1. Introduction

The recent studies on metamaterial and plasmonic structures have been gaining enormous interest experimentally and theoretically in a broad range of disciplines [1–3]. The initial research has paved a way for a series of fundamental understandings of the rich phenomena and thus has raised the possibility of delivering unique structures unavailable in natural for controlling electromagnetic waves. Continued interest in the subject is fueled by various promising applications in nanofabrication, biochemical sensing, integrated devices, and so on [4–6].

Among these, the research into optical devices at terahertz (THz) frequencies gathered a great attention due to the unique and important applications of THz technology, which has a large impact on various research fields such as material characterizing, security detection, molecule sensing, imaging, and etc [7–9]. A THz device is desired to control the pulsed or continuous-wave freely propagating THz radiation. Depending on the application, the frequency, bandwidth, transmission power and modulation scheme of THz radiation may vary widely. Typical THz devices usually include resonant filters, polarizers, compensators and modulators [10]. There is an increasing demand for a THz bandpass resonant filter to be designed for ensuring high tolerances to manufacturing parameters and multi-frequency operations. In this study, we report on a strategy to create a novel structure that combines a metal-dielectric-metal (MDM) sandwich with a periodic slot structure to perform an ultrabroadband THz resonant filter with flatter transmission top. Such a device may provide a desirable filtering method and operation to select frequency band in the THz regime and thus lead to most practical applications.

2. Analysis and numerical results

Variant of the metallic subwavelength hole arrays related to unique extraordinary resonant transmission had been discussed broadly at THz frequencies [11–13]. However, few attempts were made to provide a filter with a wideband transmission based on such a metallic hole array design. Motivated by this, our design for the resonant THz bandpass filter is a sandwich structure consisting of periodic square-loop hole array. Figure 1(a) illustrates the schematic of a unit cell of the chosen structure with normal incident electromagnetic field orientations. A pair of 200-nm thick patterned metallic cladding layers sandwiches a dielectric layer of thickness d. Each metallic layer was perforated with an array of square-loop-shaped slots with dimensions: linewidth W, periodicity P and length L, as shown in Fig. 1(b). The chosen square-loop slot pattern is a simple and symmetric structure, which exhibits excellent transmission performance and is also easy for fabrication in practice. Such a MDM structure is typically of linear dimensions in the THz community [14,15]. Simulations of the spectral response were performed using a 3D full-wave solver employing CST Microwave studio TM.

 

Fig. 1 (a) The unit cell of the sandwich metal-dielectric-metal structure with normal incident electromagnetic field. (b) Schematic of a square array of square-loop-shaped slots with a period of P, linewidth W and length L. The thickness of the middle dielectric substrate is d.

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Figure 2(a) shows the simulated transmission of a typical MDM structure with dimensional parameters: P = 120 μm, L = 100 μm, W = 20 μm and d = 21 μm, where the simulated model assumes that the metal is chosen as Aluminum and the middle dielectric is Mylar of relative permittivity ε _d = 2.89. For comparison, a MD structure with only one single metallic layer of the same square-loop hole array as that in MDM is also presented by the blue curve. Inspection of the transmission clearly shows that the MDM structure of double metallic layers has a much flatter transmission top as compared to that in MD. Clearly, the additional second array has the significant effect of flattering the transmission top and thus leads to an ultrawide passband. The resonance top in the MDM structure is pulled broadly by the two resonance frequency f _i = 0.95 THz and f _a = 1.28 THz away from each other, and the simulated passband response centers at f ₀ = 1.12 THz.

 

Fig. 2 (a) Comparison of the transmission spectra of the chosen MDM with the MD structure of only one single metallic layer, as well as the sandwich patch array. The parameters are: L = 100 μm, P = 120 μm, W = 20 μm, d = 21 μm and ε _d = 2.89. The metal is Aluminum of thickness 200 nm. (b) and (c) are electric field distributions at lower resonance frequency for the MD and MDM structures, respectively.

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Recently, a lot of works have been reported to explore the interaction of electromagnetic wave with periodically arranged subwavelength structures [3,16,17]. For example, the extraordinary optical transmission through subwavelength hole arrays was demonstrated and often explained in terms of the resonant excitation of surface plasmons, where the excitation of surface plasmons is widely believed responsible for resonant transmission based on the interference of multiple electromagnetic wave scattered by periodically arranged holes. For our case, we noticed that lower resonance frequency f _i is located near the resonance frequency of the MD structure, as shown in Fig. 2(a). The excitation of the surface plasmons by the periodically arranged slot arrays in the MD structure is considered to be responsible for this resonant peak. The electric field distributions in Fig. 2(b) also represent this feature clearly. Because the excitation occurs in the single-layer MD structure, namely within one plane, we call such a resonance an in-plane resonance. On the other hand, however, f _a is located at a higher frequency. When we search the origin of the resonance f _a, it is interesting to notice that the resonance f _a is close to the resonance frequency excited in a sandwich metallic patch, as shown in Fig. 2(a). The localized surface plasmons are excited in the metallic patch in each plane, and when two-metallic-patch interfaces are brought together, the resonance modes around each interface start to interact and couple together and thus produces the resonance f _a. The coupling between the front and back patch can be seen obviously through the electric field distributions in Fig. 2(c). Considering that the resonance involves two planes, we call f _a an out-of-plane resonance. Therefore, in a complete MDM structure, it is no doubt these two kinds of resonances, which are dominated respectively by surface plasmons and coupled localized surface plasmons, interact each other and then give rise to the broad transmission band. For convenience, we define Δf = f _a - f _i to characterize such a unique resonant passband transmission top and indicate the center resonance frequency as f ₀ [18–20].

For such a MDM filter design, the permittivity ε _d and the thickness d of the substrate dielectric and the main geometry parameters of the slot naturally influence the optical response. In following, we investigate the effect of these factors and aim to provide a greater control and optimized design. Because the variation of periodicity P only induces slight changes of both f ₀ and Δf, P is assumed the fixed value of 120 μm throughout the aftermentioned simulations. To illustrate interaction between metallic arrays, the transmission of the chosen sandwich MDM structure at normal incidence for different spacing d are plotted in Fig. 3(a) , while the changes of f ₀ and Δf as a function of d are summarized in Fig. 3(b). Increasing d from 5 to 65 μm, f ₀ is reduced from 1.26 to 0.91 THz, accompanying an increase of Δf from 0.23 to 0.35 THz. For spacing above 21 μm, Δf stays approximately the same with increasing d, but the resonance occurring above 1.5 THz is seen to be enhanced obviously, which is related to a higher-order excitation of surface plasmons.

 

Fig. 3 (a) Computed transmission spectra of MDM structure with P = 120 μm, L = 100 μm, W = 20 μm, and ε _d = 2.89 for various d. (b) Δf and center resonant frequency f ₀ as a function of d. The solid line is the fitting. (c) and (d) are effect on the transmission using different linewidth W of the slot, where other parameters are fixed as: P = 120 μm, L = 100 μm, d = 50 μm, and ε _d = 1.50. (e) and (f) are effect of various L on the transmission of the MDM structure with P = 120 μm, W = 20 μm, d = 50 μm, and ε _d = 1.50.

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The effect of linewidth W of the square loop can be seen in Figs. 3(c) and 3(d). With increase of W from 5 to 25 μm, we can see that the center resonance frequency f ₀ blueshifts from 0.84 to 1.44 THz, approximately twice variations. Meanwhile, Δf is significantly broadened from 0.16 to 0.47 THz, corresponding 294% variations. Although both f ₀ and Δf are enhanced with increasing W, the variations are not linear. We now consider the influence of the length L in the square loop. Similar as the case of changing W, L also affects the transmission profile of the MDM structure remarkably. The pronounced feature can be seen from Figs. 3(e) and 3(f) that f ₀ is reduced from 1.82 to 1.24 THz if L becomes longer from 70 to 100 μm. However, it is of interest to notice that a maximum value of Δf is achieved when L equals to 85 μm, and further increased L leads to a decrease of Δf. This may suggest an optimum length for device design for performance at various center resonance frequencies with different passbands.

In practice, except for the aforementioned dimensional parameters that influence the transmission profile naturally, we can deduce that variation of permittivity ε _d of the dielectric spacer has a similar effect on the response of the MDM structure. Actually, the permittivity of substrate dielectric is flexible depending on the material selection and at THz frequencies we also have various dielectric substrates with good transparent features such as Mylar, Quartz, Teflon, Zitex (a kind of porous Teflon) and so on. The transmission of the MDM structure with different dielectrics is plotted in Fig. 4 . The primary effect of varying the dielectric is to tune the center frequency f ₀ and Δf. Decreasing the permittivity ε _d, f ₀ is blueshifted and Δf is broadened. The decrease of ε _d also makes the transmission top flatter.

 

Fig. 4 (a) Computed transmission spectra for various permittivity ε _d of the middle dielectric substrate. (b) Dependence of the simulated values of the center resonance frequency f ₀ with corresponding Δf on ε _d. The solid line shows the fitting result.

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The preceding discussion concerning the effect of various dimensional parameters and permittivity of middle dielectric on the response of the presented MDM structure demonstrated that these parameters are essentially that of making the resonant transmission curve broader, or flatter, or making the center resonance frequency shift. All may be taken as optima in the practical device designs owing to their simplicity in fabrications. The appropriate choice of these parameters of the MDM structure thus provides to obtain desired center frequency and bandwidth, but if an analytical model can be given, it is of more help. An analytical model for the center resonance frequency can be developed approximately in a similar way as that proposed in Ref [20]. based on a circuit theory approach of microstrip patch antennas, given as:

correction index. ${\epsilon }_{eff}$is the effective permittivity considering an effective contribution of the middle dielectric and air, and can be calculated from [14]:

Figures 5(a) and 5(b) show the computed transmission curves of the MDM structure in the H- and E-planes, respectively, for various angles of incidence θ. For TE-incidence, the passband stays almost the same over wide angles of wave incidence. For TM-incidence, the higher resonance frequency f _a is shifted towards lower frequency slightly with increasing incident angles. The simulated Δf is 0.36 THz for normal incidence and 0.17 THz for TM 45°, respectively. Hence, the presented MDM structure normally provides a stable resonant passband with incident angles.

 

Fig. 5 The 3D profile of simulated transmission response for various incident angles θ in (a) TE polarization and (b) TM polarization, respectively. The parameters are: P = 120 μm, L = 100 μm, W = 20 μm, d = 50 μm, and ε _d = 1.50.

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We now consider the effect of placing multiple layers. In Fig. 6(a) , we compare the simulated transmission of the design of different MDM layers, where up to four layers are cascaded. It was not found significant effect when stack more layers, and the passband keeps approximately the same as that of the two-array configuration, although more arrays causes increased ripple and slightly broaden Δf. The ripple may be due to the scattering of different layers. Finally, as an extension, we present the simulated transmission of a complementary structure of the chosen MDM structure in Fig. 6(b), namely, a metallic square-ring array printed on both sides of the middle dielectric substrate, where a broad stopband can be found. This provides a good choice for stopband THz devices and our recent research also demonstrate such a structure exhibit a negative index in the THz regime [21].

 

Fig. 6 (a) Effect on the transmission response using various MDM layers. (b) Comparison of the MDM structure with its complementary structure. The used dimensional parameters are as same as those in Fig. 5.

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3. Conclusion

In conclusion, a unique plasmonic sandwich configuration has been considered to produce a structure having a broad passband at THz frequencies. We found that the geometry parameters, as well as the permittivity of the dielectric substrate, have visible influence on the transmission width and the center resonance frequency, which are capable of giving us the versatility required in the practical device design. The stability in the passband transmission response of the proposed structure is also obtained over wide angles of wave incidences, as well as in placing a multiple-layers case. The structure could lead to potential applications in THz optical devices, such as filters, etc.