1. Introduction

Manipulating or shaping of light using nanostructures is one of the most important and fundamental topics in nanophotonics. The successful development of nanophotonics originated in research into the unique optical properties of simple nanostructures, including metallic thin films and nanoparticles, in which propagating or localized surface plasmons play crucial roles [1–3]. Recent advances in nanofabrication techniques have raised the possibility of efficient light management using complex nanostructures. Metamaterials, which consist of subwavelength dielectric or conducting “meta-atoms” in periodic arrangements [4], can provide new optical properties that do not occur in nature, including a negative refractive index [5], and offer potential benefits for various applications including superlenses [6], cloaking [7], hyperinterface [8] and light storage [9]. However, because of the high intrinsic losses of the metals used and the complexity of metamaterial fabrication, metasurfaces, which are the two-dimensional (2D) counterparts of metamaterials, have been preferred for use in light field manipulation in recent years [10].

Metasurfaces composed of arrays of holes in metallic films exhibit some remarkable optical phenomena, including extraordinary transmission (EOT) [11], and offer ways to enhance and shape the fluorescent emission [12], nanolasing [13], etc. As an extension of these monolayer metasurfaces, a 2D array of holes penetrating a metal-dielectric-metal (MDM) film stack was proposed by Zhang and associates and was termed a “fishnet” structure [14]. This structure has received considerable attention because of its negative refractive index (NRI) at visible [15,16] and near infrared [17,18] frequencies. Additionally, MDM fishnet structures have been successfully used to design optical devices such as polarizers, lenses, demultiplexers and light-emitting devices [19–22]. All the exotic properties of these structures are dependent on the unique electromagnetic modes supported by the MDM fishnet structures. Therefore, it is both necessary and useful to perform a comprehensive investigation of these modes in the fishnet structures.

In this paper, we design, fabricate and measure an MDM fishnet structure that has multiple electromagnetic resonances, including magnetic plasmon polaritons (MPPs), localized surface plasmon resonance (LSPR) and surface plasmon polariton-Bloch waves (SPP-BWs) at visible frequencies. Additionally, a reasonable inductor-capacitor (LC) circuit model is constructed to describe the MPPs. All the resonant modes are corroborated using finite-difference time-domain (FDTD) simulations. In addition, geometric parameters such as the gap size, the neck length and the period of the fishnet are investigated, along with the polarization angle of the incident light, and the dependences of the resonant wavelengths on these properties are carefully measured and interpreted using some reliable physical models. Our results show that the magnetic mode is more sensitive than the other modes. The analysis of the electromagnetic field distributions of these multiple resonance modes demonstrates the structure’s excellent ability to confine light within a nanoscale volume, which indicates the possibility of enhancement of the spontaneous emission of fluorescence by increasing the excitation and the emission rate simultaneously. This work will lead to guidelines for the design of fishnet and other related metasurface structures for specific applications.

1. Sample descriptions

The samples geometries were first defined by evaporation deposition of a thin layer of silver on a glass substrate. Then, a FOX-15 spin-on resist (Dow Corning) layer based on hydrogen silsesquioxane (HSQ) was used to produce the interlayer dielectric (which had a refractive index of 1.41). The resist was diluted in methyl isobutyl ketone at a ratio of 1:8 and spun at 5000 rpm with an acceleration of 1000 rpm∙s⁻¹ for 40 s, and the mixture was then baked at 120°C for 1 min to remove the solvents. An additional silver layer with the same thickness (t_Ag) was subsequently deposited on the HSQ layer. To create a periodic pattern of rectangular apertures through the stack of three alternating silver and HSQ films, focused ion beam (FIB; FEI Helios NanoLab 650) milling was used because of its ability to produce high-aspect-ratio geometries. The ion current used throughout the fabrication process was maintained at a maximum of 1.1 pA at an accelerating voltage of 30 kV.

Figure 1(a) shows a schematic of the metal-dielectric-metal (MDM) fishnet structure, which comprises MDM films that are deposited on a glass substrate (with a refractive index of 1.518) and then perforated using rectangular holes. The top and bottom silver films in the MDM films are deposited by evaporating and have the same thickness t_Ag, while the gap dielectric film is spin-coated hydrogen silsesquioxane (HSQ) and has a thickness of t_HSQ. Figure 1(b) presents a scanning electron microscopy (SEM) image of a typical MDM fishnet sample with $t_{Ag}=35\text{nm,}$$t_{HSQ}=30\text{nm,}$hole length $a=250\text{nm,}$width $b=250\text{nm,}$and the rectangular lattice constants $P_x=P_y=400\text{nm}\text{.}$

 

Fig. 1 MDM fishnet metasurface. (a) Schematic of the structure. (b) Scanning electron microscopy image of the fabricated structure.

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2. Multiple resonant modes

Since the MDM fishnet can be regarded as a compound structure that inherits the optical properties of both the MDM structure and the rectangular lattice, multiple resonant modes are naturally expected in our samples. Experimentally, we measured the transmission spectra of both MDM fishnet and pure Ag fishnet (where the metallic film thickness is equal to that of the MDM film) samples to reveal the resonances of the MDM fishnet. Linearly-polarized white light with polarization along the x-axis was used to provide normal illumination of the sample. The transmitted light was collected using an objective lens (60 × , NA = 1.42, Olympus) and recorded using an automated imaging spectrometer (Jobin Yvon iHR550). All the transmission spectra were normalized with respect to the background spectrum of the glass substrate. As shown in Fig. 2(a), two transmission dips (labeled dip 1 and dip 2) that were centered at ${\lambda }_{\text{1}}=530\text{nm}$and ${\lambda }_{\text{2}}=642\text{nm}$were observed for both structures, and were assigned to the LSPR and the SPP-BWs, respectively. Based on the rule of momentum conservation, SPP-BWs supported by the rectangular lattice occur at the following wavelength:

 

Fig. 2 Multiple resonant modes in MDM fishnet structure. (a) Experimental and (b) simulated transmission spectra of the structures with and without the dielectric layer for normally incident light with polarization along the x-axis. (c) Schematic showing detection plane A (blue plane) for the MPPs used in the FDTD simulations. (d) Electric field and vectors mapped on plane A for MPP mode. Arrows represent the field direction and colors indicate the field strength, where red indicates higher strength and blue indicates lower strength. The red dashed ring with arrows indicates the current loop. (e) Schematic showing detection plane B (orange plane) for the LSPR and SPP-BWs used in the FDTD simulations. Electric fields mapped on plane B for the (f) LSPR and (g) SPP-BW modes.

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The three-dimensional finite-difference time-domain (FDTD) method is used to simulate the transmission spectra and the electromagnetic field distributions of the resonant modes that were observed in the experimental spectra using normally incident light with polarization along the x-axis. We performed 3D FDTD simulations of the MDM fishnet structure using commercial software (FDTD Solutions, Lumerical Solutions Ltd.). A theoretical model was configured to aid in the analysis. In this case, the specific geometry was defined based on the SEM image (Fig. 1(b)) and the dielectric coefficient of Ag was taken from Palik’s data (0–2 μm) [23]. Perfectly matched layer (PML) boundary conditions were set at the upper and lower boundaries in the z-direction to eliminate reflective waves from the boundaries, and periodic boundary conditions were used along the x and y directions to simulate the infinite expansibility of the fishnet structure. The plane wave used for excitation of the sample was incident normal to the xy-plane in the z-direction, and the polarization direction of the excitation was along the x-axis. The conformal uniform mesh size used for the MDM fishnet region was set at 2 nm in all three dimensions. The transmitted spectra were monitored at a plane located 1μm below the sample surface.

Figure 2(d) shows the electric field distribution of the MPP mode (dip 3) in the xoz plane (sketched as plane A in Fig. 2(c)). The color in the map indicates the field magnitude while the arrows represent the directions of the electric vectors. It is noted that the electric field is mainly concentrated near the ends of the metal layers and is confined within the dielectric layer. Because of the opposite charges that accumulate at the ends of the metal layers, the antiparallel currents along the upper and lower slabs produced a current loop (the red loop shown in Fig. 2(d)), which implied an explicit magnetic resonance. The electric field distributions of the LSPR and SPP-BW modes are inspected at the xoy plane located 5 nm below the silver-glass interface (sketched as plane B in Fig. 2(e)). Figure 2(f) presents the electric field distribution at ${\lambda }_{\text{1}}=530\text{nm}$(dip 1). It should be noted that, unlike the LSPR of an isolated nanoparticle [24], the electromagnetic field of the LSPR around the air hole is mainly bounded at the edge along the x-axis, but also spills out slightly towards the edge along the y-axis; this can be ascribed to the fact that the nanoscale aperture excitation decays not only into the LSPR, but also into the surface plasmon polaritons (SPPs) that emanate from the aperture to the plane of the film. Figure 2(g) shows the electric field distribution at${\lambda }_{\text{2}}=642\text{nm}$(dip 2) that was captured at plane B, as sketched in Fig. 2(e). The electromagnetic field is enhanced and trapped at the Ag-glass interface along the continuous silver slabs [25]. The nodal structure along the x-axis rather than the y-axis indicates a zero-order (1,0)_glass SPP-BW mode, which is consistent with the results anticipated from the resonance wavelength measurements and calculations.

3. Effective LC circuit model for magnetic resonance

Based on the electromagnetic field distribution in the MDM fishnet structure, it is both convenient and useful to describe the magnetic resonance using an effective inductor-capacitor (LC) circuit model [26]. As shown in Fig. 3, a unit cell of the fishnet structure indicated by the dashed box (Fig. 3(a)) can be modeled using the effective LC circuit shown in Fig. 3(b). The inductances L_s and L_n arise from the upper and lower silver slabs and the neck separated by the dielectric layer [27], and can be expressed as $L_s=\frac{{\mu }_0{l}_s{t}_{HSQ}}{2w_s}$ and $L_n=\frac{{\mu }_0{l}_n{t}_{HSQ}}{2w_n},$respectively, where μ₀ is the permeability of vacuum, l_s(l_n) is the length of the slab (neck) along the x-direction, and w_s(w_n) is the corresponding width (Fig. 3(a)). When the effects of the drifting electrons that arise from the nanometric dimensions of the fishnet structure are considered, the inductances of the slab and the neck should both be corrected by introducing additional inductances of$L_{es}=\frac{l_s}{{\epsilon }_0{\omega }_p^2\delta w_s}$and$L_{en}=\frac{l_n}{{\epsilon }_0{\omega }_p^2\delta w_n},$respectively, where ε₀ is the permittivity of vacuum, ${\omega }_p=1.364\times {10}^{16}rad/s$ is the plasma frequency of Ag, and δ is the power penetration depth, which can be estimated to be 13 nm in our experiments [28]. The capacitance between the two parallel plates is written as $C=\frac{c_1{\epsilon }_d{\epsilon }_{0}S}{t_{HSQ}},$ where ε_d is the permittivity of the dielectric layer, $S=l_s{w}_s+l_n{w}_n$ is the plate area, and c₁ is a correction factor related to the nonuniform charge distribution near the metal surface. Good agreement is obtained between the resonance wavelengths predicted by the LC model and the experimental data with c₁ = 0.13.

 

Fig. 3 LC circuit model. (a) The dashed box defines a unit cell in the proposed structure that is used to build the LC circuit. (b) Equivalent LC circuit of unit cell in the periodic structure, where the arrows indicate current flow direction.

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The total impedance of the closed LC circuit (Fig. 3(b)) can be written as $Z_{tot}(\omega )=2\frac{j\omega (L_n+L_{en})(L_s+L_{es})}{(L_n+L_{en}+L_s+L_{es})}+2\frac{1}{j\omega C},$ in which the magnetic resonance frequency ω_m is obtained by setting the total impedance to zero, i.e., $Z_{tot}=0.$ Let ${\gamma }_1=\frac{{\mu }_0}{2},{\gamma }_2=\frac{1}{{\epsilon }_0{\omega }_p^2\delta },{\gamma }_3=c_1{\epsilon }_d{\epsilon }_0,$ and we obtain ${\omega }_m=\sqrt{\left(\frac{w_s}{l_s}+\frac{w_n}{l_n}\right)\frac{1}{\left({\gamma }_1+\frac{{\gamma }_2}{t_{HSQ}}\right){\gamma }_{3}S}}.$ The magnetic resonance wavelength of the structure can accordingly be written as

4. Effects of geometric parameters and light polarization

Because the MDM fishnet structure can produce multiple responses, it is important to investigate the dependences of the resonant wavelengths on the geometric parameters of the structure, from which the different tunabilities of the LSP, SPP-BW and MPP modes will be disclosed. We measured the transmission spectra of a series of samples by varying the gap thickness t_HSQ, the array period P_x, the neck length l_n, and the incident light polarization angle θ. All the experimental results are compared quantitatively to the results of the FDTD simulations. It is worth noting that all the spectra have more obvious noise fluctuation at longer and shorter wavelength in normalized transmission spectra. This can be explained by the principle that noise of the normalized transmission is inversely proportional to the background spectrum. Since the background spectrum of white light illumination is intense in central band and much weak at longer and shorter wavelength, it is understandable that noise fluctuation is boosted at longer and shorter wavelength.

First, we varied the gap thickness t_HSQ by modulating the ratio between the HSQ content and the methyl isobutyl ketone solvent used along with the spin speed. The optical transmission spectra were measured and simulated for the different gap layer thicknesses (t_HSQ = 25 nm, 30 nm, 40 nm and 45 nm). As shown in Fig. 4(a), the MPP mode shifts towards shorter wavelengths as the gap layer thickness t_HSQ increases; this is consistent with the behavior predicted by Eq. (2). In general, the coupling effect between the upper and lower silver layers weaken as the gap layer becomes thicker, and this makes the resonant frequency of the coupled mode (MPP mode) shifts monotonically towards the resonant frequency of an individual mode. Therefore, with increased spacing, the LSPR mode supported in the air aperture will dominate the transmission response and produce the observed blue shift [29]. However, variation of t_HSQ does not cause any notable modification of the resonant wavelengths of the LSPR and SPP-BW modes because these two modes are primarily dependent on aspects of the in-plane geometry of the fishnet structure other than the interlayer coupling of the MDM structures. Additionally, we should note that all measured transmission spectra are identical to those obtained from the FDTD simulations.

 

Fig. 4 Changes in the geometric parameters of the structure. (a) Experimental and simulated transmission spectra of the MDM fishnet structures with increased gap layer thicknesses of 25 nm, 30 nm, 40 nm, and 45 nm. Black dotted lines indicate the trend for the magnetic resonance wavelength. (b) Experimental and simulated transmission spectra as period length P_x increases from 370 nm to 400 nm in 10 nm steps at a fixed aperture dimension (l_n = 250nm). Black dotted lines indicate the trends for variation of the LSPR, SPP-BW and MPP resonances. (c) Experimental and simulated transmission spectra as aperture length l_n increases from 230 nm to 260 nm in steps of 10 nm at a fixed period (P_x = 400 nm). Black dotted lines indicate the trend for variation of the magnetic resonance wavelength λ_m. (d) Relationship between λ_m and l_n with constant P_x. The black line corresponds to the theoretically predicted relationship based on Eq. (2). Colored circles correspond to the experimental results.

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Second, we varied the period P_x along the incident electric orientation (x-direction) from 370 nm to 400 nm in steps of 10 nm while keeping the air aperture dimension l_n constant; this means that l_s will increase from 120 nm to 150 nm and the unit metallic plate area S will increase simultaneously. The gap layer thickness is 30 nm and the other structural parameters remain unchanged. A distinct redshift in the MPP mode is observed in both the measurements and the simulations (Fig. 4(b)). Additionally, the redshift of the SPP-BW mode can be corroborated by evaluating the resonant wavelength using Eq. (1), which gives values of 608 nm, 622 nm, 636 nm, and 649 nm for P_x = 370 nm, 380 nm, 390 nm, and 400 nm, respectively. All these values agree well with the values from the experimental measurements (610 nm, 623 nm, 633 nm, and 643 nm) and the FDTD simulations (604 nm, 616 nm, 627 nm, and 640 nm), as shown in Fig. 4(b). A tiny redshift can be found for the LSPR mode as P_x increases from 370 nm to 400 nm that is caused by coupling between adjacent apertures. For the periodic nanohole array, the presence of the metallic film that connects the adjacent apertures could provide an additional coupling channel between the localized resonances of the nanoscale holes via excitation of SPPs, which determine the response and allow the LSPR modes of adjacent apertures to interact [30]. As a result, a spectral redshift will occur when the distance between the apertures increases. While unambiguous redshifts are observed for the resonant wavelengths of the SPP-BW and LSPR modes, the shifts are not as great as those for the MPP mode. More sensitive dependence of MPP mode on P_x can be qualitatively explained according to the specific electromagnetic field distribution of the modes. As shown in Figs. 2(d), 2(f) and 2(g), electric field of MPP mode is mainly located within the gap, however, electric fields of LSPR and SPP-BW mode are located mainly at the edges of the air holes. Because the unit metallic plate area S enlarges with P_x, the electric field with the gap will strongly modulated by P_x, but the electric field along the edges changes little.

Third, we varied the neck length l_n from 230 nm to 260 nm in steps of 10 nm while maintaining the period P_x = l_n + l_s at 400 nm, which implies that l_s varies simultaneously from 170 nm to 140 nm. The measured and calculated transmission spectra that are dependent on the variation of l_n are presented in Fig. 4(c). Unlike the dependence on the period P_x (Fig. 4(b)), a blueshift in the MPP resonance is observed for increasing l_n because both the capacitance and the parallel inductance from slabs and necks of fishnet will decrease as length l_n grows. The relationship between the magnetic resonance wavelength λ_m and l_n is shown in Fig. 4(d). The dark line represents the theoretical prediction based on Eq. (2). The colored circles represent the experimental data and fit the theoretical results very well, with an average relative difference of less than 1.5%, which implies that the LC circuit model is quite reasonable for our samples. Simultaneously, no obvious shifts were observed for the LSPR and SPP-BW modes. It can be deduced from Eq. (1) that the resonant wavelength of the SPP-BW is irrelevant to the other parameters, except for the aperture period. For the LSPR, an increase in the air aperture length l_n leads to a redshift in the resonance wavelength [31], which is compensated by a blueshift caused by the reduction in the distance between neighboring apertures that was described in the previous paragraph. Therefore, the LSPR dips remain almost stationary in the experiments, and this behavior is corroborated by the simulation results.

We end this study with polarization-dependent transmittance measurements on an MDM fishnet structure with a rectangular period and square air holes. As shown in Fig. 5(a), the rectangular period of the structure is 365 × 400 nm, while the square air holes have dimensions of 250 × 250 nm and the gap layer thickness is 23 nm. The incident light is linearly polarized, with its polarization oriented at an angle of θ relative to the x-axis. Because all three resonant modes (LSPR, SPP-BWs and MPP modes) are dependent on the period (Fig. 4(b)), we expect that the transmission spectra will be shaped by rotation of the polarization of the incident light. As shown in Fig. 5(b), the transmission spectra were measured and simulated as the polarization angle θ was varied from 0°to 90°in steps of 15°. For x-polarized (θ = 0°) or y-polarized (θ = 90°) light, the three distinct LSPR, SPP-BW and MPP-based resonant modes are observed and obvious redshifts are seen in all three modes as the polarization is switched from x to y orientation; this is consistent with the results shown in Fig. 4(b). At the other polarization angles, the transmission spectra can be regarded as linear superpositions of the transmission spectra of the x-polarization and the y-polarization. We note that the resonant dips of the x-polarization fade while the y-polarization dips gradually grow as the polarization angle is switched from 0°to 90°. When the limited resolutions of the experimental measurements are taken into consideration, all the experimental results agree well with the simulated results (Fig. 5(b)). The experiments described here demonstrate a feasible way to manipulate the optical spectrum through simple light polarization control.

 

Fig. 5 Changes in the polarization angle of incident light. (a) Schematic of a unit cell of the MDM fishnet structure with polarization angle θ. The Ag and HSQ layer thicknesses are 35 nm and 23 nm, respectively. The period of the structure has dimensions of 365 × 400 nm. The rectangular aperture size is 250 × 250 nm. (b) Experimental and simulated transmission spectra of the structure with polarization angle variation from 0°to 90°in steps of 15°for fixed aperture dimensions. The LSPR, SPP-BW and MPP modes for the transverse (x) and longitudinal (y) directions are depicted using colored dot lines.

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5. Conclusion

In conclusion, we have presented a systematic parametric study of the multiple electromagnetic resonances that occur in an MDM fishnet structure, including magnetic plasmon polaritons (MPPs), localized surface plasmon resonance (LSPR) and surface plasmon polariton-Bloch wave (SPP-BWs) at visible frequencies. An inductor-capacitor (LC) circuit model is constructed to describe the MPPs. The dependence of these resonances on parameters such as the gap distance, the period, the neck length of the fishnet structure and the polarization angle of the incident light are investigated both experimentally and numerically. The results agree well with each other and show that the magnetic modes are more sensitive than the other modes. In addition, an analysis of the electromagnetic field distributions of the multiple resonance modes demonstrates their excellent capability for light confinement within a nanoscale volume, thus offering the possibility for modification of the spontaneous emission of fluorescence through simultaneous use of the excitation and the emission rate. This work can be regarded as a foundation for the optimization of MDM fishnet structures for realization of more practical applications, including color filters, sensors, color light-emitting devices, and laser sources, on the nanoscale.