscope objective (100×, numerical aperture = 0.8) is used to collect the decoupled photons. The standard constructive and destructive interference conditions can be used to find the real part of SPP wave number

(2)Peaks:2Re(kSPP)D=2qπDips:2Re(kSPP)D=(2q+1)π,

where D is the distance between two grooves, and q is an arbitrary integer number (q = 0, 1, 2, 3, …). In order to determine the exact q value and the real part of neff, we utilize the extracted dielectric function by SE in the long wavelength region for this purpose. After that, we can apply the Drude–Lorentz model (Eq. 1) to determine the imaginary part of neff. In general, the dielectric function acquired in this approach can match well with that determined by SE, and it has been confirmed for the present case of aluminum epitaxial film.

By using the conventional theory of Fabry–Pérot interferometry [57], we can further derive the electric field of scattered SPPs at the incident groove (ESPP(λ)) as the following:

(3)ESPP(λ)=Iinc(λ)1Rexp(2Im(kSPP)D)exp(2iRe(kSPP)D)=Iinc(λ)1(RA)exp(2iRe(kSPP)D),

where Iinc(λ) is the incident SPP field intensity at the incident groove, R is the SPP reflectivity of both grooves, and Aexp(2Im(kSPP)D)=exp(D/Lspp) is the plasmonic propagation loss (absorption) factor between two grooves. Here, Lspp1/2Im(kSPP)=λ/4πIm(neff) is defined as the surface plasmon propagation length. According to Eq. (3), the ratio of interference maximum (Imax) and minimum (Imin) intensities can be expressed as the following:

(4)ImaxImin=max(|ESPP|2)min(|ESPP|2)=(1+RA)2(1RA)2=(1+r)2(1r)2,

where rRA is the round-trip reflectivity between two grooves, taking into account the plasmonic material loss. Furthermore, we can define the relative modulation depth [47]

(5)ΔIImin=ImaxIminImin=4r(1r)2,

where ΔI=ImaxImin is the difference between the envelopes enclosing the intensity maxima and minima of the WLI pattern, and it indicates quantitatively how pronounced the SPP interference effect is.

In our measurements, Imax(λ), Imin(λ), as well as r(λ) can be determined by experiment, as shown in Figure 3B. Furthermore, we can determine the values of A, Lspp and R=r/A by using the dielectric function. Significant advantages of the WLI method are that we can directly correlate with the dielectric function determined by SE and measure the surface plasmon propagation lengths on the actual film surface in the full visible spectral range. As shown in Figure 3B, we can also numerically fit the experimental interference pattern with the following expression

(6)Iinterference(λ)=Imax(λ)(1r)2|1Rexp(4πi(nSPP)D/λ)|2,

where the fitting parameters Rmax is found to be ∼0.25 at 550 nm and LSPP ranges from 5 to 13 μm in the spectral range of 400–700 nm. The plasmon propagation length measured for the aluminum epitaxial film is comparable to that measured for single-crystalline silver nanowires at 785 nm (10 μm [47]).

5 Surface-enhanced Raman spectroscopy

Following the discussion of fundamental structural and optical properties, we now turn to the demonstration of epitaxial film–based plasmonic applications, including aluminum SERS substrate [15] and plasmonic surface lattices [22], [34], [58]. For the SERS study (see Supplementary material for experimental setup), we use a vertically stacked molybdenum disulfide (MoS2)/tungsten diselenide (WSe2) heterostructures on top of the aluminum SERS substrate (nanogroove grating) as a uniform two-dimensional analyte to evaluate the SERS performance (Figure 4A). The nanogroove array structure fabricated on the aluminum epitaxial film has the benefits of large-area spatial uniformity and wide-spectral tunability because of high-quality material properties.

Figure 4: Raman intensity mapping of a vertically stacked monolayer transition metal dichalcogenide (TMDC) heterostucture. (A) Schematic of the surface-enhanced Raman spectroscopy (SERS) substrate structure, consisting of a grating with the size of 12 × 8 µm2. The grating is sequentially stacked with MoS2 and WSe2 monolayers (WSe2 on top). (B) Combining Raman intensity mapping of the A1g peak (403 cm−1) of MoS2 monolayer and the E2g1+A1g${E}_{2g}^{1}+{A}_{1g}$ mixed peak (250 cm−1) of WSe2 monolayer. The 532-nm excitation laser has a spot size ∼2 µm, which limits the lateral resolution. (C) Enhanced Raman signals of MoS2 and WSe2 monolayers, which are recorded at the circled area in Figure 4D. The Raman signal of MoS2 monolayer is still present since it is directly below the WSe2 monolayer. (D) Raman intensity mapping at 250 cm−1, corresponding to the E2g1+A1g${E}_{2g}^{1}+{A}_{1g}$ mixed peak of WSe2 monolayer. (E) Enhanced Raman signal of MoS2 monolayer. (F) Raman intensity mapping at 403 cm−1, corresponding to the A1g peak of MoS2 monolayer. The laser power density is ∼30 kW/cm2 and the exposure time is 1 s per data point. Scanning area is 20 × 20 µm2.
Figure 4:

Raman intensity mapping of a vertically stacked monolayer transition metal dichalcogenide (TMDC) heterostucture. (A) Schematic of the surface-enhanced Raman spectroscopy (SERS) substrate structure, consisting of a grating with the size of 12 × 8 µm2. The grating is sequentially stacked with MoS2 and WSe2 monolayers (WSe2 on top). (B) Combining Raman intensity mapping of the A1g peak (403 cm−1) of MoS2 monolayer and the E2g1+A1g mixed peak (250 cm−1) of WSe2 monolayer. The 532-nm excitation laser has a spot size ∼2 µm, which limits the lateral resolution. (C) Enhanced Raman signals of MoS2 and WSe2 monolayers, which are recorded at the circled area in Figure 4D. The Raman signal of MoS2 monolayer is still present since it is directly below the WSe2 monolayer. (D) Raman intensity mapping at 250 cm−1, corresponding to the E2g1+A1g mixed peak of WSe2 monolayer. (E) Enhanced Raman signal of MoS2 monolayer. (F) Raman intensity mapping at 403 cm−1, corresponding to the A1g peak of MoS2 monolayer. The laser power density is ∼30 kW/cm2 and the exposure time is 1 s per data point. Scanning area is 20 × 20 µm2.

The nanogroove array structure was fabricated by FIB milling for precise control of LSP resonance wavelength (plasmonic gap mode) via nanogroove grating dimensions (for the present case: width ∼70 nm, depth ∼110 nm, pitch ∼250 nm). The Raman measurements were performed in the backscattering configuration using a 532-nm solid-state laser. Using this SERS substrate design [15], large-area chemical vapor deposition–grown MoS2 and mechanically exfoliated WSe2 stack on Al-SERS substrate can be clearly distinguishable (Figure 4B, D, and F) by Raman intensity mapping because of a spatially uniform Raman hot zone and atomically smooth film surface, which prevent the formation of inhomogeneous stochastic hot-spots.

In the Raman scattering spectra shown in Figure 4C and E, three prominent Raman active peaks can be identified with E2g1 (384 cm−1), A1g (403 cm−1), and 2LA(M) (447 cm−1) vibrational modes, originating from monolayer MoS2. On the other hand, a mixed Raman active peak E2g1+A1g (250 cm−1) is identified for monolayer WSe2. The E2g1 and A1g Raman peaks arise from the first-order, in-plane vibration of two S(Se) atoms relative to Mo(W) atom and out-of-plane vibration of S(Se) atoms, respectively. Due to the strong plasmonic field enhancement, we can also clearly observe the 2LA(M) peaks of MoS2 (452 cm−1) and WSe2 (266 cm−1), originating from a second-order process involving the longitudinal acoustic phonons at the M point of the Brillouin zone.

6 Plasmonic surface lattice

Generally, aluminum nanostructure dipolar resonators can only exhibit a small quality factor (Q < 5) due to a high radiative loss in the visible range [8], [11]. Here, we fabricate aluminum nanohole arrays (i.e., “antipartcle” arrays, in contrast to conventional nanoparticle arrays) on the aluminum epitaxial films as the plasmonic surface lattices to demonstrate high-Q plasmonic surface lattice [34], [58] modes based on propagating SPPs (the nanoholes are used to define the spatial periodicities their LSP resonances do not play a significant role in these surface lattices). Since the nonradiative damping of plasmonic material is an intrinsic property originating from inter and intra band transitions, we focus on reducing the radiative loss by increasing the local effective index to enhance the near-field confinement factor. This is particularly important to realize high-Q plasmonic surface lattices based on SPPs. In this work, to improve the Q-factor, we cap one-mm-thick polydimethylsiloxane (PDMS) layer (refractive index: ∼1.4) on the aluminum nanohole arrays to boost the effective index. The angle-resolved spectroscopic measurement results are shown in Figure 5, which is based on a back-focal-plane imaging technique (Figure 5B). In this setup, the angle-resolved spectra collect photons emitted by the aluminum plasmonic surface lattices along a specific emission angle with respect to the normal direction (see Supplementary material for experimental setup).

Figure 5: Optical properties of plasmonic surface lattices on epitaxial aluminum film. (A) Sample configuration of surface lattices patterned on epitaxial aluminum film. (B) Schematic of the optical setup for angle-resolved reflectance measurements, illustrating the orientations of spectrometer slit and polarizer with respect to the Al nanohole array capped with a polydimethylsiloxane (PDMS) layer. The Fourier spectra were collected by a 100× objective (N.A. = 0.55). (C) Angle-resolved reflectance mapping of the Al nanohole arrays, showing the evolution of the plasmonic surface lattice modes while the pitch along the x-axis (px) is increased from 280 to 400 nm. (D) Reflectance spectra of Al nanohole arrays extracted from the angle-resolved reflectance spectra (Figure 5C). All of resonance peaks are shown at the emission angle (θ) equal to 0°. (E) Measured quality factor of plasmonic surface lattice modes, which is defined as Q=λres/Δλ$Q={\lambda }_{\text{res}}/{\Delta}\lambda $.
Figure 5:

Optical properties of plasmonic surface lattices on epitaxial aluminum film. (A) Sample configuration of surface lattices patterned on epitaxial aluminum film. (B) Schematic of the optical setup for angle-resolved reflectance measurements, illustrating the orientations of spectrometer slit and polarizer with respect to the Al nanohole array capped with a polydimethylsiloxane (PDMS) layer. The Fourier spectra were collected by a 100× objective (N.A. = 0.55). (C) Angle-resolved reflectance mapping of the Al nanohole arrays, showing the evolution of the plasmonic surface lattice modes while the pitch along the x-axis (px) is increased from 280 to 400 nm. (D) Reflectance spectra of Al nanohole arrays extracted from the angle-resolved reflectance spectra (Figure 5C). All of resonance peaks are shown at the emission angle (θ) equal to 0°. (E) Measured quality factor of plasmonic surface lattice modes, which is defined as Q=λres/Δλ.

The nanohole arrays were fabricated by FIB milling on aluminum epitaxial film with different periodicities px = 280, 300, 330, 350, 380, 400 nm along the x-direction, while keeping a constant py = 200 nm, in order to tune the plasmonic surface lattice resonances at the Γ point of the lattice Brillouin zone. The angle-resolved reflectance spectra shown in Figure 5C illustrate the plasmonic surface lattice modes are well controlled by changing the pitch (px) and the filling factor of nanoholes. The reflectance spectra at the emission angle (θ) equal to 0° (Figure 5D) show the SPP resonance peaks, resulting from the band edge modes of plasmonic gaps at the Γ point, can be tuned in the entire visible range (from 450 to 600 nm). The Q-factor of plasmonic surface lattice modes (Figure 5E) can be evaluated by λres/Δλ, where Δλ is the spectral linewidth (full width at half maximum) at resonance. Figure 5E shows the Q-factor can be improved to ∼20 for this example. Using this method, we can design high Q-factor Al nanohole arrays over the entire visible spectral range, in comparison with colloidal aluminum nanoparticles [8], [11]. In addition, the plasmonic gap opening at the Γ point becomes very pronounced and we can produce both “dark” (subradiative) and “bright” (superradiative) band edge modes [59], [60], as shown in Figure 5C. Very recently, using more optimized nanofabrication conditions, a higher Q-factor aluminum surface lattice (shown in Figure 6) has also been realized by us (Q ∼ 25, which is close to the theoretical limit reported in the literature for gold plasmonic surface lattices [61]).

Figure 6: Optimization of aluminum nanohole surface lattice. (A) SEM image of the optimized aluminum plasmonic surface lattice. The inset shows the lattice constants (px and py) are 350 nm. (B) Angle-resolved reflectance mapping of the Al nanohole surface lattice. (C) Reflectance spectrum extracted from the angle-resolved reflectance mapping. The resonance peak is shown at the emission angle (θ) equal to 0°.
Figure 6:

Optimization of aluminum nanohole surface lattice. (A) SEM image of the optimized aluminum plasmonic surface lattice. The inset shows the lattice constants (px and py) are 350 nm. (B) Angle-resolved reflectance mapping of the Al nanohole surface lattice. (C) Reflectance spectrum extracted from the angle-resolved reflectance mapping. The resonance peak is shown at the emission angle (θ) equal to 0°.

7 Conclusions and outlook

In summary, we have demonstrated that epitaxial aluminum films are a promising material platform for general plasmonic applications for both ultraviolet and visible spectral regions. White-light surface plasmon interferometry measurement in the entire visible range (400–700 nm) shows that long SPP propagation lengths (5–13 μm) can be achieved due to high-quality Al film. As the first example of plasmonic applications, the aluminum epitaxial film is used to fabricate large-area, highly uniform SERS substrates at 532 nm. A vertically stacked monolayer WSe2/MoS2 heterostructure is adopted as a uniform analyte to show the chemical mapping capability of SERS for two-dimensional material characterization. In the second application, large-area plasmonic surface lattices (periodic hole arrays) with precisely engineered lattice parameters are fabricated on an aluminum epitaxial film. By tuning the lattice parameter along one axis, we can control dark and bright band edge modes over the full visible spectrum. To improve the Q-factor of surface lattice modes, we cap the surface lattices with a PDMS dielectric layer to increase the local effective index. The Q-factor can be improved to ∼25, compared to bare Al nanostructures without capping (Q < 5). The epitaxial approach reported here paves the way for widespread applications of aluminum plasmonics, especially for sensing, photonic system integration, and novel devices requiring ultrathin plasmonic layers. Moreover, it also can be applied for quantum information processing requiring high-quality aluminum superconducting qubits.


Corresponding author: Shangjr Gwo, Department of Physics, National Tsing-Hua University, Hsinchu30013, Taiwan; Institute of NanoEngineering and Microsystems, National Tsing-Hua University, Hsinchu30013, Taiwan; and Research Center for Applied Sciences, Academia Sinica, Nankang, Taipei11529, Taiwan, E-mail:

Award Identifier / Grant number: MOST-108-2119-M-007-008

Award Identifier / Grant number: MOST-107-2923-M-007-004-MY3

Funding source: Ministry of Education

Acknowledgments

We would like to acknowledge funding support from the Ministry of Science and Technology in Taiwan for this research and Ragini Mishra for her help in XRD measurements. S.G. and Y.-H.L. were partially supported by Frontier Research Center on Fundamental and Applied Sciences of Matters at National Tsing-Hua University, the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education in Taiwan. C.-K.S was partially supported by the Yushan Scholar Program by the Ministry of Education in Taiwan.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This research was supported by the Ministry of Science and Technology in Taiwan under grants numbers MOST-108-2119-M-007-008 and MOST-107-2923-M-007-004-MY3.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature, vol. 424, pp. 824–830, 2003. https://doi.org/10.1038/nature01937.Search in Google Scholar PubMed

[2] S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys., vol. 98, p. 011101, 2005. https://doi.org/10.1063/1.1951057.Search in Google Scholar

[3] M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science, vol. 358, p. eaam8100, 2017. https://doi.org/10.1126/science.aam8100.Search in Google Scholar PubMed

[4] I. Zorić, M. Zach, B. Kasemo, and C. Langhammer, “Gold, platinum, and aluminum nanodisk plasmons: material independence, subradiance, and damping mechanisms,” ACS Nano, vol. 5, pp. 2535–2546, 2011. https://doi.org/10.1021/nn102166t.Search in Google Scholar PubMed

[5] G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater., vol. 25, pp. 3264–3294, 2013. https://doi.org/10.1002/adma.201205076.Search in Google Scholar PubMed

[6] B. Doiron, M. Mota, M. P. Wells, et al., “Quantifying figures of merit for localized surface plasmon resonance applications: a materials survey,” ACS Photonics, vol. 6, pp. 240–259, 2019. https://doi.org/10.1021/acsphotonics.8b01369.Search in Google Scholar

[7] H. Ehrenreich, H. R. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev., vol. 132, pp. 1918–1928, 1963. https://doi.org/10.1103/physrev.132.1918.Search in Google Scholar

[8] M. W. Knight, N. S. King, L. Liu, H. O. Everitt, P. Nordlander, and N. J. Halas, “Aluminum for plasmonics,” ACS Nano, vol. 8, pp. 834–840, 2014. https://doi.org/10.1021/nn405495q.Search in Google Scholar PubMed

[9] C. W. Cheng, Y. J. Liao, C. Y. Liu, et al., “Epitaxial aluminum-on-sapphire films as a plasmonic material platform for ultraviolet and full visible spectral regions,” ACS Photonics, vol. 5, pp. 2624–2630, 2018. https://doi.org/10.1021/acsphotonics.7b01366.Search in Google Scholar

[10] M. J. McClain, A. E. Schlather, E. Ringe, et al., “Aluminum nanocrystals,” Nano Lett., vol. 15, pp. 2751–2755, 2015. https://doi.org/10.1021/acs.nanolett.5b00614.Search in Google Scholar PubMed

[11] A. Sobhani, A. Manjavacas, Y. Cao, et al., “Pronounced linewidth narrowing of an aluminum nanoparticle plasmon resonance by Interaction with an aluminum metallic film,” Nano Lett., vol. 15, pp. 6946–6951, 2015. https://doi.org/10.1021/acs.nanolett.5b02883.Search in Google Scholar PubMed

[12] H. W. Liu, F. C. Lin, S. W. Lin, et al., “Single-crystalline aluminum nanostructures on a semiconducting GaAs substrate for ultraviolet to near-infrared plasmonics,” ACS Nano, vol. 9, pp. 3875–3886, 2015. https://doi.org/10.1021/nn5070887.Search in Google Scholar PubMed

[13] F. Cheng, P.-H. Su, J. Choi, S. Gwo, X. Li, and C.-K. Shih, “Epitaxial growth of atomically smooth aluminum on silicon and its intrinsic optical properties,” ACS Nano, vol. 10, pp. 9852–9860, 2016. https://doi.org/10.1021/acsnano.6b05556.Search in Google Scholar PubMed

[14] S. K. Jha, Z. Ahmed, M. Agio, et al., “Deep-UV surface-enhanced resonance Raman scattering of adenine on aluminum nanoparticle arrays,” J. Am. Chem. Soc., vol. 134, pp. 1966–1969, 2012. https://doi.org/10.1021/ja210446w.Search in Google Scholar PubMed

[15] S. S. Raja, C.-W. Cheng, Y. Sang, et al., “Epitaxial aluminum surface enhanced Raman spectroscopy substrates for large-scale 2D material characterization,” ACS Nano, vol. 14, pp. 8838–8845, 2020. https://doi.org/10.1021/acsnano.0c03462.Search in Google Scholar PubMed

[16] Q. Zhang, G. Y. Li, X. F. Liu, et al., “A room temperature low-threshold ultraviolet plasmonic nanolaser,” Nat. Commun., vol. 5, p. 4953, 2014. https://doi.org/10.1038/ncomms5953.Search in Google Scholar PubMed

[17] Y.-H. Chou, Y.-M. Wu, K.-B. Hong, et al., “High-operation-temperature plasmonic nanolasers on single-crystalline aluminum,” Nano Lett., vol. 16, pp. 3179–3186, 2016. https://doi.org/10.1021/acs.nanolett.6b00537.Search in Google Scholar PubMed

[18] B.-T. Chou, Y.-H. Chou, Y.-M. Wu, et al., “Single-crystalline aluminum film for ultraviolet plasmonic nanolasers,” Sci. Rep., vol. 6, p. 19887, 2016. https://doi.org/10.1038/srep19887.Search in Google Scholar PubMed PubMed Central

[19] Y. Chou, K. Hong, Y. Chung, et al., “Metal for plasmonic ultraviolet laser: Al or Ag?,” IEEE J. Sel. Top. Quant. Electron., vol. 23, pp. 1–7, 2017. https://doi.org/10.1109/jstqe.2017.2748521.Search in Google Scholar

[20] Y. J. Liao, C. W. Cheng, B. H. Wu, et al., “Low threshold room-temperature UV surface plasmon polariton lasers with ZnO nanowires on single-crystal aluminum films with Al2O3 interlayers,” RSC Adv., vol. 9, pp. 13600–13607, 2019. https://doi.org/10.1039/c9ra01484e.Search in Google Scholar PubMed PubMed Central

[21] H. Li, J. H. Li, K. B. Hong, et al., “Plasmonic nanolasers enhanced by hybrid graphene-insulator-metal structures,” Nano Lett., vol. 19, pp. 5017–5024, 2019. https://doi.org/10.1021/acs.nanolett.9b01260.Search in Google Scholar PubMed

[22] R. Li, D. Wang, J. Guan, et al., “Plasmon nanolasing with aluminum nanoparticle arrays,” J. Opt. Soc. Am. B, vol. 36, pp. E104–E111, 2019. https://doi.org/10.1364/josab.36.00e104.Search in Google Scholar

[23] G. Maidecchi, G. Gonella, R. P. Zaccaria, et al., “Deep ultraviolet plasmon resonance in aluminum nanoparticle arrays,” ACS Nano, vol. 7, pp. 5834–5841, 2013. https://doi.org/10.1021/nn400918n.Search in Google Scholar PubMed

[24] T. Xu, Y.-K. Wu, X. Luo, and L. J. Guo, “Plasmonic nanoresonators for high-resolution colour filtering and spectral imaging,” Nat. Commun., vol. 1, p. 59, 2010. https://doi.org/10.1038/ncomms1058.Search in Google Scholar PubMed

[25] S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett., vol. 12, pp. 4349–4354, 2012. https://doi.org/10.1021/nl302110z.Search in Google Scholar PubMed

[26] J. Olson, A. Manjavacas, L. Liu, et al., “Vivid, full-color aluminum plasmonic pixels,” Proc. Natl. Acad. Sci. U.S.A., vol. 111, p. 14348, 2014. https://doi.org/10.1073/pnas.1415970111.Search in Google Scholar PubMed PubMed Central

[27] S. J. Tan, L. Zhang, D. Zhu, et al., “Plasmonic color palettes for photorealistic printing with aluminum nanostructures,” Nano Lett., vol. 14, pp. 4023–4029, 2014. https://doi.org/10.1021/nl501460x.Search in Google Scholar PubMed

[28] D. Fleischman, K. T. Fountaine, C. R. Bukowsky, G. Tagliabue, L. A. Sweatlock, and H. A. Atwater, “High spectral resolution plasmonic color filters with subwavelength dimensions,” ACS Photonics, vol. 6, pp. 332–338, 2019. https://doi.org/10.1021/acsphotonics.8b01634.Search in Google Scholar

[29] L. Zhou, C. Zhang, M. J. McClain, et al., “Aluminum nanocrystals as a plasmonic photocatalyst for hydrogen dissociation,” Nano Lett., vol. 16, pp. 1478–1484, 2016. https://doi.org/10.1021/acs.nanolett.5b05149.Search in Google Scholar PubMed

[30] D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: gold, silver, copper, aluminium, and tantalum,” J. Appl. Phys., vol. 96, pp. 3626–3634, 2004. https://doi.org/10.1063/1.1786341.Search in Google Scholar

[31] M. Castro-Lopez, D. Brinks, R. Sapienza, and N. F. van Hulst, “Aluminum for nonlinear plasmonics: resonance-driven polarized luminescence of Al, Ag, and Au nanoantennas,” Nano Lett., vol. 11, pp. 4674–4678, 2011. https://doi.org/10.1021/nl202255g.Search in Google Scholar PubMed

[32] W. P. Guo, W. Y. Liang, C. W. Cheng, et al., “Chiral second-harmonic generation from monolayer WS2/aluminum plasmonic vortex metalens,” Nano Lett., vol. 20, pp. 2857–2864, 2020. https://doi.org/10.1021/acs.nanolett.0c00645.Search in Google Scholar PubMed

[33] S. Tian, O. Neumann, M. J. McClain, et al., “Aluminum nanocrystals: a sustainable substrate for quantitative SERS-based DNA detection,” Nano Lett., vol. 17, pp. 5071–5077, 2017. https://doi.org/10.1021/acs.nanolett.7b02338.Search in Google Scholar PubMed

[34] X. Zhu, G. M. Imran Hossain, M. George, et al., “Beyond noble metals: high Q-factor aluminum nanoplasmonics,” ACS Photonics, vol. 7, pp. 416–424, 2020. https://doi.org/10.1021/acsphotonics.9b01368.Search in Google Scholar

[35] I. Levine, A. Yoffe, A. Salomon, W. J. Li, Y. Feldman, and A. Vilan, “Epitaxial two dimensional aluminum films on silicon (111) by ultra-fast thermal deposition,” J. Appl. Phys., vol. 111, p. 124320, 2012. https://doi.org/10.1063/1.4730411.Search in Google Scholar

[36] Y. H. Tsai, Y. H. Wu, Y. Y. Ting, C. C. Wu, J. S. Wu, and S. D. Lin, “Nano-to atomic-scale epitaxial aluminum films on Si substrate grown by molecular beam epitaxy,” AIP Adv., vol. 9, p. 105001, 2019. https://doi.org/10.1063/1.5116044.Search in Google Scholar

[37] S. W. Lin, J. Y. Wu, S. D. Lin, M. C. Lo, M. H. Lin, and C. T. Liang, “Characterization of single-crystalline aluminum thin film on (100) GaAs substrate,” Jpn. J. Appl. Phys., vol. 52, p. 045801, 2013. https://doi.org/10.7567/jjap.52.045801.Search in Google Scholar

[38] K. D. Zhang, S. J. Xia, C. Li, et al., “Interface engineering and epitaxial growth of single-crystalline aluminum films on semiconductors,” Adv. Mater. Interfaces, p. 2000572, 2020. https://doi.org/10.1002/admi.202000572.Search in Google Scholar

[39] Y. N. Zhu, W. L. Wang, W. J. Yang, H. Y. Wang, J. N. Gao, and G. Q. Li, “Nucleation mechanism for epitaxial growth of aluminum films on sapphire substrates by molecular beam epitaxy,” Mater. Sci. Semicond. Process., vol. 54, pp. 70–76, 2016. https://doi.org/10.1016/j.mssp.2016.06.011.Search in Google Scholar

[40] S. W. Hieke, G. Dehm, and C. Scheu, “Annealing induced void formation in epitaxial Al thin films on sapphire (α-Al2O3),” Acta Mater., vol. 140, pp. 355–365, 2017. https://doi.org/10.1016/j.actamat.2017.08.050.Search in Google Scholar

[41] G. Davy and K. G. Stephen, “Aluminium plasmonics,” J. Phys. D Appl. Phys., vol. 48, p. 184001, 2015. https://doi.org/10.1088/0022-3727/48/18/184001.Search in Google Scholar

[42] C. J. DeSantis, M. J. McClain, and N. J. Halas, “Walking the walk: a giant step toward sustainable plasmonics,” ACS Nano, vol. 10, pp. 9772–9775, 2016. https://doi.org/10.1021/acsnano.6b07223.Search in Google Scholar PubMed

[43] R. A. Maniyara, D. Rodrigo, R. Yu, et al., “Tunable plasmons in ultrathin metal films,” Nat. Photonics, vol. 13, pp. 328–333, 2019. https://doi.org/10.1038/s41566-019-0366-x.Search in Google Scholar

[44] B. Frank, P. Kahl, D. Podbiel, et al., “Short-range surface plasmonics: localized electron emission dynamics from a 60-nm spot on an atomically flat single-crystalline gold surface,” Sci. Adv., vol. 3, p. e1700721, 2017. https://doi.org/10.1126/sciadv.1700721.Search in Google Scholar PubMed PubMed Central

[45] S. Campione, I. Brener, and F. Marquier, “Theory of epsilon-near-zero modes in ultrathin films,” Phys. Rev. B, vol. 91, p. 121408, 2015. https://doi.org/10.1103/physrevb.91.121408.Search in Google Scholar

[46] J. M. Martinis, M. H. Devoret, and J. Clarke, “Quantum Josephson junction circuits and the dawn of artificial atoms,” Nat. Phys., vol. 16, pp. 234–237, 2020. https://doi.org/10.1038/s41567-020-0829-5.Search in Google Scholar

[47] H. Ditlbacher, A. Hohenau, D. Wagner, et al., “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett., vol. 95, p. 257403, 2005. https://doi.org/10.1103/physrevlett.95.257403.Search in Google Scholar

[48] P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science, vol. 325, pp. 594–597, 2009. https://doi.org/10.1126/science.1174655.Search in Google Scholar PubMed

[49] J. H. Park, P. Ambwani, M. Manno, et al., “Single-crystalline silver films for plasmonics,” Adv. Mater., vol. 24, pp. 3988–3992, 2012. https://doi.org/10.1002/adma.201200812.Search in Google Scholar PubMed

[50] Y.-J. Lu, J. Kim, H.-Y. Chen, et al., “Plasmonic nanolaser using epitaxially grown silver film,” Science, vol. 337, pp. 450–453, 2012. https://doi.org/10.1126/science.1223504.Search in Google Scholar PubMed

[51] Y. Wu, C. Zhang, N. M. Estakhri, et al., “Intrinsic optical properties and enhanced plasmonic response of epitaxial silver,” Adv. Mater., vol. 26, pp. 6054–6055, 2014. https://doi.org/10.1002/adma.201403674.Search in Google Scholar

[52] F. Cheng, C.-J. Lee, J. Choi, et al., “Epitaxial growth of optically thick, single crystalline silver films for plasmonics,” ACS Appl. Mater. Interfaces, vol. 11, pp. 3189–3195, 2019. https://doi.org/10.1021/acsami.8b16667.Search in Google Scholar PubMed

[53] C. Y. Wang, H. Y. Chen, L. Y. Sun, et al., “Giant colloidal silver crystals for low-loss linear and nonlinear plasmonics,” Nat. Commun., vol. 6, p. 7734, 2015. https://doi.org/10.1038/ncomms8734.Search in Google Scholar PubMed PubMed Central

[54] S. Gwo, H.-Y. Chen, M.-H. Lin, et al., “Nanomanipulation and controlled self-assembly of metal nanoparticles and nanocrystals for plasmonics,” Chem. Soc. Rev., vol. 45, pp. 5672–5716, 2016. https://doi.org/10.1039/c6cs00450d.Search in Google Scholar PubMed

[55] A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt., vol. 37, pp. 5271–5283, 1998. https://doi.org/10.1364/ao.37.005271.Search in Google Scholar PubMed

[56] F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett., vol. 97, p. 206806, 2006. https://doi.org/10.1103/physrevlett.97.206806.Search in Google Scholar

[57] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, New York, John Wiley & Sons, 1991.10.1002/0471213748Search in Google Scholar

[58] V. G. Kravets, A. V. Kabashin, W. L. Barnes, and A. N. Grigorenko, “Plasmonic surface lattice resonances: a review of properties and applications,” Chem. Rev., vol. 118, pp. 5912–5951, 2018. https://doi.org/10.1021/acs.chemrev.8b00243.Search in Google Scholar PubMed PubMed Central

[59] S. R. K. Rodriguez, A. Abass, B. Maes, O. T. A. Janssen, G. Vecchi, and J. Gómez Rivas, “Coupling bright and dark plasmonic lattice resonances,” Phys. Rev. X, vol. 1, p. 021019, 2011. https://doi.org/10.1103/physrevx.1.021019.Search in Google Scholar

[60] T. K. Hakala, H. T. Rekola, A. I. Väkeväinen, et al., “Lasing in dark and bright modes of a finite-sized plasmonic lattice,” Nat. Commun., vol. 8, p. 13687, 2017. https://doi.org/10.1038/ncomms13687.Search in Google Scholar PubMed PubMed Central

[61] S. R. K. Rodriguez, M. C. Schaafsma, A. Berrier, and J. Gómez Rivas, “Collective resonances in plasmonic crystals: size matters,” Phys. B Condens. Matter, vol. 407, pp. 4081–4085, 2012. https://doi.org/10.1016/j.physb.2012.03.053.Search in Google Scholar


Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/nanoph-2020-0402).


Received: 2020-07-19
Accepted: 2020-09-18
Published Online: 2020-11-25

© 2020 Chang-Wei Cheng et al., published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

Downloaded on 26.4.2024 from https://www.degruyter.com/document/doi/10.1515/nanoph-2020-0402/html
Scroll to top button