The electromagnetic waves in the terahertz (THz) band have attracted extensive attention and researches from scholars in recent years. A major research direction is building compact and practical terahertz systems, which depends on the development of miniaturized components including terahertz detectors, modulators, switches, and absorbers [1]. The advancement of electromagnetic metamaterials has made great progress in manipulating terahertz waves, providing important opportunities for constructing practical terahertz devices [2].

Terahertz metamaterial absorbers have aroused interest among scholars due to their potential applications in wireless communication [3], biosensing [4], optoelectronic detection [5], and nondestructive imaging [6]. Previously reported metamaterial absorbers mostly have a three-layer structure of metal-medium-metal, and the inherent bandwidth of surface plasmon polaritons (SPPs) or localized surface plasmon resonance (LSPR) generated on nanoscale metal surfaces is narrow. Moreover, most metamaterial absorbers have fixed absorption characteristics after designing and manufacturing, which limits their application in a wider field. To overcome this difficulty, using active photonic materials to dynamically modulate the absorption characteristics of metamaterial absorbers has become a quite good choice. Adjusting the carrier density of semiconductor silicon has been proven to be an effective optical modulation method [7,8]. By changing the interaction between incident light and semiconductor photoconductive silicon, it helps to generate more photogenerated carriers, thereby further improving the modulation performance of terahertz metamaterial absorbers. By using this method, the modulation ability of terahertz metamaterial absorbers has been enhanced to a certain extent. However, the generation rate of photogenerated carriers is slower and requires a higher incident light power. Therefore, we urgently need a more effective way to improve this situation.

Gold nanoparticles are currently popular nanomaterials, and they have strong light-matter interaction characteristics. When gold nanoparticles interact with photons with surface valence electrons that match the collective oscillation frequency, localized surface plasmon resonance (LSPR) occurs, resulting in a strong electromagnetic field and high concentration of high-energy carriers on the surface of the nanostructure [9–11]. This ability enables gold nanoparticles to meet various needs [12–15]. Meanwhile, different gold nanoparticles exhibit different characteristics, and gold nanospheres (AuNPs) can effectively increase optocoupling and exhibit higher modulation depth [16,17]. The end of gold nanorods (AuNRs) has a certain enhancement effect on the local electric field, and, when applied to purified silicon modulators, it will produce a significant modulation effect [18,19]. The modulation enhancement effect of gold nanobipyramids (AuNBPs) will be more significant, because the tips of AuNBPs can concentrate light radiation into a strong local electric field and increase the local density of photons, which is more conducive to spectral enhancement [20–22]. It seems to be a good choice that adding gold nanoparticles into terahertz metamaterial absorbers and utilizing the strong light-matter interaction characteristics of gold nanoparticles are implemented to improve the optical tuning method of MA.

Here, we propose a scheme to integrate different gold nanoparticles with terahertz metamaterial absorbers, utilizing the localized surface plasmon resonance (LSPR) effect of gold nanoparticles to improve the modulation performance of THz MA. First, we simulated the absorption characteristics of MA without gold nanoparticles for comparison and found that its peak absorption efficiency was over 99% in the bandwidth range of ∼486GHz, achieving perfect broadband absorption performance. Subsequently, we added gold nanospheres (AuNPs), gold nanobipyramids (AuNBPs), and gold nanorods (AuNRs) to the all-dielectric double-layer honeycomb metamaterial absorber, respectively, to form a mixed sample of AuNPs/MA, AuNBPs/MA, and AuNRs/MA. Meanwhile, according to the effective medium theory (EMT) to quantitatively calculate the optical response of a metamaterial absorber with an integrated gold nanoparticle equivalent gold layer, it was found that the integrated gold nanoparticle equivalent gold layer can achieve modulation enhancement of one order of magnitude. Finally, our samples were prepared and tested through experiments. We propose a broadband all-dielectric metamaterial absorber with optically tunable response, and significantly improve the modulation characteristics of terahertz devices by utilizing the optical tuning ability of gold nanoparticles. This work is compatible with CMOS technology and has potential applications in THz modulators and optical switches.

The SEM images of AuNPs, AuNBPs, and AuNRs are shown in Figs. 1(a)–1(c). Compared with AuNPs, AuNBPs and AuNRs exhibit better uniformity in shape and size. Afterward, we prepared an all-dielectric double-layer honeycomb-shaped metamaterial absorber and, in a dry environment at room temperature, dropped solutions of AuNPs, AuNBPs, and AuNRs onto the surface of MA to form a mixed sample of AuNPs/MA, AuNBPs/MA, and AuNRs/MA, respectively. In our experiment, the volume and concentration of gold nanoparticles were 50 μL and 100 μg/mL, respectively. We fabricated MA samples using bulk micromachining processes and characterized the resultant devices using a terahertz time-domain spectrometer (THz-TDS). We use photolithography and inductively coupled plasma (ICP) etching to pattern silicon and form a metamaterial (MM) layer. Figure 1(d) shows the SEM image of the all-dielectric double-layer honeycomb shaped metamaterial absorber, and the etching process is well controlled, keeping the manufacturing errors and defects within a controllable range.

Figure 1(e) shows the absorption spectra of three types of gold nanoparticles, where the plasmon peak of AuNPs is around 520 nm, while the transverse dipole plasmon wavelengths of AuNBPs and AuNRs are also close to 520 nm, but with very low intensity, while their longitudinal wavelengths are around 805 and 1007 nm, respectively. When the excitation wavelength matches the peak value of plasmon polaritons, the electric field of gold nanoparticles is much higher. The tip of AuNBPs can concentrate light radiation into a strong local electric field and increase the local density of photons, which is beneficial to spectral enhancement [23]. In Fig. 1(f), we further demonstrate the schematic diagram of the all-dielectric double-layer honeycomb metamaterial absorber with the addition of AuNPs, AuNBPs, and AuNRs, respectively. Terahertz waves are normally incident on the surface of the sample, and the optical pump beam is at 30° angle of incidence. The absorption spectra of MA, AuNPs/MA, AuNBPs/MA, and AuNRs/MA are measured using THz-TDS to study their optically induced behavior.

We use the finite integration technique (FIT) for simulation calculations. In the simulation, the dielectric constant of doped silicon is described by the Drude model: ε=ε∞−ωp2ω2+iγω.(1)

Among them, ε∞ is the dielectric constant of intrinsic silicon, γ is the Drude collision frequency, ωp=nde2/ε0meff is the plasma frequency, nd is the doping concentration of silicon, e is the charge amount of electrons, ε0 is the vacuum dielectric constant, meff=0.37m0 is the effective mass of charge carriers in doped silicon, and m0 is the free electron mass. When the carrier concentration of doped silicon is nd=3×1016cm−3, the conductivity of doped silicon is σ=0.54Ω·cm.

Figure 2(c) shows a comparative image of the simulation and experimental absorption characteristics of the metamaterial absorber. We can see that the simulation and experimental results are basically consistent. In order to gain a deeper understanding of the physical mechanism of the metamaterial absorber, we conducted full wave simulations, as shown in Figs. 2(d) and 2(e). The resonance modes correspond to waveguide modes, which are a hybrid of magnetic (EH) and electric (HE) modes [24]. An EH mode represents a hybrid mode in which the transverse magnetic (TM) mode dominates, whereas an HE mode represents a hybrid mode in which the transverse electric (TE) mode dominates [25]. The first and second columns in Figs. 2(d) and 2(e) show the distribution of electric and magnetic fields at 1.55 and 2.99 THz, respectively, to classify the resonant modes in MA. In the low-frequency mode, as shown in the left two columns of Fig. 2(d), it is dominated by the TE field in the metamaterial layer, indicating the HE mode. The high-frequency mode is dominated by the transverse magnetic mode, indicating the EH mode, as shown in the left two columns of Fig. 2(e). The incident wave couples into the structure with little reflection through these waveguide modes and is absorbed in the metamaterial layer and the substrate [1]. The third column in Figs. 2(d) and 2(e) shows cross-sectional views of the power loss density for two resonant modes. Both the metamaterial layer and substrate play a significant role in the incident wave power loss, with power loss becoming more severe in high-frequency mode. Therefore, broadband absorption originates from two resonant modes, where the metamaterial layer and the silicon substrate contribute to absorbing incident energy.

Figures 2(f) and 2(g), respectively, show the absorption characteristics of a double-layer honeycomb metamaterial absorber at different incident angles under transverse electric (TE) and transverse magnetic (TM) polarizations. In TE mode, the resonance frequency of MA is almost unaffected by the incident angle, and, even when the incident angle is 60°, it still maintains efficient absorption performance with a peak absorption rate greater than 90%. However, its absorption bandwidth decreases continuously with the increase of the incident angle. In TM mode, as the incident angle increases, the overall absorption efficiency decreases. This is because when incident at a large angle, the incident magnetic field component parallel to the surface ring strain magnetic field decreases, and the induced magnetic field cannot effectively counteract the incident magnetic field, resulting in a decrease in absorption. As the frequency of the incident wave increases, the magnetic resonance continues to increase, leading to a gradual enhancement of the absorption efficiency of MA. In summary, the double-layer honeycomb metamaterial absorber achieves wide angle and efficient absorption in both polarization conditions.

We use the effective medium theory (EMT) to quantitatively analyze the various responses of double-layer honeycomb MA. Figure 3(a) shows a comparative image of the absorption characteristics of MA simulation, experiment, and calculation. We can see that the absorption effects of the three are quite consistent. Due to the subwavelength structure period of MA, the MM layer can be treated as an equivalent medium with the same thickness at the top of the silicon substrate. In order to extract equivalent characteristics, we simulated the reflection and transmission responses of independent MM layers, as shown in Fig. 3(b). The MM layer exhibits sharp resonance at ∼1.3 and ∼1.9THz, where both reflection and transmission are local minima, causing narrowband absorption near the resonance frequency. The peak absorption rate of the independent MM layer is ∼0.9. Although the independent MM layer also has a good absorption effect, its disadvantage is still significant compared with the broadband perfect absorption of MA in Fig. 3(a). This means that the silicon substrate plays an indelible role in the dissipation of incident THz waves.

We use transfer matrix method (TMM) for parameter retrieval to extract relative permittivity and magnetic permeability [26]. At low frequencies, the real part of the relative dielectric constant continuously decreases and the imaginary part continuously increases. There is a peak in the relative dielectric constant associated with the resonance of MA around ∼1.4THz, as shown in Fig. 3(c). At low frequencies, the magnetic resonance excited by the incident THz wave is weak, and the amplitude of relative permeability change is small. As the frequency of the incident THz wave increases, the induced magnetic field increases, and the relative permeability changes dramatically [27]. The real and imaginary parts of relative magnetic permeability have peaks around ∼1.6 and ∼1.8THz, respectively. The schematic diagram of the equivalent model based on the effective medium theory is shown in Fig. 3(d), which divides MA into the first layer structure, the second layer structure, and the substrate. Figure 3(d) (I) is an equivalent dielectric layer with the same thickness as Fig. 3(d) (II), and its equivalent dielectric constants are ε1, ε2, and εbase, respectively. Figure 3(d) (III) shows the equivalent dielectric layer and substrate with the same thickness as MM, and their equivalent dielectric constant is εeff. Both have the same reflection S11 and transmission S21 coefficients when subjected to incident THz waves. The relative dielectric constants (real part) of the three types of gold nanoparticles are around ∼1.583×10−1, ∼1.381×10−1, and ∼1.097×10−1, respectively, as shown in Fig. 3(e). For relative magnetic permeability, AuNPs are significantly higher than AuNBPs and AuNRs, which may be due to the magnetic field focusing effect generated by the sharp ends of AuNBPs, and the end of AuNRs also has a certain aggregation effect on the magnetic field. Both of them reduce the degree of freedom of electrons in space, resulting in a significant decrease in relative magnetic permeability, as shown in Fig. 3(f).

If gold nanoparticles are equivalent to an equal thickness gold layer covering the entire surface of the structure, the existence of this equivalent layer will result in a transmission of 0 and a reflection close to 1, which is what we do not want to see. Therefore, based on the shape characteristics of different gold nanoparticles, we transformed the equal thickness gold layer that originally covered the entire surface of the structure into an equivalent gold layer that did not fully cover the surface of the structure, as shown in Fig. 3(d) (IV, V).

In our experiment, the volume and concentration of added gold nanoparticles were 50 μL and 100 μg/mL, respectively. Therefore, we can calculate the total number of individual gold nanoparticles and their distribution within the structure by calculating their mass. We take the ideal scenario where gold nanoparticles are uniformly distributed on the surface of the structure during simulation, with a density of ρ=19.32g/cm2 for the gold nanoparticles. Taking AuNPs as an example, their size is 40 nm; according to m=(4/3)ρπr3, it can be obtained that mAuNPs=6.47×10−10μg, so the total number of gold nanospheres nall=7.72×109. The MA we prepared has a total of 90×90 periodic structures, so the average number of gold nanoparticles distributed in each periodic structure is nT=9.53×105. We will divide each unit structure into an average of 18×18 units, with each unit having a size of 10μm×10μm. Therefore, the average number of gold nanoparticles distributed in each unit is np=2.94×103. We placed the gold nanospheres on an equally sized rectangular substrate and observed from the top view that a spherical shadow was projected onto the rectangular substrate. The shading rate of this spherical shadow on a rectangular substrate is cov=4r2/2πr2=0.637. We uniformly distributed np gold nanospheres in a region of 0.637×10μm×10μm and then conducted parameter retrieval to extract the relative dielectric constant and magnetic permeability. The thickness of the equivalent structure is consistent with the thickness of the gold nanoparticles, and its top view shape is consistent with the shape of the gold nanoparticles projected onto a rectangular substrate. In the end, 54×54 equivalent structures were obtained within one unit, which together constitute the equivalent gold layer we need, with a relative dielectric constant of εeff′. The calculation methods for AuNBPs and AuNRs are consistent with it, and the ideal equivalent situations for the three types of gold nanoparticles are shown in Table 2.Table 2.

Ideal Equivalence of Three Types of Gold Nanoparticles

We calculate the relative dielectric constant and magnetic permeability of MA using the following equation [28]. First, the transfer matrix equation for metamaterial structures is T=[cos(nkd)−Zksin(nkd)Zksin(nkd)cos(nkd)].(2)

Among them, d is the thickness of the equivalent optical active material, n is the refractive index, and Z represents the impedance. The relationship between the S parameter of metamaterial structure and the transfer matrix T satisfies the following equation: S12=S21=1[sin(nkd)−i2(Z+1Z)cos(nkd)]eikd,(3)S11=S22=i2(1Z−Z)sin(nkd).(4)

Using the above two equations, the expressions for the equivalent refractive index n and relative impedance Z can be obtained as follows: n=1kdarccos[12S21(1−S112+S212)+2πm],(5)Z=(1+S11)2−S212(1−S11)2−S212.(6)

The relative dielectric constant and relative magnetic permeability of metamaterials can be characterized by relative impedance Z and equivalent refractive index n: ε=nZ,(7)μ=nZ.(8)

In the model, we use the retrieved effective parameters for the MM layer to calculate the reflection coefficient and transmission of the system, including the substrate using the TMM [1]. The stacked (1/2/3/4) layers are configured as air/MM/Si/air. The reflection (r) and transmission (t) coefficients for normal incidence are [1] r=e−iδ3(r1,2e−iδ2+r2,3eiδ2)+r3,4eiδ3(r1,2r2,3e−iδ2+eiδ2)e−iδ3(e−iδ2+r1,2r2,3eiδ2)+r3,4eiδ3(r2,3e−iδ2+r1,2eiδ2),(9)t=t1,2t2,3t3,4e−iδ3(e−iδ2+r1,2r2,3eiδ2)+r3,4eiδ3(r2,3e−iδ2+r1,2eiδ2).(10)

Here rm,m+1 and tm,m+1 are the reflection and transmission at the interface between layers m and m+1, and δm=nmkdm is the phase delay in layer m, where nm (nm=εmμm) and dm are the refractive index and thickness for layer m, respectively, k is the wavenumber, and εm and μm are the relative permittivity and permeability of layer m, respectively. Based on the Fresnel equations, the reflection (rm,m+1) and transmission (tm,m+1) coefficients for waves propagating from layer m to layer m+1 can be calculated by rm,m+1=nm−nm+1nm+nm+1,(11)tm,m+1=2nmnm+nm+1.(12)

We use an equivalent model of the effective medium theory to analyze the absorption characteristics of all-dielectric double-layer honeycomb metamaterial absorber. Figure 4(a) corresponds to the schematic diagrams of MA, AuNPs/MA, AuNBPs/MA, and AuNRs/MA with 520, 805, and 1007 nm pump light, respectively, in the equivalent model. Figure 4(b) shows the corresponding simulated absorption spectrum. The terahertz absorption rate calculated by integrating the frequency of the resonant region in Fig. 4(c) indicates that the introduction of an equivalent gold layer based on the effective medium theory can greatly change the absorption efficiency of the overall structure. The absorption efficiency of adding an equivalent gold layer when the incident pump power is 1.6 mW is almost the same as when the incident pump power is 0.1 mW without an equivalent gold layer, indicating that the introduction of an equivalent gold layer of integrated gold nanoparticles can achieve modulation enhancement of one order of magnitude. In order to compare the performance of MA, AuNPs/MA, AuNBPs/MA, and AuNRs/MA more intuitively, we introduced the average modulation depth (MD) and modulation enhancement factor (ME). Modulation depth MD=|(Ap−A0)/max[A0,Ap]|, where A0 and Ap are the absorption rates of the samples without and with pump light, respectively. The modulation enhancement factor is represented by ME=MDA/MD0, where MD0 and MDA are the modulation depths without and with gold nanoparticles, respectively. The average modulation depth and modulation enhancement factor corresponding to MA, AuNPs/MA, AuNBPs/MA, and AuNRs/MA are shown in Figs. 4(d) and 4(e). Although the modulation depth increases with the increase of pump power, the presence of an EMT equivalent gold layer results in significant differences in the modulation depth of the structure. The reason for the difference may be that the equivalent parameters of MA do not fully match the three types of gold nanoparticles, and there are chaotic peaks in the equivalent parameters of MA, which affect the efficient change of modulation depth. Meanwhile, the equivalent gold layer based on EMT can also cause significant reflection of incident terahertz waves, further reducing absorption and increasing modulation depth.

Three different types of gold nanoparticles themselves exhibit different characteristics. AuNPs can effectively increase optical coupling and exhibit higher modulation depth. The ends of AuNRs have a certain enhancement effect on the local electric field, while the tips of AuNBPs can concentrate light radiation into a strong local electric field and increase the local density of photons, which is more conducive to spectral enhancement. Therefore, in the equivalent gold layer based on EMT, AuNBPs/MA exhibits the best modulation depth and modulation enhancement factor.

Meanwhile, we can also observe that, at low pump power, the modulation effect of the incident pump light on the metamaterial structure itself is not significant. This is due to the uneven distribution of photogenerated carriers in the all-dielectric metamaterial structure excited by pump light. According to Beer–Lambert’s law, the pump power decays exponentially along the propagation direction [29]. In the structure, the surface layer with higher carrier density has lower power loss, while as the incident depth increases, there are still a large number of parts with lower carrier density in the bottom layer and substrate of the structure, which plays a huge role in the dissipation of pump power. As the pump power continues to increase, the carrier density in the structure also increases. The high carrier density region almost completely shields electromagnetic waves, and it ultimately leads to a significant decrease in the absorption rate of the structure.

In order to experimentally verify the design of the all-dielectric double-layer honeycomb metamaterial absorber, we manufactured MA samples using bulk micromachining processes, and the preparation process is as shown in Fig. 5. We used photolithography and inductively coupled plasma (ICP) etching techniques to etch onto copper-plated silicon wafers, followed by a second photolithography and etching on top of the first layer of the MA structure, resulting in a double-layer structure. Due to the Bosch process of ICP etching (using passivation gas to protect the side to ensure steepness), the high steepness of the MA structure is available [30–32].

Figure 6(a) shows the absorption spectra of all-dielectric double-layer honeycomb metamaterial absorber at different pump powers. The fluctuation of absorption spectra may be caused by three reasons: partial aggregation of gold nanoparticles; subtle water films that are invisible to the naked eye; and errors and defects in MA preparation. In the experiment, we used a terahertz time-domain spectrometer (THz-TDS) to characterize the experimental results. The terahertz beam was incident normally, and the optical pump beam was incident at a 30° angle. The focused spot size on the sample was 2mm×2mm. The experimental measurements were conducted at room temperature and in dry air (humidity≤1%) to eliminate the effects caused by water vapor absorption. Observing the SEM images, we found that there was partial aggregation of gold nanoparticles, which suppresses the absorbance of the LSPR characteristic peak. This is because the clustered particles reduce the number of free gold nanoparticles, and, at the same time, the free electrons on the surface of the gold nanoparticles are shared by other gold nanoparticles within the clustered particles, causing them to resonate below the frequency of the original LSPR. Meanwhile, the clustered particles may lead to enhanced reflection in some areas of the structure; thereby, it results in reduced absorption. In the SEM images, we can also observe some residual water stains on the surface of the MA structure. We speculate that there may be subtle water films that are invisible to the naked eye, which have had a certain impact on the absorption of the structure. At the same time, errors and defects in the preparation process make the surface of the MA structure not smooth, and the diffuse reflection on the surface of the MA structure prevents terahertz waves from returning to THz-TDS along the optical path, resulting in experimental errors.

As is well known, by exploring photon-induced carrier absorption in semiconductors, all-dielectric metamaterials perfect absorbers can be used as effective THz switches and modulators. In the absence of pump light irradiation, there was no significant change in the terahertz absorption rate among MA, AuNPs/MA, AuNBPs/MA, and AuNRs/MA, indicating that the added gold nanoparticles did not cause insertion loss. However, under pump excitation, there was a significant change in the absorption of MA when it does or does not contain gold nanoparticles. This is because as the pump power increases, the resonance will weaken with the blueshift of frequency and the widening of bandwidth due to the presence of photogenerated carriers [33]. Figure 6(b) shows the comparison of peak absorption of AuNPs/MA, AuNBPs/MA, and AuNRs/MA under different pump powers.

In all the three cases, the absorption efficiency of the structure decreases with the increase of incident pump light power. Among them, AuNBPs/MA has the highest modulation depth and modulation enhancement factor, as shown in Fig. 6(c). This is due to the LSPR effect of the AuNBPs, which generates a larger local field enhancement, further enhancing the optical coupling effect of the structure and thus increasing the modulation ability of the metamaterial absorber [34]. Therefore, the photoexcitation of pump light and the carrier generated by the LSPR effect of gold nanoparticles play an undeniable role in the modulation behavior. As the pump power increases, the density of photogenerated carriers gradually saturates and the enhancement effect weakens. Figures 6(d)–6(f) show the absorption spectra of AuNPs/MA, AuNBPs/MA, and AuNRs/MA at different pump powers, respectively. Compared with MA, the addition of gold nanoparticles resulted in a better modulation effect for MA. However, the difference among AuNPs/MA, AuNBPs/MA, and AuNRs/MA is not significant. We speculate that the similarity between these values is the result of dense stacking of gold nanoparticles.

We have designed and prepared an all-dielectric double-layer honeycomb-shaped metamaterial perfect absorber and improved the modulation performance of terahertz metamaterial absorbers by utilizing the optical coupling ability of gold nanoparticles. In the simulation, when it does not contain gold nanoparticles, the metamaterial absorber achieves broadband perfect absorption characteristics with an absorption efficiency of over 99% in the range of 1.446–1.932 THz. The EMT is used to quantitatively calculate the optical response of a metamaterial absorber with an integrated gold nanoparticle equivalent gold layer. The absorption efficiency of adding an equivalent gold layer when the incident pump power is 1.6 mW is almost the same as when the incident pump power is 0.1 mW without an equivalent gold layer, indicating that the introduction of an equivalent gold layer of integrated gold nanoparticles can achieve modulation enhancement of one order of magnitude. In the experiment, we used photolithography and inductively coupled plasma etching techniques to etch onto copper-plated silicon wafers, thereby preparing an all-dielectric double-layer honeycomb-shaped metamaterial absorber. We propose a broadband all-dielectric metamaterial absorber with optically tunable response and significantly improve the performance of terahertz devices by utilizing the optical tuning ability of gold nanoparticles. This work can be used to construct CMOS compatible devices for terahertz sensing and imaging applications.