Dual-layer metallic wire-hole structures were fabricated and their terahertz transmission properties were measured. They exhibit polarization-dependent transmittance with large extinction ratios. Simulation and experimental results on structures with different wire-to-hole orientations provide strong evidence that the resonance peaks are caused by plasmonic coupling between the two metallic layers. A simplified LC-circuit model is proposed to explain the coupling mechanism and to estimate the peak frequencies. Our results suggest that specific electromagnetic response can be achieved by appropriate design of the geometrical patterns on the two metallic layers and a suitable polarization of the incident wave.
© 2011 OSA
The research on surface plasmon resonance (SPR) has stimulated intense investigation on micro- and nano-structures for a wide range of applications . Many fascinating features were found in metal optics, such as extraordinary optical transmission (EOT) , negative refractive index  and etc. Although the physics of plasmons has been extensively discussed for a long time [4,5], there is still a lack of systematic study of how the geometric features of the structures, such as hole-shape or periodicity, affect the electromagnetic properties of the devices [6,7]. In certain simple single-layer designs, some basic theory such as Babinet principle  and Wood’s anomaly  have been employed to understand their experimental results. An introduction of surface roughness or artificial structures to these devices provides a convenient way to modify their electromagnetic response. In the terahertz (THz) range, the properties of metals are different from those in the optical range. Plasmons in the THz range are called “spoof plasmons” to indicate their distinct features, such as poor confinement on the metal-dielectric interface [10,11]. Recently, microscopic coupling in sub-wavelength structures has attracted much attention for its interesting macroscopic behavior . To explore more exotic devices, complementary plasmonic structures have been proposed and demonstrated in the THz range  and optical range [14,15]. They provide a simple but useful platform for studies on the 3-dimensional couplings between two patterned metallic layers separated by a dielectric.
In this letter, the interaction between two patterned metallic layers in the THz range is reported. Our simulation and experimental results show that when excited by a certain polarized wave, the wire-and-hole structure proposed here can achieve the same transmittance response as the complementary cross structure reported earlier . The numerical results demonstrate that the electric or magnetic fields of the incident wave can be modulated by the wire array or hole array, respectively, on either of the two metallic patterns. Besides, the response of the structure can be described by a simplified LC-model and Lagrangian formalism can be applied to analyze the resulting circuit. The polarization-dependent feature of the structures is useful for tailoring the transmission characteristics of devices made from them by changing the geometry of the two metallic patterns. It is believed that the same idea can be extended to the optical range to cover more applications.
The proposed structure is composed of one layer of metal wire array (WL) and one layer of metal hole array (HL) separated by a layer of polyimide of thickness d. The schematic of the structure is shown in Fig. 1 . The parameters l, w, and p define the wire/hole length, wire/hole width and period of the unit cell respectively. The angle between the long side of the holes and the y-axis, β, can be adjusted between and as shown in Fig. 1(b). A cross section view cut through the holes shown in Fig. 1(a) is given in Fig. 1(c).
The patterns were written by conventional photolithography on both sides of the polyimide film. The 2-μm-thick copper layers were deposited by sputtering followed by liftoff. Samples with different β values but identical p, l, w and d values of 402, 260, 76 and 50 μm, respectively, were fabricated in this study. The measurement was conducted in a standard 8-F confocal THz time domain spectroscopy (THz-TDS) system. The THz emitter and detector in the THz beam waist is around 5mm. The system works in an environment of dry compressed air with negligible water absorption. Our simulations were carried out by CST Micro Wave Studio (CST-MWS). The copper layer was modeled as a perfect electric conductor (PEC) and the permittivity of polyimide was taken as 3.9. The experimental transmittance of the structures was normalized by that of a single polyimide layer. Figure 2 compares the experimental transmittance (red line with circles) with the simulation results (black line with squares). Figure 2(a) and 2(d) show the transmittance of the sample with β = . The inset shows the polarization directions of the incident wave. In Fig. 2(a), the electric field is parallel to the wire and both the WL and HL are in resonance at the three major plasmonic peaks shown.These plasmonic peaks are exactly the same as those obtained from the complementary cross structure with cross dimensions identical to those formed by the wire and hole in the present structure . This result implies that the complementary (complicated) structure can be replaced by the present (simple) wire-hole structure to achieve the same transmittance. Figure 2(d) shows that when the electric field is perpendicular to the wire, the transmittance of the structure is much smaller. In this case, both the WL and HL are non-resonant with the incident wave over the measured range of frequencies, with the WL exhibiting almost unity transmission and the HL showing little transmission. Despite the nearly opaque behavior of the HL, the WL-HL coupling produces some enhancements in the transmittance at some frequencies. But the overall transmittance of the structure is low. The physics of the coupling mechanism will be analyzed in below by introducing the LC-model. Similarly, Fig. 2(b) and 2(e) show the transmission spectra with β = while Fig. 2(c) and 2(f) are for β = . All of the results show a fairly good match between simulation and experiment. They demonstrate that β affects the response of the device according to the polarization direction of the excitation wave. In fact this polarization selection property with large extinction ratios has indeed been observed in complementary structures in the optical range .
As the single layer structure can be described by an LC-circuit model, whether it be WL (capacitive and corresponding to a series resonant circuit) or HL (inductive and corresponding to a parallel resonant circuit), here we represent our dual-layer structure by two LC-circuits coupled by a mutual inductance M as shown in Fig. 3(a) . In this circuit, C1, C2 and L1, L2 denote the respective native capacitance and inductance of the HL and WL, with Z0 and Zd representing the impedance of air and dielectric, respectively. The mutual inductance, L1 and L2 have been redistributed as 3 inductances L1-M, L2-M and M and connected as shown in the figure. The parallel circuit should behave like an open circuit whereas the series circuit should behave like a short circuit at resonance. Hence Fig. 3(b) or 3(c) is the equivalent circuit at resonance, differing only in the sign of the inductive coupling. In order to obtain a simplified equation of mode hybridization or splitting due to the coupling effect, two approximations are assumed: (1) The resonant frequencies of the single WL and HL are the same, i.e.. This condition implies that the Babinet principle is obeyed in this case. In reality, and will differ slightly owing to the substrate effect. (2) Resistive dissipation is neglected so that the equivalent circuit does not contain any resistor. Then two differential equations can be obtained:Fig. 3(b) or by the subtractive induction currents in Fig. 3(c). The magnetic field intensity in the structure is calculated to verify this mode hybridization. Figure 3(d) and 3(e) show the simulated magnetic field distributions in the structure at the resonant frequencies of 0.21THz and 0.52THz, respectively, given in Fig. 2(a). They show clearly the additive and subtractive field effects as expected. A pictorial description of the magnetic field vectors caused by conducting currents is given by the white arrows. The surface currents, indicated by and , flow in opposite directions on WL and HL for additive magnetic field coupling but along the same direction for subtractive field coupling.
To get a deeper insight into the relationship between the parameters of the LC-circuit to the coupling effect, the circuit shown in Fig. 3(a) was studied by Advanced Design System (ADS). The inductance and capacitance values in the LC-circuit are difficult to estimate without knowing the transmission loss of the structure, although some empirical calculations of resonant frequencies and transmittance of mesh structures have been reported [16,17]. From the resonant frequency and 3dB-bandwidth, the parameters in the LC-circuit of dual-layer structure can be estimated. Table.1 lists the parameters which are used to calculate the blue curves shown in Fig. 2(a)–2(c). The parameters C1, C2, L1 and L2 were estimated from the single layer case and mutual inductance M was deduced from Eq. (1). It is clear that our simple LC-circuit model can reproduce approximately the same frequency response as obtained by electromagnetic simulation.In order to demonstrate the effect of variable coupling between the two metal layers without changing their spacing, the transmittance of the structure was simulated while rotating the hole counterclockwise by , i.e. changing the angle β from to , for two orthogonal polarizations and the results are shown in Fig. 4 . For the single WL or single HL, each has two special states: the incident electric (for WL) or magnetic (for HL) field is either parallel or perpendicular to its long edge, labeled respectively as WL//, WL⊥, HL// and HL⊥. The properties of the single layer structures are quite well understood. For the WL//, it exhibits a band-stop response where the electric field is strongly modulated at the resonant frequency. When the wire is rotated by as in WL⊥, broadband unity transmittance without resonance is obtained because of the large capacitive reactance in the structure. According to the Babinet principle, the case of HL// and HL⊥ can be inferred as: HL// exhibits a bandpass resonance whereas HL⊥ stops all the energy in a broadband range. When these two layers are coupled together, mode hybridization is produced and has been explained in above. When the two layers are both at resonance (WL//, HL//), which is the initial state of Fig. 4(a), mode hybridization is especially conspicuous and multi-mode transmission is experimentally confirmed as shown in Fig. 2(a). When the initial state changes from (WL//, HL//) to (WL//, HL⊥), the HL⊥ layer will stop most of the transmitted energy and the two hybridized modes tend to merge together because of the weakened coupling resulting from a significantly reduced mutual inductance M in Fig. 3(a). Likewise, Fig. 4(b) shows the case when (WL⊥, HL⊥) changes to (WL⊥, HL//) where the WL⊥ layer is non-resonant throughout while the HL layer varies from non-resonant state to resonant state, finally resulting in a bandpass response which is also experimentally observed as shown in Fig. 2(f). Intermediate values of β will produce intermediate response, such as that observed experimentally for β = [Fig. 2(b) and 2(e)]. Rotation of the wire will produce similar results and not be discussed here. Figure 4 clearly shows that the dual-layer structure can selectively modulate the electromagnetic wave as desired according to how the coupling is varied. In this investigation, the wire and hole of the same dimension have been chosen for modulating the electromagnetic wave. Other geometric patterns with different dimensions and symmetry properties can be employed to explore different modulations of the electromagnetic wave.
In conclusion, we have demonstrated a dual-layer wire-hole structure and analyzed its polarization dependent properties in detail and approximately reproduced its frequency response by an LC-circuit model. When the wire and hole structures are resonantly coupled, mode hybridization will lead to multi-mode transmission. By varying the angle between the wire and the hole and their orientation with respect to the polarization of the incident wave, one can tune the resonant states and the coupling strength in the dual-layer structure. Hence such structures and their variations should provide a versatile platform to custom-design specific electromagnetic response for useful applications.
Z. X. Zhang and K. T. Chan thank the HKSAR Government for financial support of the research through General Research Fund (GRF) Grant CUHK410606. Z. X. Zhang would like to thank L. Y. Zhao and X. Tang for useful discussions on the use of Advanced Design System 2009 and high frequency circuit theory.
References and links
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