Abstract

One composite plasmonic slab with a broad bandgap (40%) is experimentally and numerically demonstrated in the terahertz (THz) region. The composite slab consists of double-layer metallic gratings and a dielectric film, which supports two resonant modes. Electric field vectors and charge distributions proved that the low-frequency resonant mode originates from the symmetric plasmonic mode, while the high-frequency resonant mode is induced by the hybrid mode of plasmonic and dielectric modes. Compared with the double-layer metallic grating, the inserted dielectric film significantly enhances the transmission of the transverse magnetic (TM) waves and induces Fano resonances. The near-field coupling between metal gratings and dielectric film can be manipulated by changing the thickness and the refractive index of dielectric films. We further demonstrated that the plasmonic bandgap can be manipulated by tuning the grating width. These results suggest that this composite plasmonic slab is promising in terahertz integrated components development such as a filter, polarizer, or sensor.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Terahertz (THz) radiation, defined as the frequency of 0.1-10 THz, has aroused increasing interest for important applications in a wide range of fields, such as imaging [1], sensing [2], and spectroscopy [3]. A device manipulating the THz waves is highly desired in these applications. THz plasmonic structures supporting surface plasmon polaritons (SPPs) are attractive options for extreme light confinement and manipulation [46]. The SPPs originate from the coupling between light and the collective oscillations of the electron plasma at a metal–air interface. When THz wave irradiates on a periodic metallic subwavelength array, a resonance peak can be observed in the spectrum because of the excited localized SPPs [7]. Typical plasmonic structures, such as metallic hole and slit arrays with extraordinary transmission properties, are extensively used for the purpose of confining the optical energy in a nanoscale spatial region and tailoring the spectra response [616]. Tremendous efforts are proposed in order to achieve multi-functional plasmonic devices, including changing the geometrical shapes and the interval between the structure units, as well as the structure stacks. Two-layered metal stacked structures have been proposed to enhance the SPPs coupling [1720]. Double-layer metal hole arrays with unexpected transmission characteristics have been found by varying the layer spacing and the lateral displacement, where the near-field coupling of surface wave plays a key role [17]. Unfortunately, two separated metal layers structures with precisely control generally suffer from a giant loss, showing a limitation in these practical applications. An efficient approach to simultaneously achieve low propagation loss and high mode confinement is to naturally use metals/dielectric hybrid structures to design devices. The combination of dielectric films and metal surfaces forms novel structures called hybrid plasmonic structures, which can improve the trade-off between the propagation loss and field confinement by adjusting the coupling between SPPs and dielectric modes [2131]. The induced hybrid mode can be strongly confined into a small size, while maintaining propagation distances exceeding those of SPPs. For instance, a double-layer metal grating array with a silicon film spacer has been reported, which shows a low propagation loss less than 1 dB [30]. The thin dielectric layer with a thickness of 2 µm eliminates the multireflection effects and obtains a strongly SPPs coupling in the metal grating layers [3031]. Recently, a multi-layer structure composed of metal gratings with asymmetric transmissions is proposed, where the substrate realizes an asymmetric environment [32]. However, in these multi-layer structures, the induced SPPs mode is dominant and the dielectric is only utilized for enhancing SPPs coupling [3038]. The dielectric film that contributes to the hybrid mode has not been well analyzed in previous studies. Additionally, little analysis of the field coupling in multi-layer hybrid plasmonic slabs has been done in the terahertz frequencies.

In this work, a composite plasmonic slab composed of double-layer metallic gratings and a dielectric film is investigated at THz frequencies. Compared with the double-layer metal grating, the inserted dielectric film not only significantly enhances the transmission of the transverse magnetic (TM) waves but also induces Fano resonances. The slab exhibits two resonant peaks in the transmission spectrum, corresponding to the symmetric plasmonic mode and the hybrid mode. The experimental results agree well with that of simulation, and the calculated field profiles confirm the physical mechanisms of the two transmission peaks. The hybrid mode originates from the mixing of plasmonic and dielectric modes, which has been analyzed by the charge distributions and electric field vectors. We also investigated the effect of the structural parameters such as the thickness and refractive index of the dielectric film on the resonant peaks. Furthermore, the influence of the grating width on the plasmonic bandgap has been well discussed. Our works analyzed the role of the dielectric film and near-field coupling in the hybrid slab, which is attractive for the design of the optoelectronic device in the THz gap.

2. Composite plasmonic slabs

The proposed composite plasmonic slab (CPS) consists of double-layered metal gratings and a dielectric film. The schematic diagram of this structure with all geometric parameters is illustrated in Fig. 1. The structural parameters are as follows: Λ=1.5 mm, w = 0.5 mm, s = 1.0 mm, t = 0.2 mm. The upper and lower metal gratings are isolated by a dielectric spacer of 0.2 mm-thick polyethylene terephthalate (PET) with a refractive index of n = 1.6 and a loss tangent (${\delta }$) of 0.0442 [39]. The metallic layers on opposing sides of the dielectric film are copper with a thickness of 0.1 mm. The total thickness of the structure is 0.4 mm, which is smaller than the operating wavelength of light. The image of the experimental sample of a single-layer metal grating is given in Fig. 1(c). The CPS in the measurement is a rough sample, which is assembled by hand. As a result, the alignment between the upper and lower metal gratings is not good. The transverse magnetic (TM) polarization is defined as a polarization state, where the electric field orientation is perpendicular to the metal grating. In the simulation, we apply periodic boundary conditions in the X- and Y- directions and open condition along the Z-direction. The mesh size in X-, Y- and Z-directions is set as 0.01 mm, 0.01 mm and 0.005 mm, respectively. Simulations of the structures are mainly achieved by the finite element method (FEM) [40].

 figure: Fig. 1.

Fig. 1. Sketch of the composite plasmonic slab (CPS). The slab consists of double-layer metal gratings and a dielectric film. (a) The side view of the CPS. (b) The 3D model of the CPS. (c) The image of the experimental sample of a single-layer metal (copper) grating.

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3. Results and discussion

3.1 Experimental and simulated results

The experimental results are measured using a terahertz time-domain spectroscopy (THz-TDS). With the femtosecond laser (780 nm), and a computer together with the home-made software, this spectrometer can equip an ultrafast optical lab for extending into the research field of THz spectroscopy with high cut-off frequency (3 THz) [15]. Photoconductor antenna (PCA), illuminated by ultra-short laser pulses, is used for THz radiation and detection. Figure 2(a) shows the THz waveform of reference, single-layer metal grating, and CPS. A signal of air space is used as a reference. The time-domain signal is attenuated by the metal grating due to the rough metal edges. The THz signal shows clear attenuating oscillation after passing through the double-layer metal gratings combining with a PET film, indicating a strong interaction between the THz waves and the formed composite slab. The frequency-domain spectra obtained by Fourier transformation are shown in Fig. 2(b). A dip at around 0.2 THz in the reference spectrum may come from the experiment system (a dry-air pump is used for the measurement). Because of the absorption from water vapor, a sharp dip at around 0.55 THz is observed in the reference spectrum. For the red symbol line, a resonant peak is occurred at 0.184 THz, resulting from the fundamental mode of metal gratings. The transmission power of single-layer metal gratings decays with the increase of frequency. The blue symbol line is the experimental spectrum of the CPS. The resonant peak is occurred at 0.166 THz, which shows a redshift compared to the spectrum of the single-layer metal grating. Interestingly, a resonant peak with high transmission power occurs at 0.312 THz. The experimental spectrum is in good agreement with the simulated spectrum. For instance, the second resonant peak is 0.332 THz in the simulated spectrum. Note that the discrepancy in the peak frequency and amplitude between the experiment and simulated spectra is possibly due to imperfections of the hand-made sample. Two resonant peaks are separated by a bandgap with a bandwidth of 0.102 THz. These results revel that this CPS can be used as THz filters.

 figure: Fig. 2.

Fig. 2. (a) THz waveform and (b) transmission spectra of reference, single-layer metal grating, in Fig. 2(b) is the simulation result.

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3.2 Propagation modes in composite plasmonic slabs

To better understand the composite slab, we analyzed the propagation mode of TM waves in metal gratings. We supposed that TM waves propagate in the Z-direction. The cut-off frequency of propagation modes can be expressed as follows [13,41]:

$${f_c} = \frac{{cm}}{{2s{n_{eff}}}}$$
where c, m, and ${n_{eff}}$ are light speed in vacuum, the number of propagation modes, and the effective refractive index, respectively. For the case of s = 1.0 mm, the fundamental TM mode (or TEM mode) (m = 0) has no cut-off frequency. In contrast, the TM1 mode (m = 1) has a cut-off frequency of 0.15 THz (the effective refractive index = 1), TM2 mode has a cut-off frequency of 0.30 THz, and the TM3 mode has a cut-off frequency of 0.45 THz. The metal grating consists of periodic slits, which can be regarded as periodic parallel-plate waveguides with a length of 0.1 mm [13,4142]. Based on the theory of waveguides, the TM0 mode having the lowest cut-off frequency is called the dominant mode of the waveguides [41]. Therefore, the mode in the frequency of 0.30-0.45 THz is a mixing mode of TM0, TM1, and TM2, which shows low transmittance than that of the pure TM0. As shown in Fig. 3(a), for the metal grating, it is very clear that the transmittance change is occurred at 0.2 and 0.4 THz (the blue dot line) because of the Wood-Rayleigh anomaly (WA) [43]. The blue line is the transmittance spectrum of the dielectric film, which exhibits a high transmittance in the frequency region of interest. Owing to the Fabry-Perot (FP) effect, a spectral peak is located at 0.465 THz. When the metal grating integrated with a dielectric film, a sharp Fano resonance with a quality (Q) of 31.5 occurs at 0.189 THz, indicating the interplay between dielectric modes and SPPs on the grating surfaces by comparing the simulation results of single-layer gratings [4446]. The single-layer metal grating is a symmetric structure, which is not allowed for the excitation of Fano resonances. An asymmetry in the structure is introduced when the single-layer metal grating integrated with a dielectric film [46]. The Fano resonance is a resonant scattering phenomenon due to the interference between a broad continuum and a discrete resonant scattering process [44]. In this case, the dielectric mode corresponds to one continue state of wave propagation. In addition, one new resonant peak is occurred at 0.345 THz. It means that these resonances are induced by the dielectric film. Also, the transmittance at 0.195 THz for the single-layer metal grating with the film is higher than that of the film because of the coupling between the SPPs, dielectric modes, and FP modes [3031]. Figure 3(b) shows the simulated transmittance spectra of double-layer gratings (black line) and composite slabs consisting of double-layer metal gratings with a dielectric film (red line). The double-layer metal grating structure behaves as a FP cavity where multiple reflections occur at two interfaces. Furthermore, localized fields on surface of double-layer metal gratings are coupling with each other and consequently result in a clearly change in the transmission spectrum [30,32]. In the region of 0.2–0.7 THz, the double-layer metal grating exhibits a lower transmittance compared to the single-layer metal grating. The resonant mode at 0.190 THz is enhanced by the double-layer metal gratings due to the coupling of SPPs on metal gratings. An obviously change can be found at 0.2 THz and 0.4 THz because of the enhanced WA modes. The similar phenomenon can also be observed in the Ref. [17]. Resonant modes can be enhanced by using a dielectric film. A dielectric film embedding inside the double-layer metal gratings forms a CPS. We note that there is a slight difference in the frequency of the lower peak transmission for double-layer metal gratings and CPS, which is probably attributed to the coupling between SPPs, FP resonance, and dielectric modes. As shown in Fig. 3(b) (red line), the transmittance at 0.332 THz increases from 0.23 to 0.98, which is significantly improved by the dielectric film. However, the resonant peak at 0.195 THz shows a low transmittance of 0.4 in contrast to the high transmittance of 0.98 in Fig. 3(a) (blue arrows), which can be improved by decreasing the metal thickness. Owing to the coupling between localized SPPs and the dielectric film, a dip around 0.557 THz can be found in the CPS transmittance spectrum, which is mainly relies on the thickness and refractive index of dielectric films. To further understand the effect of dielectric films, we simulated the electric field distribution of single-layer metal grating with a film at 0.195 THz and 0.345 THz. The result is presented in Figs. 3(c) and (d), where the color bar value is the normalization of the local electric field to the incident electric field. From Fig. 3(c), it is clear that the strong electric field is confined in the surface region of the dielectric film and metal gratings. Similar phenomenon can also be found in Fig. 3(d). It is noted that the dielectric mode combining with SPPs fields improves the field confinement and thus causes the high transmittance at 0.195 THz and 0.345 THz.

 figure: Fig. 3.

Fig. 3. (a) The transmission spectra of single-layer metal grating, single-layer metal grating with a dielectric film, and the dielectric film. (b) The spectra of double-layer metal gratings with air space and a dielectric film. (c-d) The electric field distribution of single-layer metal grating with a dielectric film at 0.195 THz and 0.345 THz, where the color bar value is the normalization of the local electric field to the incident electric field.

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Figure 4(a) shows the transmission spectra of CPSs for various structural parameters. Two noticeable transmission peaks with high transmittance (>80%) at 0.176 and 0.332 THz can be clearly observed (black line). Two peaks in the spectrum are separated by a broad bandgap from 0.198 THz to 0.3 THz, where a 0.102 THz (40%) bandgap centered in the vicinity of 0.25 THz. This bandgap is broader than the previous studies of photonic crystals [4748]. By changing the period and grating width of CPSs, the bandgap frequency and spectral contrast can be manipulated. For the case of 1.0 mm-Λ and 0.4 mm-w CPS, a bandgap with a bandwidth of 0.15 THz is achieved. Electric field distributions of 0.176 and 0.332 THz for the 1.5 mm-Λ CPS are demonstrated in Figs. 4(b) and (c). The localized electric field of 0.176 THz is mainly confined at the edge of metal gratings, indicating that this resonant mode is induced by the SPPs and thus can be termed as plasmonic modes. The field pattern at 0.332 THz behaves as a hybrid mode of the mixing of plasmonic and dielectric modes, where the strong field locates at the edge of metal gratings and dielectric surfaces. Similar field distributions can also be found in Figs. 4(d) and (f), where 0.240 THz and 0.480 THz corresponding to the low- and high-frequency spectral peaks of CPSs with 1.0 mm-Λ and 0.4 mm-w.

 figure: Fig. 4.

Fig. 4. (a) The transmission spectrum of hybrid plasmonic waveguides with a different metal period and width. (b-c) The electric field distribution of 0.176 THz and 0.332 THz in the transmission spectral peaks for Λ=1.5 mm-CPS. (d-e) The electric field distribution of 0.240 THz and 0.450 THz in the transmission spectral peaks for Λ=1.0 mm-CPS.

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To further understand the induced resonant mode at 0.332 THz, we plot in Figs. 5(a) and (b) the charge distribution of 0.176 THz and 0.332 THz. Figure 5(a) clearly shows that the resonant mode at 0.176 THz is a pure symmetric mode, where the charge distributions in the two metal grating layers are identical. However, as shown in Fig. 5(b), the resonance at 0.332 THz is a anti-symmetric mode, where the charge distributions in the two metal grating layers have opposite signs [49]. We also simulated the electric field vector of 0.176 and 0.332 THz for the CPS. As presented in Fig. 5(c), the plasmonic mode at 0.176 THz behaves as a symmetric mode with two symmetric parallel dipoles, which coincides with the symmetric mode or anti-bonding mode that has been observed in previous studies [1819,50]. Figure 5(d) demonstrated that the mode at 0.332 THz shows asymmetric parallel dipoles, which is different from that at 0.176 THz. Based on the transmission spectra analysis and the field distributions, we thus consider the mode at 0.332 THz is a hybrid mode of dielectric modes and plasmonic modes.

 figure: Fig. 5.

Fig. 5. The charge distribution in CPS for the frequencies of 0.176 THz (a) and 0.332 THz (b). The electric field vectors of 0.176 THz (c) and 0.332 THz (d).

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3.3 Resonant modes dependent on the structural parameters

3.3.1 Film thickness dependent resonant modes

The near-field coupling between metal gratings and dielectric film can be controlled by changing the structural parameters. Since the proposed slab consisting of double-layer gratings and the thickness of the dielectric film is less than the operation wavelength, a strong near-field coupling effect exists between the two gratings. The near-field coupling in general can be divided into vertical and lateral couplings, where the vertical coupling is mainly determined by the dielectric film thickness, and the lateral coupling not only depends on the width of metal gratings, but also indirectly relies on the dielectric film thickness [32]. In this part, we investigate the vertical coupling effect in this composite slab. We simulated the transmission spectra and electric field distribution by varying the dielectric film thickness from 0.10 to 0.30 mm, where the refractive index of the dielectric film is set to 1.6. From Fig. 6(a), we can observe that the spectral responses such as transmittance and resonance frequency exhibit different trends as the film thickness increases. As shown in Fig. 6(b), the spectral peak is shifted to lower frequencies as the film thickness increases. However, the transmittance of low-frequency band peak increases from 0.74 to 0.99 when the film thickness increases from 0.10 to 0.30 mm. It means that the resonant mode in the low-frequency band is improved by the thick dielectric film. Contrarily, the transmittance of the high-frequency band peak first increases and then decreases. The hybrid mode is enhanced when the film thickness increases from 0.10 to 0.20 mm. When the film thickness is larger than 0.2 mm, the coupling between SPPs and dielectric modes becomes weaker and thus results in a lower transmittance. It suggests that if the upper grating is far enough from the lower one, no near-field coupling effect exists [17]. For larger film thickness, more and more modes are present leading to an increased number of resonant features in the transmission spectrum [20]. For example, the CPS supports FP modes for larger film thickness. Electric field distributions of 0.362 and 0.308 THz for 0.10 and 0.30 mm is shown in Figs. 6(c) and (d), where the magnitude of color bar is the normalization of the local electric field to the incident electric field. Obviously, the thin film shows a strong coupling in CPSs in which the strong field is located at the surface of the dielectric film and the edge of metal gratings. When the film thickness changes to 0.30 mm, the field becomes weaker compared with that of 0.10 mm. The vertical coupling strength can be optimized by changing the film thickness [34]. Therefore, the film thickness provides an additional degree of freedom for tuning the resonance frequency.

 figure: Fig. 6.

Fig. 6. (a) The transmission spectra of CPSs for various dielectric films with different thicknesses. (b) The spectral peak frequency and transmittance for various dielectric films with different thicknesses. The electric field distribution of 0.362 THz (c) and 0.308 THz (d) for 0.10- and 0.30-mm dielectric films, respectively, where the color bar value is the normalization of the local electric field to the incident electric field.

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3.3.2 Refractive index of dielectric films dependent resonant modes

Figure 7 shows the transmission spectra and field distribution of CPSs varying with the refractive index of the dielectric film when its thickness is fixed as 0.20 mm. As shown in Fig. 7(a), with the film refractive indices increasing, the spectral peaks are shifted to lower frequencies. The bandwidth of high-frequency mode and bandgap become narrower, which can also be observed from the contour map in Fig. 7(b). Figures 7(c) and (d) depicted the electric field distribution of CPSs with different dielectric films. At 0.373 THz, an enhanced electric field is achieved by the dielectric film with a low refractive index of n = 1.2, which is tightly confined in the slab. The confined field of the resonant mode at 0.299 THz becomes weaker when the refractive index of the dielectric film is altered to be n = 2.0, which is presented in Fig. 7(d). By changing the film refractive index, the transmission spectra and enhanced field of CPSs can be manipulated. These results mean that the vertical coupling can be enhanced by changing the refractive index of the dielectric film.

 figure: Fig. 7.

Fig. 7. (a) The transmission spectrum of CPSs for various dielectric film refractive indices. (b) The contour map for various dielectric film refractive indices. (c-d) The electric field distribution of 0.373 THz and 0.299 THz for n = 1.2 film and n = 2.0 film, respectively, where the color bar value is the normalization of the local electric field to the incident electric field.

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3.3.3 Width of metal gratings dependent resonant modes

We further performed the simulation for the various widths of metal grating when the dielectric film thickness is 0.20 mm and the refractive index is 1.6. Results are illustrated in Fig. 8. The transmission band from 0.197 to 0.34 THz shows high transmittance when the grating width is 0.20 mm. With the grating width increasing, the bandgap occurs. The transmittance at 0.3 THz drops from 0.9 to 0.06 when the grating width alters from 0.2 mm to 0.7 mm. Figure 8(b) presented the contour map of the transmission spectra of CPS with various grating width, where the value of the color bar is the magnitude of transmittance. Results indicate that the smaller grating width achieves a higher transmittance due to the weak coupling in the CPS. For the hybrid mode at high-frequency band, its bandwidth becomes narrower as the grating width increases. In other words, the Q of hybrid modes is improved by increasing the grating width. It is interesting that only two bands with high transmittance exist when the metal grating width is larger than 0.50 mm, suggesting that higher-order modes cannot propagate through this composite slab. However, when the grating width larger than 0.7 mm, the transmittance of the hybrid mode is sharply decreased. For example, the transmittance in the region of 0.5-0.4 THz is lower than 0.1 when the grating width of CPSs is 0.9 mm. Figures 8(c)–(e) shows simulated power distribution of CPSs with w = 0.5 mm in the Z–X plane for different frequencies, where the simulation region in the X-axis is 8 mm (about five periods). Frequencies of 0.176 THz, 0.250 THz, and 0.332 THz respectively corresponding to the low-frequency spectral peak, the center of bandgap, and the high-frequency spectral peak. The white-dot region in Figs. 8(c)–(e) is one period of CPSs. As shown in Figs. 8(c)–(e), these frequencies show different power distributions. For the low-frequency resonant mode at 0.176 THz, the intense power is located at the center of the gap between metal gratings. However, at 0.250 THz, the center frequency of the bandgap, the strong power is confined in the upper surface of metal gratings. For the resonant mode at 0.332 THz, the maximum power is concentrated in the gap region of CPSs. An intense power can be found in the position of Z=-2.4 mm, which indicates that the CPS is possible to be used as a plasmonic lens by carefully designed.

 figure: Fig. 8.

Fig. 8. (a) The transmission spectrum of CPSs for various grating widths. (b) The contour map of CPSs for various grating widths. Simulated power distribution of CPS with w = 0.5 mm in Z-X plane for different frequencies: (c) 0.176 THz, (d) 0.250 THz, and (e) 0.332 THz.

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4. Conclusions

In this work, we proposed a composite plasmonic slab based on double-layers metallic gratings and a dielectric film, which exhibit two resonant modes and a broad bandgap (40%). The experimental results agree well with that of simulation. Charge distributions and electric field vectors demonstrated that the low-frequency resonant mode at 0.176 THz is a plasmonic mode with symmetric dipole alignment, and the high-frequency resonant mode at 0.332 THz belongs to a hybrid mode that originates from the mixing of plasmonic and dielectric modes. In contrast to the single-layer metal grating, the dielectric film attaching metal gratings introduces an asymmetry in the structure and thus results in a sharp Fano resonance with Q of 31.5 at 0.189 THz. In addition, compared with the double-layer metal grating, the inserted dielectric film significantly enhances the transmission of the transverse magnetic (TM) waves. We also investigate the influence of other structural parameters such as the thickness and refractive index of the dielectric film on the two resonant peaks. The spectral response of this structure can be efficiently tailored by these structural parameters because of the near-field coupling. The broad bandgap ranges from 0.198 THz to 0.30 THz, which is greatly influenced by the width of metal gratings. For example, when the grating width is larger than 0.7 mm, the transmittance of high-frequency resonance at 0.296 THz is lower than 0.3 and the broad bandgap does not exist. We believe that this composite plasmonic slab is attractive for the design of the optoelectronic device in the THz gap and higher frequency regions.

Funding

Science and Technology Commission of Shanghai Municipality (17142200100, 18590780100, 19590746000); Shanghai Municipal Education Commission (2019-01-07-00-02-E00032); National Natural Science Foundation of China (61671302); Shuguang Program (18SG44); Shanghai Normal University (309-AC7001-20-003040).

Acknowledgments

The authors would like to thank Dr. Hao Xu and Dr. Xiaowen Li for the result discussion.

Disclosures

The authors declare no conflicts of interest.

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25. A. Markov, H. Guerboukha, and M. Skorobogatiy, “Hybrid metal wire–dielectric terahertz waveguides: challenges and opportunities,” J. Opt. Soc. Am. B 31(11), 2587–2600 (2014). [CrossRef]  

26. M. Mbonye, R. Mendis, and D. M. Mittleman, “A terahertz two-wire waveguide with low bending loss,” Appl. Phys. Lett. 95(23), 233506 (2009). [CrossRef]  

27. K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef]  

28. H. B. Chan, Z. Marcet, K. Woo, and D. B. Tanner, “Optical transmission through double-layer metallic subwavelength slit arrays,” Opt. Lett. 31(4), 516–518 (2006). [CrossRef]  

29. Y. Cui, K. H. Fung, J. Xu, J. Yi, S. He, and N. X. Fang, “Exciting multiple plasmonic resonances by a double-layered metallic nanostructure,” J. Opt. Soc. Am. B 28(11), 2827–2832 (2011). [CrossRef]  

30. Z. Huang, E. P. Parrott, H. Park, H. P. Chan, and E. Pickwell-MacPherson, “High extinction ratio and low transmission loss thin-film terahertz polarizer with a tunable bilayer metal wire-grid structure,” Opt. Lett. 39(4), 793–796 (2014). [CrossRef]  

31. L. Y. Deng, J. H. Teng, L. Zhang, Q. Y. Wu, H. Liu, X. H. Zhang, and S. J. Chua, “Extremely high extinction ratio terahertz broadband polarizer using bilayer subwavelength metal wire-grid structure,” Appl. Phys. Lett. 101(1), 011101 (2012). [CrossRef]  

32. S. Li, L. Huang, Y. Ling, W. Liu, C. Ba, and H. Li, “High-performance asymmetric optical transmission based on coupled complementary subwavelength gratings,” Sci. Rep. 9(1), 17117 (2019). [CrossRef]  

33. Y. Shen, T. Liu, Q. Zhu, J. Wang, and C. Jin, “Dislocated Double-Layered Metal Gratings: Refractive Index Sensors with High Figure of Merit,” Plasmonics 10(6), 1489–1497 (2015). [CrossRef]  

34. X. Liu, Z. Huang, C. Zhu, L. Wang, and J. Zang, “Out-of-Plane Designed Soft Metasurface for Tunable Surface Plasmon Polariton,” Nano Lett. 18(2), 1435–1441 (2018). [CrossRef]  

35. Y. Liang, N. I. Ruan, S. Zhang, Z. Yu, and T. Xu, “Experimental investigation of extraordinary optical behaviors in a freestanding plasmonic cascade grating at visible frequency,” Opt. Express 26(3), 3271–3276 (2018). [CrossRef]  

36. M. Stolarek, D. Yavorskiy, R. Kotyński, C. J. Z. Rodríguez, J. Łusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013). [CrossRef]  

37. G. Li, Y. Shen, G. Xiao, and C. Jin, “Double-layered metal grating for high-performance refractive index sensing,” Opt. Express 23(7), 8995–9003 (2015). [CrossRef]  

38. D. Liu, Z. Xiao, X. Ma, L. Wang, K. Xu, J. Tang, and Z. Wang, “Dual-band asymmetric transmission of chiral metamaterial based on complementary U-shaped structure,” Appl. Phys. A 118(3), 787–791 (2015). [CrossRef]  

39. J. W. Lamb, “Miscellaneous data on materials for millimeter and submillimeter optics,” Int. J. Infrared Millimeter Waves 17(12), 1997–2034 (1996). [CrossRef]  

40. J. Jin, The Finite-Element Method in Electromagneticsx (Wiley-IEEE Press, 2015).

41. D. K. Cheng, Field and wave electromagnetics, (MA, Reading: Addison-Wesley, 1989, 2nd ed.), chap. 5.

42. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]  

43. Y. W. Jiang, L. D. C. Tzuang, Y. H. Ye, Y. T. Wu, M. W. Tsai, C. Y. Chen, and S. C. Lee, “Effect of Wood’s anomalies on the profile of extraordinary transmission spectra through metal periodic arrays of rectangular subwavelength holes with different aspect ratio,” Opt. Express 17(4), 2631–2637 (2009). [CrossRef]  

44. S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère, and J. L. Pelouard, “Nearly Perfect Fano Transmission Resonances through Nanoslits Drilled in a Metallic Membrane,” Phys. Rev. Lett. 104(2), 027401 (2010). [CrossRef]  

45. I. M. Mandel, A. B. Golovin, and D. T. Crouse, “Fano phase resonances in multilayer metal-dielectric compound gratings,” Phys. Rev. A 87(5), 053847 (2013). [CrossRef]  

46. A. Enemuo, M. Nolan, Y. Uk Jung, A. B. Golovin, and D. T. Crouse, “Extraordinary light circulation and concentration of s- and p-polarized phase resonances,” J. Appl. Phys. 113(1), 014907 (2013). [CrossRef]  

47. T. Ma, H. Guerboukha, M. Girard, A. D. Squires, R. A. Lewis, and M. Skorobogatiy, “3D printed hollow-core terahertz optical waveguides with hyperuniform disordered dielectric reflectors,” Adv. Opt. Mater. 6, 2085–2094 (2016). [CrossRef]  

48. D. Liu, J. Y. Lu, B. You, and T. Hattori, “Geometry-dependent modal field properties of metal-rod-array-based terahertz waveguides,” OSA Continuum 2(3), 655–666 (2019). [CrossRef]  

49. M. L. Tseng, X. Fang, V. Savinov, P. C. Wu, J.-Y. Ou, N. I. Zheludev, and D. P. Tsai, “Coherent selection of invisible high-order electromagnetic excitations,” Sci. Rep. 7(1), 44488 (2017). [CrossRef]  

50. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem., Int. Ed. 49(51), 9838–9852 (2010). [CrossRef]  

References

  • View by:

  1. K. E. Peiponen, A. Zeitler, and M. Kuwata-Gonokami, Terahertz spectroscopy and imaging (Springer-Verlag Berlin Heidelberg, 2012).
  2. X. Yin, B. W. H. Ng, and D. Abbott, Terahertz imaging for biomedical applications: pattern recognition and tomographic reconstruction (Springer Science & Business Media, 2012).
  3. Y. S. Lee, Principles of terahertz science and technology (Springer Science & Business Media, 2009).
  4. A. Ahmadivand, B. Gerislioglu, and Z. Ramezani, “Gated graphene island-enabled tunable charge transfer plasmon terahertz metamodulator,” Nanoscale 11(17), 8091–8095 (2019).
    [Crossref]
  5. A. Ahmadivand, B. Gerislioglu, R. Ahuja, and Y. K. Mishra, “Terahertz plasmonics: The rise of toroidal metadevices towards immunobiosensings,” Mater. Today 32, 108–130 (2020).
    [Crossref]
  6. L. Chen, Y. M. Wei, X. F. Zang, Y. M. Zhu, and S. L. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
    [Crossref]
  7. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
    [Crossref]
  8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref]
  9. C. Winnewisser, F. Lewen, and H. Helm, “Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy,” Appl. Phys. A: Mater. Sci. Process. 66(6), 593–598 (1998).
    [Crossref]
  10. F. J. G. de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
    [Crossref]
  11. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
    [Crossref]
  12. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength hole arrays,” Appl. Phys. Lett. 81(23), 4327–4329 (2002).
    [Crossref]
  13. J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Terahertz transmission properties of an individual slit in a thin metallic plate,” Opt. Express 17(15), 12660–12667 (2009).
    [Crossref]
  14. B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405 (2018).
    [Crossref]
  15. L. Chen, D. Liao, X. Guo, J. Zhao, Y. Zhu, and S. Zhuang, “Terahertz time-domain spectroscopy and micro-cavity components for probing samples: a review,” Front. Inform. Tech. El. 20(5), 591–607 (2019).
    [Crossref]
  16. M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, “Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays,” Opt. Lett. 30(10), 1210–1212 (2005).
    [Crossref]
  17. F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B 71(16), 165408 (2005).
    [Crossref]
  18. R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79(7), 075425 (2009).
    [Crossref]
  19. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8(8), 2171–2175 (2008).
    [Crossref]
  20. R. Taubert, R. Ameling, T. Weiss, A. Christ, and H. Giessen, “From near-field to far-field coupling in the third dimension: retarded interaction of particle plasmons,” Nano Lett. 11(10), 4421–4424 (2011).
    [Crossref]
  21. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
    [Crossref]
  22. Y. Bian, Z. Zheng, X. Zhao, J. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express 17(23), 21320–21325 (2009).
    [Crossref]
  23. Z. L. Zhang and J. Wang, “Long-range hybrid wedge plasmonic waveguide,” Sci. Rep. 4(1), 6870 (2015).
    [Crossref]
  24. C. Gui and J. Wang, “Wedge hybrid plasmonic THz waveguide with long propagation length and ultra-small deep-subwavelength mode area,” Sci. Rep. 5(1), 11457 (2015).
    [Crossref]
  25. A. Markov, H. Guerboukha, and M. Skorobogatiy, “Hybrid metal wire–dielectric terahertz waveguides: challenges and opportunities,” J. Opt. Soc. Am. B 31(11), 2587–2600 (2014).
    [Crossref]
  26. M. Mbonye, R. Mendis, and D. M. Mittleman, “A terahertz two-wire waveguide with low bending loss,” Appl. Phys. Lett. 95(23), 233506 (2009).
    [Crossref]
  27. K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
    [Crossref]
  28. H. B. Chan, Z. Marcet, K. Woo, and D. B. Tanner, “Optical transmission through double-layer metallic subwavelength slit arrays,” Opt. Lett. 31(4), 516–518 (2006).
    [Crossref]
  29. Y. Cui, K. H. Fung, J. Xu, J. Yi, S. He, and N. X. Fang, “Exciting multiple plasmonic resonances by a double-layered metallic nanostructure,” J. Opt. Soc. Am. B 28(11), 2827–2832 (2011).
    [Crossref]
  30. Z. Huang, E. P. Parrott, H. Park, H. P. Chan, and E. Pickwell-MacPherson, “High extinction ratio and low transmission loss thin-film terahertz polarizer with a tunable bilayer metal wire-grid structure,” Opt. Lett. 39(4), 793–796 (2014).
    [Crossref]
  31. L. Y. Deng, J. H. Teng, L. Zhang, Q. Y. Wu, H. Liu, X. H. Zhang, and S. J. Chua, “Extremely high extinction ratio terahertz broadband polarizer using bilayer subwavelength metal wire-grid structure,” Appl. Phys. Lett. 101(1), 011101 (2012).
    [Crossref]
  32. S. Li, L. Huang, Y. Ling, W. Liu, C. Ba, and H. Li, “High-performance asymmetric optical transmission based on coupled complementary subwavelength gratings,” Sci. Rep. 9(1), 17117 (2019).
    [Crossref]
  33. Y. Shen, T. Liu, Q. Zhu, J. Wang, and C. Jin, “Dislocated Double-Layered Metal Gratings: Refractive Index Sensors with High Figure of Merit,” Plasmonics 10(6), 1489–1497 (2015).
    [Crossref]
  34. X. Liu, Z. Huang, C. Zhu, L. Wang, and J. Zang, “Out-of-Plane Designed Soft Metasurface for Tunable Surface Plasmon Polariton,” Nano Lett. 18(2), 1435–1441 (2018).
    [Crossref]
  35. Y. Liang, N. I. Ruan, S. Zhang, Z. Yu, and T. Xu, “Experimental investigation of extraordinary optical behaviors in a freestanding plasmonic cascade grating at visible frequency,” Opt. Express 26(3), 3271–3276 (2018).
    [Crossref]
  36. M. Stolarek, D. Yavorskiy, R. Kotyński, C. J. Z. Rodríguez, J. Łusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013).
    [Crossref]
  37. G. Li, Y. Shen, G. Xiao, and C. Jin, “Double-layered metal grating for high-performance refractive index sensing,” Opt. Express 23(7), 8995–9003 (2015).
    [Crossref]
  38. D. Liu, Z. Xiao, X. Ma, L. Wang, K. Xu, J. Tang, and Z. Wang, “Dual-band asymmetric transmission of chiral metamaterial based on complementary U-shaped structure,” Appl. Phys. A 118(3), 787–791 (2015).
    [Crossref]
  39. J. W. Lamb, “Miscellaneous data on materials for millimeter and submillimeter optics,” Int. J. Infrared Millimeter Waves 17(12), 1997–2034 (1996).
    [Crossref]
  40. J. Jin, The Finite-Element Method in Electromagneticsx (Wiley-IEEE Press, 2015).
  41. D. K. Cheng, Field and wave electromagnetics, (MA, Reading: Addison-Wesley, 1989, 2nd ed.), chap. 5.
  42. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
    [Crossref]
  43. Y. W. Jiang, L. D. C. Tzuang, Y. H. Ye, Y. T. Wu, M. W. Tsai, C. Y. Chen, and S. C. Lee, “Effect of Wood’s anomalies on the profile of extraordinary transmission spectra through metal periodic arrays of rectangular subwavelength holes with different aspect ratio,” Opt. Express 17(4), 2631–2637 (2009).
    [Crossref]
  44. S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère, and J. L. Pelouard, “Nearly Perfect Fano Transmission Resonances through Nanoslits Drilled in a Metallic Membrane,” Phys. Rev. Lett. 104(2), 027401 (2010).
    [Crossref]
  45. I. M. Mandel, A. B. Golovin, and D. T. Crouse, “Fano phase resonances in multilayer metal-dielectric compound gratings,” Phys. Rev. A 87(5), 053847 (2013).
    [Crossref]
  46. A. Enemuo, M. Nolan, Y. Uk Jung, A. B. Golovin, and D. T. Crouse, “Extraordinary light circulation and concentration of s- and p-polarized phase resonances,” J. Appl. Phys. 113(1), 014907 (2013).
    [Crossref]
  47. T. Ma, H. Guerboukha, M. Girard, A. D. Squires, R. A. Lewis, and M. Skorobogatiy, “3D printed hollow-core terahertz optical waveguides with hyperuniform disordered dielectric reflectors,” Adv. Opt. Mater. 6, 2085–2094 (2016).
    [Crossref]
  48. D. Liu, J. Y. Lu, B. You, and T. Hattori, “Geometry-dependent modal field properties of metal-rod-array-based terahertz waveguides,” OSA Continuum 2(3), 655–666 (2019).
    [Crossref]
  49. M. L. Tseng, X. Fang, V. Savinov, P. C. Wu, J.-Y. Ou, N. I. Zheludev, and D. P. Tsai, “Coherent selection of invisible high-order electromagnetic excitations,” Sci. Rep. 7(1), 44488 (2017).
    [Crossref]
  50. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem., Int. Ed. 49(51), 9838–9852 (2010).
    [Crossref]

2020 (1)

A. Ahmadivand, B. Gerislioglu, R. Ahuja, and Y. K. Mishra, “Terahertz plasmonics: The rise of toroidal metadevices towards immunobiosensings,” Mater. Today 32, 108–130 (2020).
[Crossref]

2019 (4)

A. Ahmadivand, B. Gerislioglu, and Z. Ramezani, “Gated graphene island-enabled tunable charge transfer plasmon terahertz metamodulator,” Nanoscale 11(17), 8091–8095 (2019).
[Crossref]

L. Chen, D. Liao, X. Guo, J. Zhao, Y. Zhu, and S. Zhuang, “Terahertz time-domain spectroscopy and micro-cavity components for probing samples: a review,” Front. Inform. Tech. El. 20(5), 591–607 (2019).
[Crossref]

S. Li, L. Huang, Y. Ling, W. Liu, C. Ba, and H. Li, “High-performance asymmetric optical transmission based on coupled complementary subwavelength gratings,” Sci. Rep. 9(1), 17117 (2019).
[Crossref]

D. Liu, J. Y. Lu, B. You, and T. Hattori, “Geometry-dependent modal field properties of metal-rod-array-based terahertz waveguides,” OSA Continuum 2(3), 655–666 (2019).
[Crossref]

2018 (3)

X. Liu, Z. Huang, C. Zhu, L. Wang, and J. Zang, “Out-of-Plane Designed Soft Metasurface for Tunable Surface Plasmon Polariton,” Nano Lett. 18(2), 1435–1441 (2018).
[Crossref]

Y. Liang, N. I. Ruan, S. Zhang, Z. Yu, and T. Xu, “Experimental investigation of extraordinary optical behaviors in a freestanding plasmonic cascade grating at visible frequency,” Opt. Express 26(3), 3271–3276 (2018).
[Crossref]

B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405 (2018).
[Crossref]

2017 (1)

M. L. Tseng, X. Fang, V. Savinov, P. C. Wu, J.-Y. Ou, N. I. Zheludev, and D. P. Tsai, “Coherent selection of invisible high-order electromagnetic excitations,” Sci. Rep. 7(1), 44488 (2017).
[Crossref]

2016 (2)

T. Ma, H. Guerboukha, M. Girard, A. D. Squires, R. A. Lewis, and M. Skorobogatiy, “3D printed hollow-core terahertz optical waveguides with hyperuniform disordered dielectric reflectors,” Adv. Opt. Mater. 6, 2085–2094 (2016).
[Crossref]

L. Chen, Y. M. Wei, X. F. Zang, Y. M. Zhu, and S. L. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
[Crossref]

2015 (5)

Y. Shen, T. Liu, Q. Zhu, J. Wang, and C. Jin, “Dislocated Double-Layered Metal Gratings: Refractive Index Sensors with High Figure of Merit,” Plasmonics 10(6), 1489–1497 (2015).
[Crossref]

G. Li, Y. Shen, G. Xiao, and C. Jin, “Double-layered metal grating for high-performance refractive index sensing,” Opt. Express 23(7), 8995–9003 (2015).
[Crossref]

D. Liu, Z. Xiao, X. Ma, L. Wang, K. Xu, J. Tang, and Z. Wang, “Dual-band asymmetric transmission of chiral metamaterial based on complementary U-shaped structure,” Appl. Phys. A 118(3), 787–791 (2015).
[Crossref]

Z. L. Zhang and J. Wang, “Long-range hybrid wedge plasmonic waveguide,” Sci. Rep. 4(1), 6870 (2015).
[Crossref]

C. Gui and J. Wang, “Wedge hybrid plasmonic THz waveguide with long propagation length and ultra-small deep-subwavelength mode area,” Sci. Rep. 5(1), 11457 (2015).
[Crossref]

2014 (2)

2013 (3)

M. Stolarek, D. Yavorskiy, R. Kotyński, C. J. Z. Rodríguez, J. Łusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013).
[Crossref]

I. M. Mandel, A. B. Golovin, and D. T. Crouse, “Fano phase resonances in multilayer metal-dielectric compound gratings,” Phys. Rev. A 87(5), 053847 (2013).
[Crossref]

A. Enemuo, M. Nolan, Y. Uk Jung, A. B. Golovin, and D. T. Crouse, “Extraordinary light circulation and concentration of s- and p-polarized phase resonances,” J. Appl. Phys. 113(1), 014907 (2013).
[Crossref]

2012 (1)

L. Y. Deng, J. H. Teng, L. Zhang, Q. Y. Wu, H. Liu, X. H. Zhang, and S. J. Chua, “Extremely high extinction ratio terahertz broadband polarizer using bilayer subwavelength metal wire-grid structure,” Appl. Phys. Lett. 101(1), 011101 (2012).
[Crossref]

2011 (2)

R. Taubert, R. Ameling, T. Weiss, A. Christ, and H. Giessen, “From near-field to far-field coupling in the third dimension: retarded interaction of particle plasmons,” Nano Lett. 11(10), 4421–4424 (2011).
[Crossref]

Y. Cui, K. H. Fung, J. Xu, J. Yi, S. He, and N. X. Fang, “Exciting multiple plasmonic resonances by a double-layered metallic nanostructure,” J. Opt. Soc. Am. B 28(11), 2827–2832 (2011).
[Crossref]

2010 (3)

S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère, and J. L. Pelouard, “Nearly Perfect Fano Transmission Resonances through Nanoslits Drilled in a Metallic Membrane,” Phys. Rev. Lett. 104(2), 027401 (2010).
[Crossref]

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem., Int. Ed. 49(51), 9838–9852 (2010).
[Crossref]

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[Crossref]

2009 (5)

2008 (2)

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8(8), 2171–2175 (2008).
[Crossref]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

2007 (1)

F. J. G. de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[Crossref]

2006 (1)

2005 (2)

M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, “Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays,” Opt. Lett. 30(10), 1210–1212 (2005).
[Crossref]

F. Miyamaru and M. Hangyo, “Anomalous terahertz transmission through double-layer metal hole arrays by coupling of surface plasmon polaritons,” Phys. Rev. B 71(16), 165408 (2005).
[Crossref]

2004 (1)

K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[Crossref]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref]

2002 (1)

A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength hole arrays,” Appl. Phys. Lett. 81(23), 4327–4329 (2002).
[Crossref]

1998 (3)

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[Crossref]

C. Winnewisser, F. Lewen, and H. Helm, “Transmission characteristics of dichroic filters measured by THz time-domain spectroscopy,” Appl. Phys. A: Mater. Sci. Process. 66(6), 593–598 (1998).
[Crossref]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

1996 (1)

J. W. Lamb, “Miscellaneous data on materials for millimeter and submillimeter optics,” Int. J. Infrared Millimeter Waves 17(12), 1997–2034 (1996).
[Crossref]

Abbott, D.

X. Yin, B. W. H. Ng, and D. Abbott, Terahertz imaging for biomedical applications: pattern recognition and tomographic reconstruction (Springer Science & Business Media, 2012).

Ahmadivand, A.

A. Ahmadivand, B. Gerislioglu, R. Ahuja, and Y. K. Mishra, “Terahertz plasmonics: The rise of toroidal metadevices towards immunobiosensings,” Mater. Today 32, 108–130 (2020).
[Crossref]

A. Ahmadivand, B. Gerislioglu, and Z. Ramezani, “Gated graphene island-enabled tunable charge transfer plasmon terahertz metamodulator,” Nanoscale 11(17), 8091–8095 (2019).
[Crossref]

B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405 (2018).
[Crossref]

Ahuja, R.

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L. Y. Deng, J. H. Teng, L. Zhang, Q. Y. Wu, H. Liu, X. H. Zhang, and S. J. Chua, “Extremely high extinction ratio terahertz broadband polarizer using bilayer subwavelength metal wire-grid structure,” Appl. Phys. Lett. 101(1), 011101 (2012).
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X. Liu, Z. Huang, C. Zhu, L. Wang, and J. Zang, “Out-of-Plane Designed Soft Metasurface for Tunable Surface Plasmon Polariton,” Nano Lett. 18(2), 1435–1441 (2018).
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Y. Shen, T. Liu, Q. Zhu, J. Wang, and C. Jin, “Dislocated Double-Layered Metal Gratings: Refractive Index Sensors with High Figure of Merit,” Plasmonics 10(6), 1489–1497 (2015).
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Figures (8)

Fig. 1.
Fig. 1. Sketch of the composite plasmonic slab (CPS). The slab consists of double-layer metal gratings and a dielectric film. (a) The side view of the CPS. (b) The 3D model of the CPS. (c) The image of the experimental sample of a single-layer metal (copper) grating.
Fig. 2.
Fig. 2. (a) THz waveform and (b) transmission spectra of reference, single-layer metal grating, in Fig. 2(b) is the simulation result.
Fig. 3.
Fig. 3. (a) The transmission spectra of single-layer metal grating, single-layer metal grating with a dielectric film, and the dielectric film. (b) The spectra of double-layer metal gratings with air space and a dielectric film. (c-d) The electric field distribution of single-layer metal grating with a dielectric film at 0.195 THz and 0.345 THz, where the color bar value is the normalization of the local electric field to the incident electric field.
Fig. 4.
Fig. 4. (a) The transmission spectrum of hybrid plasmonic waveguides with a different metal period and width. (b-c) The electric field distribution of 0.176 THz and 0.332 THz in the transmission spectral peaks for Λ=1.5 mm-CPS. (d-e) The electric field distribution of 0.240 THz and 0.450 THz in the transmission spectral peaks for Λ=1.0 mm-CPS.
Fig. 5.
Fig. 5. The charge distribution in CPS for the frequencies of 0.176 THz (a) and 0.332 THz (b). The electric field vectors of 0.176 THz (c) and 0.332 THz (d).
Fig. 6.
Fig. 6. (a) The transmission spectra of CPSs for various dielectric films with different thicknesses. (b) The spectral peak frequency and transmittance for various dielectric films with different thicknesses. The electric field distribution of 0.362 THz (c) and 0.308 THz (d) for 0.10- and 0.30-mm dielectric films, respectively, where the color bar value is the normalization of the local electric field to the incident electric field.
Fig. 7.
Fig. 7. (a) The transmission spectrum of CPSs for various dielectric film refractive indices. (b) The contour map for various dielectric film refractive indices. (c-d) The electric field distribution of 0.373 THz and 0.299 THz for n = 1.2 film and n = 2.0 film, respectively, where the color bar value is the normalization of the local electric field to the incident electric field.
Fig. 8.
Fig. 8. (a) The transmission spectrum of CPSs for various grating widths. (b) The contour map of CPSs for various grating widths. Simulated power distribution of CPS with w = 0.5 mm in Z-X plane for different frequencies: (c) 0.176 THz, (d) 0.250 THz, and (e) 0.332 THz.

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f c = c m 2 s n e f f

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