Optical properties of metal nanostructures have been a frontier research area in recent decades. Metamaterials, which focus on novel phenomena and the manipulation of light, arise from the study of metal nanostructures [1, 2]. Researchers have proposed many kinds of nanostructures to control light in various ways, such as polarization and phase tuning [3–5], light localization [6], focusing [7], and vortex-beam generation [8].

Field enhancement is an important optical property of metal nanostructures. When light of the proper frequency illuminates the nanostructures, localized or propagating surface plasmons are excited [9]. Electric fields near the nanostructure’s surfaces are greatly enhanced due to the coupling between incident light and surface plasmons, and surface-enhanced spectroscopy, the optothermal effect, and photocatalysis all benefit from it [10–12]. Researchers have designed many kinds of nanostructures to obtain strong field enhancement, such as nanopits [13], nanocrescents [14], nanomushrooms [15], and nanoparticle dimers or clusters [16, 17]. There are also combined structures of nanoparticles and nanopits [18, 19]. However, the field-enhancement hot spot usually is localized inside pits, gaps, or near tips. We design a combined nanostructure of periodic inverted pyramidal pits and nanoparticles, which can obtain strong and large-area field enhancement outside the pits, instead of localized inside them. This will benefit applications such as surface-enhanced Raman scattering (SERS), because it is easier for the sample molecules to be placed in the field-enhancement environment.

The periodic nanostructure we design is shown in Fig. 1. The periodic inverted pyramidal pits can be easily fabricated by wet etching on a silicon wafer [20, 21]. Then 200-nm-thick gold film is deposited on the structure’s surface. Since the penetration depth of gold in the 500–1,200-nm wavelength region is 60 nm at most, the silicon substrate will not influence the optical properties, so it is not considered in our simulation. Silica is filled inside the pits and to a height d = 200 nm above them. Au nanodisks are placed on the silica, right above the pits. The diameter and thickness of each Au nanodisk are D = 140 nm and t = 60 nm, respectively. In the typically designed nanostructure, the depth of the pit is h = 580 nm, the period is P = 1,360 nm, and the intersection angle of opposite side walls is fixed at φ = 70.6°, which coincides with experimental fabrication techniques.

Figure 1. Schematic of the combined nanostructure.

The finite-difference time-domain method is employed to simulate the electric field distribution of the combined nanostructure. The structure is illuminated by normally incident light, polarized along the x-axis. The electric field intensity is set as E₀ = 1 V/m, without loss of generality. Periodic boundary conditions are used in the x- and y-directions. Perfectly matched layers are applied in the propagation direction, to avoid nonphysical reflection from boundaries. The permittivity of gold is described by the experimental data of Johnson and Christy [22] and interpolated to obtain the dispersion relation. The refractive index of silica is set to 1.5.

3.1. Field Enhancement of the Combined Nanostructure, Compared to Separated Nanostructures

As for the 785-nm-wavelength laser commonly used in experiments, the nanostructure we design shows strong electric field distribution around the Au nanodisk, which is exhibited in Fig. 2. The color bar’s maximum value is set to 10 V/m, to get a better view in Fig. 2(a). The original color bar is shown in Fig. 2(b), which is an enlargement of the selected area in Fig. 2(a). As shown in Fig. 2(a), the field enhancement |E|/|E₀| is greater than 10 in a large area. In fact, the maximum electric field enhancement is greater than 60, as seen in Fig. 2(b).

Figure 2. Electric field distribution of the designed nanostructure illuminated by light of wavelength 785 nm. (a) x, y section with the maximum value of the color scale set to 10 V/m. (b) Enlarged image from the dotted box in (a), with original color scale. (c) x, y section through the center of the nanodisk.

For comparison, we simulate an Au nanodisk on silica substrate. The electric field distribution at its resonant wavelength of 705 nm is shown in Fig. 3, in which the color-bar maximum is also set to 10 V/m. Compared to Fig. 3, it can be seen that the electric field intensity and the hot-spot area are much greater in Fig. 2. This implies that the periodic pyramidal pits play an important role.

Figure 3. Electric field distribution of the Au nanodisk on silica substrate under 705-nm illumination. (a) x, y section and (b) x, y section through the center of the nanodisk.

To investigate the role of the pyramidal pit, we remove the Au nanodisk of Fig. 2 and simulate the field-enhancement effect of the periodic pyramidal pits. A point monitor is placed directly above the pyramidal pit, 30 nm from the silica film. This monitor reveals that the electric field intensity reaches its maximum at an incident wavelength of 775 nm. Figure 4(a) shows the electric field distribution. We also set the color-bar maximum to 10 V/m, which is shown in Fig. 4(b), to compare to Fig. 2(a). It can be seen that the pits provide a preliminary enhanced-field atmosphere above the pit head, though not so strong as in Fig. 2. The Au nanodisk further enhances the electric field around it; This is a double enhancement effect. So by combining the enhancement effects of periodic pyramidal pits (shown in Fig. 4) and Au nanodisks (shown in Fig. 3), we can get much stronger and large-area field enhancement (shown in Fig. 2).

Figure 4. Electric field distribution under 775-nm illumination, having removed the Au nanodisk from the nanostructure shown in Fig. 2. (a) Image with original color scale. (b) Maximum of the color scale set to 10 V/m.

The resonant wavelength in Fig. 4 is 775 nm, which is a little different from that in Fig. 2. This is because the Au nanodisk in Fig. 2 lifts up the hot spot slightly, so the optical path from the hot spot to the bottom of the pit increases, which redshifts the resonant wavelength slightly.

3.2. The Relation of Resonant Wavelength to Structural Parameters

In fact, the structural parameters shown in Figs. 1 and 2 have been optimized for 785-nm incident light. First, with the pit depth h fixed at 580 nm, the structural period P is changed from 1,220 to 1,440 nm in steps of 20 nm. A point monitor is placed 5 nm along the x-axis from the Au nanodisk. The electric field intensity (which varies with wavelength and structural period) at this point is plotted in Fig. 5.

Figure 5. Electric field intensity at a point monitor 5 nm from the Au nanodisk.

As can be seen from Fig. 5, the resonant wavelength redshifts as the structural period varies from 1,220 to 1,440 nm. The period and resonant wavelength are linearly related, as shown by the dotted line in Fig. 5. When P = 1,360 nm, we obtain good enhancement at 785 nm, as the electric field intensity is greater than 20 V/m.

Observing the electric field distributions shown in Figs. 2 and 4, the field enhancement outside the pit seems to be related to the excitation of propagating surface plasmons. A periodic nanostructure can be regarded as a kind of reflection grating. When the horizontal wave-vector component of the diffracted light matches the surface-plasmon wave vector, propagating surface plasmons are excited.

As illustrated in Fig. 6, when light illuminates the structure normally, the wave vector of the diffracted light k′ has a component along the horizontal direction. The grating constant equals the structural period P. Assuming the diffraction angle is θ, according to the grating equation P sin θ = nλ, we obtain sin θ = nλ/P, in which n is an integer and λ is the incident wavelength. Thus the horizontal component of the diffracted light’s wave vector is

Figure 6. Schematic diagram of light diffraction by the periodic nanostructure.

The horizontal component of the propagating surface plasmon’s wave vector is

in which ε_m and ε_e are the relative permittivities of the metal and the environmental dielectric respectively.

Propagating surface plasmons are excited when the diffracted light’s wave vector matches the surface plasmon’s wave vector, i.e. $k_x^{\text{'}}=k_{spp}$. Thus we obtain

This is the condition for the excitation of propagation surface plasmons when light normally illuminates a periodic metal structure. As can be seen in Eq. (3), the structural period has a linear relationship to the incident wavelength, which matches what is seen in Fig. 5.

Since there is an air—Au nanodisk—SiO₂ layer upon the periodic inverted pyramidal pits, the relative permittivity of the environmental dielectric is complicated. We arbitrarily vary the refractive index of SiO₂ layer from 1.0 to 1.5 and plot the electric field intensity near the Au nanodisk, as shown in Fig. 7. It can be seen that the environmental dielectric material does influence the resonant wavelength: As its refractive index increases, the resonant wavelength redshifts, which matches Eq. (3).

Figure 7. Electric field intensity at the point monitor.

Furthermore, the pyramidal pit’s depth is varied from 500 to 740 nm in steps of 40 nm, while the structural period is fixed at P = 1,360 nm. The electric field intensity at the point monitor is shown in Fig. 8, where we can see that the resonant wavelength slightly redshifts as the pit depth increases. A pit depth of 580 nm provides good enhancement for 785-nm incident light.

Figure 8. Electric field intensity, which varies with pit depth and incident wavelength.

Suppose the distance from Au nanodisk to pit bottom is h′, where h′ = h + d. The refractive index of SiO₂ is n = 1.5. The optical-path difference of the incident and reflected light from the bottom is ΔL = 2nh′, and the phase difference is ∆φ = 2π/λ ∙ 2nh′. The interference between incident and reflected light is enhanced when the phase difference is an integer multiple of 2π:

i.e. h′ = mλ/2n (m = 1, 2, 3, …). Substituting λ = 785 nm and n = 1.5 into Eq. (4), the relevant value of h′ is obtained as 262 nm, 523 nm, 785 nm, 1,047 nm, etc. The distance from Au nanodisk to pit bottom is h′ = 780 nm, which corresponds to m = 3.

The impact of the Au nanodisk’s size is also investigated. The diameter D is varied from 130 to 180 nm. The electric field intensity near the nanodisk is plotted in Fig. 9. As observed in the figure, the diameter D has little influence on the resonant wavelength. D = 140 nm provides good enhancement for 785-nm illumination. When D increases to 170–180 nm, the best enhancement jumps to 890–905-nm incident light, because the disk’s effect dominates as the disk’s diameter increases.

Figure 9. Electric field intensity, which varies with Au-nanodisk diameter and incident wavelength.

3.3. Polarization Insensitivity

Since the polarization angle of incident light is not so easy to control in experiments such as SERS, we also investigate the influence of polarization. The designed nanostructure is symmetric in the x- and y-directions, so the polarization angle of the incident light is changed from 0° to 45° in steps of 5°. The point monitor also rotates with polarization angle, as shown by the inset of Fig. 10. The electric field intensity, which varies with incident wavelength and polarization angle, is exhibited in Fig. 10. It can be seen that the resonant wavelength remains at 785 nm as the polarization angle changes, and |E| remains greater than 20 V/m. This polarization insensitivity is good for experiments such as SERS.

Figure 10. Electric field intensity at the point monitor as polarization changes. The inset indicates the rotation of the polarization and the point monitor.

In summary, we have proposed a combined nanostructure of inverted pyramidal pits and nanoparticles, which can obtain strong electric field enhancement outside the pits. The linear relationship of structure period to resonant wavelength provides a way to tune this phenomenon. The mechanism of the enhancement outside the pits is clarified; Excitation of a propagating surface plasmon, localized plasmon, and a standing-wave effect contribute to it. Moreover, the enhancement is polarization-insensitive, which is beneficial for experiments. We believe that the combined nanostructure proposed in this work can illustrate a new strategy for photonic nanostructure design.

Higher Education Key Program of Henan Province of China (No. 19A140014); National Natural Science Foundation of China (No. 11847162).

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.