1. Introduction

Local field enhancement in small scope is one of the most vital properties and of great importance in enhancing the interaction of electromagnetic waves with matters, such as in single molecule detection [1–3], electromagnetic manipulation [4–6], and nonlinear effect generation [7–9]. Even in terahertz (THz) region, in the frequency range of 0.1∼10 THz, the strong field concentration still pronounces powerfully in high-resolution THz imaging or the THz sensing of trace substance due to THz wave covers the vibrational and rotational resonances of most organic molecules and low energy dynamic processes in solid-state matter or devices [6,10–12]. Nanostructures with metal antennas, sharp tips, or subwavelength apertures and slits prevail widely in generating the strong localized THz field enhancement by concentrating incident THz wave in the areas of sub-nanometer scale [6,10,12–16]. It has been demonstrated that the field enhancement factor could be as high as 10⁷ in a sharp metal tip with the feature radius size of 25 nm [14] and 2.5 × 10⁴ in a nanoslit with the feature size of 1 nm [13]. Other work also exposed the remarkable influence of near-field enhancement at small metal tips and gaps in the fields of ultrafast subcycle THz nanospectroscopy, nanoscale-resolved THz scattering-type scanning near-field microscopy and THz sensing of nanoscale-thick (λ/10⁶) dielectric films [6]. Despite of the high field enhancement, huge transmission is another key property of THz metamaterials with small feature size due to its indispensible role in ultra-slight signal change detection [6,17–19]. Although lots of research attentions have unveiled the remarkable properties and applications of THz metamaterials basing on their high field enhancement [6,12–15], it is challenging to achieve high field enhancement and huge transmission simultaneously in a single structure due to the structure limited transmitting ability caused by the inherent small normalized-to-area transmittance.

Fortunately, the extraordinary optical transmission (EOT) behavior of the arrays of apertures in a metal film exposed by Ebbesen et al. in 1998 [20] provides us an effective and possible way to obtain high field enhancement and huge transmission at the same time in a single structure by reasonable and sophisticated structure design. In last two decade, the EOT behavior and related structures have been widely investigated in optical sensing and spectroscopy applications [21–24]. In compare with in visible and infrared regimes, the EOT phenomenon in THz regimes, becomes more dramatic since the optical properties of metals approach perfect electrical conductors at low frequency [18,19,25–28], which have been demonstrated in THz near-field imaging using subwavelength apertures [29], field detection and sensor [27,30,31]. In such an underexplored frequency range, confining and enhancing electric field in subwavelength apertures enable more extensive applications in sensing [27], electromagnetic modulation [26], THz fingerprinting of molecules [28] and THz metamaterials devices [32–35]. But in the past few years, researchers prefer ultra-high transmittance more rather than the localized electromagnetic field enhancement capability of the THz aperture arrays [19,36,37]. Besides, the sacrifice of the transmittance is generally inevitable in obtaining a large THz field enhancement in sub-wavelength aperture arrays with small feature gaps [6,16,38]. Achieving the strong THz field enhancement and high transmittance at the same time in sub-wavelength aperture arrays system will dramatically excite much more interesting and significant applications in THz regime. Unfortunately, the related research is rare.

Herein, we proposed a simple bow-tie aperture arrays structure (BTAAs, the complementary structure of bridging bow-tie arrays) in a metal film, which can simultaneously obtain a large electric field enhancement factor and a high optical transmission response in THz regime. In such a configuration, the EOT ability of BTAAs and the large normalized-to-area transmittance guarantee a strong optical transmission ability, and the metal tips and tiny gap make sure a huge electric field enhancement factor. The systematic simulations confirmed the remarkable optical superiorities of we designed configuration. As the feature gap is equal to 0.04 µm, the THz field enhancement factor (E/E₀) can be as high as 1.9×10⁴, two orders of magnitude higher than that in an annular nanogap arrays with 2 nm feature gap size (about 1500) [6], and the amplitude transmission of the structure reaches to around 0.8 (the corresponding normalized-to-area transmittance is about 14.3), which totally avoids serving as the sacrificial lamp in many previous large THz field enhancement systems. At the same time, a systematic and in-depth study on relationship between structural parameters of THz BTAAs and corresponding electromagnetic properties were also numerically performed. Further research results show that the intensity of electromagnetic hotspot can be enhanced by reducing the feature gap without affecting structural transmittance. In addition, we display the vital application of extremely strong electromagnetic hot spots in local terahertz refractive index detection of we designed BTAAs structure, which provides a possible straightforward path to achieve ultra-sensitive micro/nano-scale THz molecule sensing.

2. Results and discussion

Figure 1 schematically illustrates the etched symmetric BTAAs structure (L_x= 40 µm, L_y= 80 µm) in a gold (Au) nano-film with an optical thickness of 0.15 µm in THz regime, on an infinitely substrate with the refractive index of 1.68 in 0.5∼2 THz range. In which, S is the gap size between two tips of bow-tie aperture structure. P_x and P_y are the periods of the structure arrays in x- and y-axis (P_x= P_y= 120 µm), respectively. It should be noted that Au was chosen as the building material to obtain BTAAs due to its excellent structural manufacturing process compatibility and material stability. The calculated refractive index data of Au (Drude model) [39] was used for the numerical calculations. The polarization of electric field E is parallel to the long axis of Au bow-tie aperture as shown in Fig. 1 (i.e. y-polarized incidence), and the propagation direction of incident light is perpendicular to the Au film (the direction of wave vector k). In the solutions, the finite element method (FEM) were used for simulations. The transmission spectra were obtained from the S-parameter of port in simulation model by using a plane wave source with spectral range from 200 µm to 500 µm. A periodic boundary condition was set for X-Y dimensions and a perfect match layer was set for Z dimensions, respectively. The electric field distribution was extracted from the simulation model and the surface charge distribution was calculated by the boundary value expression of electromagnetic field, respectively.

 

Fig. 1. The BTAAs structure and corresponding unit cell schematic diagram of the designed Au BTAAs structure on an adhesive substrate. The Au layer with the thickness 0.15 µm is put on an infinite substrate. The refractive index of substrate is 1.68 in 0.5∼2 THz range. L_x= 40 µm, L_y= 80 µm, P_x= P_y= 120 µm.

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To make an in depth understanding of the field enhancement and transmission behavior in BTAAs structure, we systematically investigate the evolution of the BTAAs structures’ THz amplitude transmission spectra with varied geometry parameters (L_x, L_y, P_x and P_y) at a fixed gap size S of 0.2 µm, as shown in Figs. 2(a)-(d). As solely increased the period of the structure arrays in x-direction, L_x, along with a greatly enhanced transmission intensity and a broadened full width at half maximum (FWHM), the resonance peak position shifts quickly to a lower frequency due to the common action of enlarged transmission area, the enlarged counts of localized electrons and the enlarged oscillation damping at the feature tips (Fig. 2(a)). As turns to the period of the structure arrays in y-direction, L_y, (from 60 µm to 100 µm, Fig. 2(b)), the peak intensity and the bandwidth of the transmission spectra only exhibit a very weak change, while the resonance peak position experiences a significantly red-shifted due to the increased electronics density at feature tips (the angle of feature tip is decreased). It should be noted that the relatively weak transmission intensities with L_y= 20 and 40 µm are resulted by the interferences between the lattice mode of periodic arrays and the resonance mode of a single bow-tie aperture. As shown in Fig. 2(c), the increased P_x has a weak influence on the resonance position of BTAAs structure excepting for the case of P_x = 160 µm, in which the shifted resonance position may be originated from the lattice pattern of periodic arrays. With the increase of P_x, the transmission intensity gradually decreases due to the shrunken transmission area. As solely increasing P_y (Fig. 2(d)), the intensity and FWHM of BTAAs amplitude transmission spectra reduced and the resonance peak position shifts to a lower frequency. Moreover, an extremely asymmetrical spectral shape can be clearly observed due to the strong interference between the lattice mode of periodic arrays and the resonance mode of a single bow-tie aperture.

 

Fig. 2. The THz amplitude transmission spectra of the BTAAs structure with various single geometry variable. S = 0.2 µm. (a) different L_x. (b) different L_y. (c) different P_x. (d) different P_y.

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To better understand the influence of feature gaps on THz field focusing, we investigated the amplitude transmission spectra and field enhancement factors of the BTAAs structure with various feature gap size S, the corresponding results were shown in Figs. 3(a) and 3(b), respectively. As the feature gap size decreases from 80 µm to 40 µm, the resonance peak position keeps unchanged due to the influence of the lattice mode of the BTAAs structure. With the feature gap size decreases from 20 µm to 0.04 µm, the resonance peak position shifts to low frequency region due to the increased charge density at feature tips resulted from the decreased feature tip angle and the coupling interaction between two feature tips (Fig. 3(b)). However, the intensity and FWHM of the transmission peak for the BTAAs structure only have a slight variation with the feature gap size decreased from 20 µm to 0.04 µm, providing a possible platform to achieve a huge field enhancement with a barely disturbed transmittance. Figure 3(c) shows the maximum field enhancement factor of the xy-plane (z = 0, the top surface of substrate, red square-solid line) and the field enhancement factor of the zero-point (x = y = z = 0, corresponding to the center of bow-tie aperture on the top surface of substrate, blue circle-solid line) in BTAAs structure with different S, respectively. As S increases, the linear change trend of field enhancement factor in the zero-point in log-log coordinate exposed the exponential decay behavior of the electric field intensity away from the metal surface. While the quasi-linear change trend of maximum field enhancement factor in the xy-plane in log-log coordinate revealed a free-electrons localization degree dominated behavior. Note that with the decrease of the feature gap size S, the difference between above two trend lines gradually become smaller until coinciding with each other. Figure 3(d) gives out the relationship between the field enhancement factor in the zero-point and the incident THz frequency in the case of S = 0.2 µm. The maximum field enhancement factor occurs at the resonant frequency, visually demonstrating the key role of resonant state in the process of maximizing field enhancement and transmittance.

 

Fig. 3. (a) The amplitude transmission spectra of the BTAAs structure with different S. L_x = 40 µm, L_y = 80 µm, P_x = P_y = 120 µm. (b) The corresponding positions of the transmission peak with different S in (a). (c) The maximum field enhancement factor of the xy-plane (z = 0, the red line) and the field enhancement factor of the zero-point (x = y = z = 0, the blue line) in the BTAAs structure with varying S. (d) The relationship between the field enhancement factor in the zero-point and the incident THz frequency, which is consistent with the lineshape of the corresponding amplitude transmission. S = 0.2 µm.

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Figure 4(a) is the charge distribution of a BTAAs unit cell at the feature frequencies of 1.13 THz and 1.46 THz (green dotted line in Fig. 3(a)) in the case of S = 0.04 µm. The charge distributions of the top surface and bottom surface of the metal film at different frequency indicate that both of THz response are influenced by the bow-tie aperture eigenmode and the lattice mode of aperture arrays. For 1.46 THz, the weak THz transmittance is dominated by the lattice mode of aperture arrays, which can be visually proved by the large charge density on the entire bottom surface. For 1.13 THz, the high THz transmittance is dominated by the bow-tie aperture eigenmode (the quasi-dipole mode), which can be visually proved by the top surface charge density of entire feature tips. To demonstrate the distribution of the huge field enhancement of the designed BTAAs structure, the near field distribution around the feature gap (S = 0.04 µm) is shown in Fig. 4(b). The blue solid line in the top area of Fig. 4(b) represents the line field distribution on the x-axis (y = 0) with a high corresponding field enhancement factor of 3.5×10³ in the center point (x = 0). The red solid line in the left area of Fig. 4(b) is the line field distribution on the y-axis (x = 0) with the corresponding field enhancement factor of 1.9×10⁴ around feature tips. A catenary shaped field can be also observed in the left line graph of Fig. 4(b) due to the strong near-field coupling between the two tips of bow-tie aperture [40,41]. It should be noted that we chose 0.04 µm as a lower limit of feature gap size to improve the guidance accuracy of simulation data and reduce the possible sample preparation difficulties as much as possible due to the particularity of cross-scale structure configuration with a tiny feature size (generally ups from sub-10 nm to hundreds of micrometers). Table 1 shows the performance comparison of the related state-of-the-art works, indicating BTAAs is a potential structural configuration to obtain the huge field enhancement and high transmittance at the same time.

 

Fig. 4. (a) The charge distribution of a BTAAs unit cell at the feature frequencies of 1.13 THz and 1.46 THz when S = 0.04 µm, respectively. Top surface: the interface between the Au film and the vacuum. Bottom surface: the interface between the Au film and the adhesive substrate. (b) The field distribution around the feature gap size of S = 0.04 µm. Blue solid line: the line field distribution on the x-axis (y = 0). Red solid line: the line field distribution on the y-axis (x = 0).

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Table 1. The performance comparison with the related works

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To further visualize the key role of surrounded dielectric environment on the huge field enhancement in the BTAAs structure, we simulate the amplitude transmission spectra of various dielectric layers covered BTAAs structure with a filled bow-tie aperture. The refractive index of dielectric layers and filled bow-tie aperture, n, is ranging from 1 to 5 with a step size of 1. Figure 5(a) shows the normalized red-shift (Δf/f₀) of the resonance peak position in BTAAs structure with different refractive index of surrounded dielectric materials (the schematic of unit cell structure is shown in the inset). The results indicate that with increasing the refractive index of surrounded dielectric materials, the change trend of Δf/f₀ at various feature gap size S have a slight difference due to the huge damping effect on the entire contact surface of metal and dielectric covered layer. Figure 5(b) shows the normalized red-shift (Δf/f₀) of the resonance peak position in BTAAs structure only with a filled dielectric bow-tie aperture at different refractive index. The simulation results intuitively indicate that the smaller the feature gap size (the stronger THz field enhancement), the greater refractive index sensitivity. The above results indicate that the distance between the two metal tips (S) has no significant effect on the peak position change trend of the BTAAs structure as global environmental refractive index changing. But an obvious change trend difference as solely changing the refractive index of bow-tie apertures. Thus, when fixed the environmental refractive index above the BTAAs, one can obtain an ultra-sensitive THz local refractive index sensor to probe the molecular concentration in the bow-tie apertures. Through reasonable design optimization, BTAAs structure may be used in major applications such as DNA sequencing as machining nanopores in the gap between two metal tips. It should be noted that the BTAAs configuration in this paper may be fabricated by our recently developed “sketch and peel” lithography approach after process optimization, which can achieve efficient, high-speed and large-area processing of the cross-scale aperture arrays [43–45].

 

Fig. 5. (a-b) The normalized red-shift (Δf/f₀) of the resonance peak position in BTAAs structure as the refractive index of dielectric environment increase from 1 to 5. (a) The BTAAs structure covered by a dielectric layer (infinite thickness) and filled by a dielectric bow-tie structure. (b) The BTAAs structure only filled by a dielectric bow-tie structure. L_x= 40 µm, L_y= 80 µm, P_x= P_y= 120 µm, h = 0.15 µm, h_s = infinite.

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3. Conclusions

In conclusion, we design a simple THz BTAAs metamaterials configuration, which achieves the huge field enhancement factor and a high transmissivity in a single structure at the same time. The systematically investigation shows that the intensity of electromagnetic hotspot can be enhanced by continuously reducing the feature gap size of the designed structure without affecting the transmittance. As the feature gap size S reduced from 40 µm to 0.04 µm, the field enhancement factor around the feature tips of bow-tie aperture can be as high as 1.9×10⁴, and the amplitude transmission can reach to about 0.8, i.e. the corresponding normalized-to-area transmittance can be as high as 14.3. Furthermore, the stronger electromagnetic hot spots intensity (related to the smaller gap size) leads to a greater refractive index sensitivity. Our designed BTAAs THz metamaterials provides a simple potential effective configuration for huge THz field enhancement with a high amplitude transmission, and also display an intuitionistic understand and recognition to the key role of small feature gaps/tips in practical metamaterials such as in ultra-sensitive THz refractive index sensor.