1. Introduction

In the past two decades, plasmonic nanostructures have been attracted more attentions because of their unusual electromagnetic and optical characteristics, and enormous efforts have been devoted to manipulating the optical behavior of plasmonic nanostructures. Extraordinary optical properties of plasmonic nanostructures and metamaterial have been successfully applied in perfect absorption [1–4], biosensor [5–8], surface enhanced Raman spectroscopy [9–11], nanolaser [12,13], optics cloaks [14], and light beam manipulation [15,16]. The incident light can be trapped into subwavelength regions near metal nanostructure surfaces at the localized surface plasmon resonance (LSPR) wavelength. The LSPR is always accompanied by a huge near field enhancement [17], and can be affected by size, shape, arrangement, surrounding dielectric environment and substrate. In general, dielectric substrates such as silicon (Si) and silicon dioxide (SiO₂) have been widely used, and some works have used metals as substrates, such as refractive index sensors [18,19] and enhanced coherent anti-Stokes Raman scattering [20]. Recently, researchers have tried to manipulate the plasmon behavior by utilizing substrates of novel ENZ materials, a new type of materials with vanishing dielectric constant in a certain wavelength range [21–24].

ENZ materials have caused increasing attention with its exclusive linear and nonlinear optical characteristics. Materials that exhibit a near-zero real part of the dielectric constant in certain spectral regions are referred to as ENZ materials. According to impedance matching condition $Z\textrm{ = }\sqrt {\mu \textrm{/}\varepsilon }$ and boundary condition ${\varepsilon _\textrm{1}}{E_\textrm{1}}\textrm{ = }{\varepsilon _\textrm{2}}{E_\textrm{2}}$, ENZ materials exhibit extremely large impedance and mismatch with the boundary environment, resulting in extremely large electric field enhancements inside. When the near-zero conditions are satisfied, the phase velocity ${v_p} = c/\sqrt {\varepsilon \mu }$ will become exceptionally large, approaching infinity [25]. In addition, the index of refraction ($n = \sqrt {(\sqrt {\textrm{Re} {{(\varepsilon )}^\textrm{2}}\textrm{ + Im(}\varepsilon {\textrm{)}^2}} ) + \textrm{Re} (\varepsilon ))/2}$) gets vanishingly small at optical frequencies if the material is low-loss [26]. These materials have been utilized for local field enhancement [27], optical perfect absorption [28,29], radiation pattern tailoring [30], enhanced optical nonlinearity [31], and light speed controlling [32,33]. The real part of the dielectric constant of different materials vanishes at different spectral regions. For example, gold (Au) and silver (Ag), have real permittivity (Re(ɛ)) close to zero in the ultraviolet region with very high imaginary permittivity (Im(ɛ)), preventing them from being effective ENZ materials due to large loss. Moreover, a few transparent conductive oxides (TCO) have been reported to exhibit ENZ characteristics in near-infrared (NIR) and mid-infrared (MIR), such as indium tin oxide (ITO) and Al-doped zinc oxide (AZO) [34]. However, the operation wavelength of the TCO materials is always fixed and can only be slightly tuned by environmental temperature, pressure, doping, and so on. Recently, the ENZ effect has been investigated and achieved in hyperbolic metamaterials [35,36].

Generally, there are two main methods to design hyperbolic metamaterials artificially. The first is a multilayer HMM with alternating stacks of subwavelength metals and dielectrics, while the second is a nanowire HMM composed of arrays of nanowires embedded in a dielectric. Because electrons travel almost freely in each metal plane, the parallel effective medium follows the effective metal’s frequency dispersion relationship. In turn, this produces ENZ behavior in the effective plasmon resonance in the parallel direction. In the vertical direction, almost free electrons are confined within the thickness of their specific metal plane. Compared with multilayers structures, nanowire hyperbolic metamaterials allow electrons to propagate freely in the vertical direction, but not in parallel planes [37]. Electron-beam and sputter deposition, as well as electrochemical deposition, are commonly used to construct multilayer HMMs and nanowire HMMs.

HMM substrate consists of alternating gold and diamond layers and the corresponding optical properties of HMMs are modelled by the effective medium theory (EMT) [38]. Considering the fact that metal always has negative permittivity below the plasmon frequency as the polarization direction of free electron is inverse to the external electric field, negative components of permittivity tensor can be obtained by restricting free-electron motion to these directions [39]. According to the EMT, the effective permittivity components for propagating perpendicular and parallel to the axis of anisotropy can be calculated as [38]:

 

Fig. 1. (a) and (b) are schematic diagrams of the designed structure, in which the period constant of a single unit cell is p= 300 nm, the height l and width w of the NA are 50 nm, the thickness of the metal layer and dielectric layer in the substrate are h = 5 nm and d = 20 nm, and the length of the NA is varied. (c) shows the real and imaginary parts of the parallel dielectric constant components of the multilayers HMM in this paper. (d) is the calculated reflection and transmission spectra of only hyperbolic substrate. The illustration in (b) is a sectional view of the HMM substrate.

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Such hyperbolic metamaterials have reached the ultra-anisotropic limit of traditional uniaxial crystal and lead to dramatic varieties for the light propagation which shows a hyperbolic dispersion relation for specific electromagnetic waves. In order to realize hyperbolic dispersion, one of the negative components of the permittivity tensor can be obtained by confining free electrons in the direction parallel or perpendicular to the anisotropy axis. As a result, the absolute value of k-vector is not limited, and the hyperbolic metamaterials support the propagation of high-k electromagnetic wave and can excite VPP mode. The VPP mode has been confirmed to be excited at visible and infrared frequencies [41,42], however few attempts have been made to manipulated this mode. Therefore, in this work, we try to manipulate the plasmonic behavior and VPP mode in HMM substrate.

2. Numerical simulations

The dielectric and metallic properties of the substrate significantly affect the plasmon resonance. Therefore, a HMM substrate with ENZ characteristics is designed to verify its manipulation effect on optical behavior of plasmon. Numerical simulations are performed with the commercial software COMSOL Multiphysics, which is based on the finite element method (FEM) [43,44] and is used for building the HMM model and completing 3D electromagnetic simulations. Figure 1(a) schematically shows the gold NA structure on the HMM substrate, with geometrics being as follows: d = 20 nm, h = 5 nm, t = 100 nm, l = w = 50 nm, and the length of NA c is set as a variant during simulations. The multilayers HMM is made up of three pairs of Au and diamond layers, each with a thickness of 5 nm and 20 nm, respectively. We used the experimental dielectric functions provided in the literature to model diamond [45] and SiO₂ [46], and the Lorentz-Drude model is utilized to characterize the permittivity of Au [47]. The external surrounding is vacuum. The period of unit cell p is 300 nm, and the computational domain only contained a single unit cell as shown in Fig. 1(b), where Floquet periodic boundary conditions are employed for four lateral boundaries and perfectly matched layers (PML) are used in the propagation direction to eliminate the nonphysical reflections at the domain boundaries. The free tetrahedrons are used for mesh division, and local mesh refinement for hyperbolic structures and metal nanowires. The electromagnetic wave propagates along the z-direction with the electric and magnetic fields polarized along the x- and y-directions, respectively.

3. Results and discussions

Figure 2 depicts the transmitted spectra with different lengths of NA on SiO₂ substrate and HMM substrate, respectively. As shown in Fig. 2(a) and (b), there is only one LSP resonance peak on the SiO₂ substrate, the plasmon resonance moves towards the long wavelength as the length of the antenna increases. In comparison, the resonance splits into two due to hybridization between the LSP mode and VPP mode when the designed HMM is utilized as the substrate, the hybridization between localized and propagating plasmonic modes in the single layer of metal and dielectric cased has been observed in previous work, and the strong coupling mechanism is obtained through the anti-crossing behavior of hybrid plasmonic resonances [48]. The additional resonance dip in this work originates from the high-k VPP mode in HMM substrate. With the NA length increases, one of the resonances remains almost unchanged near the ENZ frequency, while the other changes and exhibits a red shift. The spectral shift of the transmission dip is shown in Fig. 2(c). The transmission dip shift width is 275 nm on the SiO₂ substrate, while the shift distances of the two dips are only 20 nm and 30 nm on the HMM substrate. To evaluate the suppression degree to the plasmon resonance shift in pinning effect, a suppression factor S has been defined as follow,

 

Fig. 2. (a) and (b) are the simulated transmitted spectra with different length (160-240 nm) of NA on SiO2 substrate and HMM substrate, respectively. (c) is the spectral displacement on different substrates.

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In this work, we are interested in the interaction between the different modes. A wider range of antenna lengths, from 80 nm to 240 nm, have been investigated, and the dipole antenna system evolution diagram is presented in Fig. 3. The wavelength shift of the dipole resonance that occurs on the SiO₂ substrate is approximately linear as shown in Fig. 3(a) and (b). However, the spectrum of the NA on the HMM substrate is characterized by two transmitted dip bands, with both an increasing extinction and increasing separation between the resonances as length raises. The transmitted spectrum map can be divided into three different regions: (1) at short wavelength, where the transmittance is greater than the transmittance at the two dips; (2) at the resonance wavelength near the ENZ wavelength, where the first resonance dip is strongly restricted to a shorter wavelength region, and a new and apparent transmission dip appears at the wavelength position slightly larger than the ENZ point; (3) at the long wavelength region, where transmission exhibits inhibition. As shown in Fig. 3(d), the plasmon system has three absorption bands, and an anti-crossover region is observed in the absorption mapping, as marked by the dots and dashed lines in Fig. 3(d).

 

Fig. 3. (a) and (b) are the simulated transmitted spectra and absorption spectra mapping of different lengths of NAs on SiO₂, (c) and (d) are the simulated transmitted spectra and absorption spectra mapping of different length of NA on HMM substrate. The other parameters: p = 300 nm, l = w = 50 nm, d = 5 nm, h = 20 nm. The LSP and VPP modes are denoted by the yellow and blue dot lines, respectively. The gray dashed lines indicate hybrid modes.

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When the length of the nano antenna is 240 nm, the resonance wavelength is 1135 nm on the SiO₂ substrate, and 885 nm and 970 nm on the HMM substrate as shown in Fig. 2. In order to understand the physical origin of these transmission resonances of the designed plasmon system, we plotted the field distributions of |E/E₀|, E_z and E_y in the y-z and x-y planes at these resonance wavelengths. The resonance electric field distribution at 1135 nm on the SiO₂ substrate is depicted in Fig. 4(a1) -(d1). There was a LSPR with substantial electric field enhancement dispersed in the near field region at both ends of NA and no evident field penetration into the substrate. Furthermore, different field excitations were observed at two resonance wavelengths on the HMM substrate, as shown in Fig. 4(a2) -(d2) and (a3) -(d3). The field distributions corresponding to the two resonance wavelengths show two different VPP modes. The field distributions for the two wavelengths are identical in the y-z direction, but the intensity of the hot spots and charges distribution are different. The region between the two cells has a 5–6 times electric field amplification at 885nm, and four field hot spots are distributed in each dielectric layer inside the HMM substrate. The positive and negative charges are alternately distributed in the x direction as “+” “-” “+” “-”. The resonance at 970 nm has a different charge distribution than for the resonance at 885 nm, and their intensity are stronger. This is due to the fact that free electrons are contained inside a particular thickness of the metal layer and that electric field radiates from the inside, resulting in 6–8 times of electric field enhancement in the HMM substrate. Furthermore, the coupling of the VPP mode and the LSP mode changes the near-field distribution of the NA array as shown in Fig. 4(d1) -(d3).

 

Fig. 4. The electric enhancement distribution $|{E\textrm{/}{E_0}} |$ (a, b) and z-direction component of electric field ${E_z}$ (c) and E_y (d) for the resonance wavelength on SiO₂ substrate at 1135 nm (a1∼d1), and two dips at 885 nm (a2∼d2) and 970 nm (a3∼d3) on HMM substrate, respectively. Picture a and c are plotted in x-z plane, b and d in x-y plane.

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Figure 5 shows the parallel component distribution of the real part of the permittivity for different metal filling rates and their transmission spectra. By controlling the thickness of the metal layer unchanged and altering the thickness of the dielectric to 30 nm, 25 nm, 10 nm and 7 nm, the metal filling rate is 14.3%, 16.7%, 33.3% and 41.7% respectively as shown in Fig. 5(b) -(f). Compared with the SiO₂ substrate, the designed structures have much smaller shift of the plasmon resonance spectrum. Besides, as the metal filling rate increases, the resonance region blue-shifted, the spectral shifts of the two transmission dips are shown in Fig. 6. In our design, the metal filling rate that makes the coupling effect most obviously is 20%. As the metal filling rate changes, the resonance deviates from around the ENZ wavelength, the coupling between the two modes becomes weak.

 

Fig. 5. (a) is the parallel component of the dielectric constant of HMM substrates with different metal filling rates. (b)-(f) show the transmission spectra of the designed NA arrays, with length of 160–240 nm on the substrates with different metal filling rates. The orange dashed line represents the ENZ wavelength position and the grey dashed line represents the position of the second dip.

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Fig. 6. Spectral displacements shift of plasmonic systems with different metal filling rates. (a) and (b) correspond to dip-1 and dip-2 respectively.

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The low-loss ENZ substrate is expected to be employed in a broader range of applications. For example, ENZ substrate can compensate for manufacturing errors from visible light to infrared region, bring further improvements to the already strong nonlinear response of the ENZ system [51], precisely control the plasmon behavior and reduce the crosstalk from other modes [50]. Dynamic tuning of HMMs using novel materials such as graphene and phase change materials is also a potential application [52,53].

4. Conclusion

In conclusion, our designed structure verifies the pinning effect of the HMM substrate on the NA from the simulation calculation. Furthermore, the VPP modes of the HMM substrate is excited and couple with the LSP modes to generate hybrid spectra. The electric field distribution exhibits that VPP modes are strongly confined within the HMM substrate, and that the near-field distribution of the NA array is greatly affected. In addition, the metal filling rate affects the coupling between modes, and there is an optimal metal filling rate that facilitates coupling between different modes. The best pinning effect with NA resonance may appear at strong coupling regions. In this work, compared with the work of Habib et al. [50], the suppression factors S are 0.073 and 0.32 respectively, indicating that the HMM substrate in this work has a stronger inhibitory effect on the LSP mode. Besides, the designed structure in this work can also lead to a mode that is strongly restricted within multiple layers – VPP modes. The coupling of the LSP mode and the VPP mode can result a splitting of the transmission spectrum and these two resonance dips will be blue-shifted with the increase of the metal filling fraction. The designed structure provides a new way to manipulate the plasmonic behavior, it may be of great help for the potential application of precise control of plasmon.