Free-space light can be coupled into propagating surface waves at a metal–dielectric interface, known as surface plasmons (SPs). This process has traditionally faced challenges in preserving the incident polarization information and controlling the directionality of the excited SPs. The recently reported polarization-controlled asymmetric excitation of SPs in metasurfaces has attracted much attention for its promise in developing innovative plasmonic devices. However, the unit elements in these works were purposely designed in certain orthogonal polarizations, i.e., linear or circular polarizations, resulting in limited two-level polarization controllability. Here, we introduce a coupled-mode theory to overcome this limit. We demonstrated theoretically and experimentally that, by utilizing the coupling effect between a pair of split-ring-shaped slit resonators, exotic asymmetric excitation of SPs can be obtained under the -, -, left-handed circular, and right-handed circular polarization incidences, while the polarization information of the incident light can be preserved in the excited SPs. The versatility of the presented design scheme would offer opportunities for polarization sensing and polarization-controlled plasmonic devices.
© 2017 Optical Society of America
Surface plasmons (SPs) are electromagnetic excitations propagating along the interface between a metal and a dielectric . The remarkable features of subwavelength field confinement and strong field enhancement of SPs have led optics to the subwavelength scale, opening up a range of new opportunities in photonics research, including miniaturized optoelectronic circuitry [2,3], light–matter interactions [4,5], high-resolution imaging [6,7], and ultrasensitive biochemical sensing . One of the most important steps toward practical applications is coupling of free-space light to SPs, which is traditionally accomplished by using prisms or gratings [9,10]. The ever-increasing demand for functional plasmonic devices has driven the exploration of new coupling methods, especially for the asymmetric excitation of SPs. In early studies, asymmetric excitation was generally achieved using obliquely illuminated apertures [11–13] or geometrically tailored metallic gratings [14–18]. These works have played an important role in exploring on-demand excitations of SPs, but the design flexibility still remains insufficient.
Recently, metasurfaces have emerged as a robust approach to manipulate either free-space light or SPs through the design of suitable subwavelength meta-atoms and the prescribed arrangement of their spatial distributions to control local light–matter interactions [19–21]. As the most simple unit element, subwavelength slit resonators made from thin metal film are commonly used in designing metasurfaces for SP manipulation [22–27]. It was shown that asymmetric excitation of SPs can be achieved by manipulating the interference of the excited SPs through two slits with different lengths . More importantly, additional design flexibility could be engineered by incorporating the polarization responses of the slit resonators to achieve polarization-controlled asymmetric excitation. For instance, the phase of two orthogonally oriented resonators can be tailored by changing the handedness of the incident circular polarization  or the direction of the incident linear polarization , and then the interference-induced asymmetric excitation can be controlled. Alternatively, since the slits are particularly suitable for geometric phase design through careful arrangement of the resonator orientations [25–27,29], a polarization-controlled asymmetric excitation can also be achieved by applying the concept of interfacial phase discontinuity under the circularly polarized incidences . Apart from the normal slit resonator, the optical responses of L- and V-shaped slits were also studied for the polarization-controlled excitation of SPs [32–34]. However, we emphasize here that the polarization-controlled excitation strategies examined thus far, as mentioned above, depend either on -polarized and -polarized incidences, or on left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) incidences [29–34]. These are referred to as two-level polarization control.
In this paper, we theoretically and experimentally demonstrate a strategy of fully polarization-controlled excitation of SPs, in which asymmetric excitation of SPs can be simultaneously controlled by both linearly and circularly orthogonal polarizations, and we refer to this as four-level polarization control with respect to the aforementioned two-level control. In fact, it is quite challenging to achieve a four-level control since any linear polarization can be treated as a superposition of two circular polarizations, and vice versa. If a unit element could achieve controllable asymmetric excitation of SPs under a linearly (circularly) polarized incidence, when being illuminated by a circular (linear) polarization, the excited SPs from the two linear (circular) polarization components would inevitably interfere with each other. To achieve a four-level asymmetric excitation, the results of such interference must further exactly satisfy asymmetric excitation conditions. However, the simple geometric or spatial design of the individual slit resonator cannot easily realize such a complicated SP response, and alternative smart designs are thus required. It is worth noting that the recently reported asymmetric excitation of SPs based on dark mode coupling paved a new way to solve this problem . The coupled resonators can acquire more exotic SP responses than the uncoupled resonator, and more important, such SP response can be modified by changing not only the structural parameters of each resonator component, but also the coupling strength through varying the relative position of the two resonators, which provides an extra design freedom. Based on this, we suggest a type of four-level polarization-controlled asymmetric excitation of SPs. The essence of the proposed metasurface here lies in a critical coupling effect between two resonators, which leads to different asymmetric excitations under the -polarized, -polarized, LCP, and RCP incidences.
2. SAMPLE DESIGN AND NEAR-FIELD SIMULATION
A proof-of-concept metasurface for the four-level polarization-controlled asymmetric excitation of SPs is designed in the terahertz regime. The metasurface comprises a 2D array of subwavelength meta-molecules, with each meta-molecule consisting of two split-ring-shaped slit resonators (SSRs) oriented along the perpendicular directions and positioned in a mirror symmetric configuration, as shown in Fig. 1(a). The metasurface is a 200-nm-thick aluminum structure patterned on a quartz substrate. Figure 1(b) illustrates a meta-molecule, the so-called SSR-pair, where , , and . The distance between the SSRs is far smaller than the wavelength, which ensures near-field coupling. The working frequency of the structure is around 0.75 THz. To enhance the directionality and overall SP field at the designed frequency and extrude the SP response of the individual unit cell at the same time, an array setup is adopted (see Supplement 1, Section 1). Since metals almost behave like perfect conductors in the terahertz regime, the SP dispersion relation is very close to that of the free-space wave. In this case, the SPs cannot be confined as well at the metal surfaces as in the visible regime. However, the excitation and propagation behaviors are similar to those at visible frequencies. To quantitatively describe this confinement, we calculated the SP decay length, which is defined as the distance for the SP field to decay by a factor of 1/e from the metal surface to the free space . The value is 83.4 mm at 0.75 THz. To increase the confinement, a thin coating of dielectric film on top of the metal surface can be utilized . Here, the period of the array was set to be 400 μm along both the - and -directions so that the excited SPs from each SSR-pair on the air side could constructively interfere with each other at 0.75 THz.
To illustrate the SP excitation behavior of the proposed design, we ran computer simulations of the spectral responses and the electric field distributions using the commercial software CST Microwave Studio. A broadband plane wave normally illuminates on the metasurface from the substrate side to excite SPs. The whole simulation area was , and the SP spectra were extracted by setting the field probes, while the field distributions of the SPs were mapped by defining the electric field monitors for . The simulated results were obtained at 50 μm above the metasurface on the air side. Figures 1(c)–1(f) illustrate the simulated -field-amplitude distributions at 0.75 THz of the SSR-pair array under the -polarized, -polarized, LCP, and RCP incidences. It can be seen that there is always a propagation direction to be suppressed. Meanwhile, the launched SPs are obviously different from each other depending on the polarization state of the incident light, as can be gathered from the presented field distributions, where a four-level control is obtained.
3. SP RESPONSE OF A SINGLE SSR
To explore the underlying physical mechanism of the SSR-pair system, we first analyze the SP response of a single SSR. As a complementary structure to the well-known metamaterial unit, i.e., the split-ring resonator, the optical response of an SSR has been studied according to Babinet’s principle [38,39]. The fundamental resonance of an SSR can be excited by a magnetic field applied perpendicular to the gap or by an electric field passing through the ring . Consider the SSR depicted in Fig. 2(a), its fundamental resonance can be excited by an -polarized incidence. By carefully tailoring the geometric parameters of the SSR, the fundamental resonance frequency can be tuned to around 0.75 THz, where the SPs can be excited most efficiently. Figure 2(b) illustrates the corresponding transmission spectrum, where a resonance peak can be clearly seen around 0.75 THz.
Figure 2(c) illustrates the simulated real-part -field distribution of a single SSR excited under the -polarized incidence. Since the SPs propagating along the and directions (the arm directions) have the same excitation situation, as shown in Fig. 2(a), they have the same initial amplitude and phase. In contrast, the SPs propagating along the and the directions have a similar initial amplitude but a different initial phase, as can be seen in Fig. 2(c). This is attributed to the fact that the SSR does not have symmetry along the direction. Such SP response is quite different from the case of a conventional slit, which functions as an in-plane dipole, giving rise to SPs that propagate only radially away from both sides with an initial phase difference equal to [24–29]. In order to quantitatively describe the SP response of the SSR at its fundamental resonance frequency, the SPs propagating along the direction (the gap direction) are defined as , the SPs along the directions are described as , and the SPs along the direction are described as , as shown in Fig. 2(c). Here, and are complex coefficients representing the amplitude and phase difference with respect to the SPs propagating along the direction. Therefore, the SP response of the SSR at its fundamental resonance can be simply described by and . More importantly, and can be manipulated by changing the geometric parameters of the SSR, which provides a possibility to achieve the desired SP responses of a single SSR and an SSR-pair. Figure 2(d) illustrates the simulated -field-amplitude distribution in such an SSR array under the -polarized incidence. It can be seen that the features of the SP response of a single SSR at the four directions are maintained. For instance, the excited SPs propagate along mainly the directions, and only small partial SPs propagate along the directions.
If the SSR’s gap is rotated to the direction, as illustrated in Fig. 2(e), under the same -polarized incidence, its fundamental resonance cannot be excited, but its second-order resonance can be excited, whose resonance frequency is higher than the fundamental resonance frequency . Figure 2(f) illustrates the corresponding transmission spectrum, where a broadband resonance peak around 1.8 THz is observed. Since the second-order resonance has a low quality factor, its resonance behavior can be extended toward 0.75 THz, but the resonance strength largely decreases. This SP response acts as an in-plane dipole, as clearly shown by the simulated real-part -field distribution in Fig. 2(g), in which the excited SPs along the directions have the same amplitude but a phase difference. Figure 2(h) illustrates the corresponding simulated -field-amplitude distribution in such an SSR array at 0.75 THz. It can be seen that the amplitude of the excited SPs is weak but still non-ignorable comparing to that in Fig. 2(d). The frequencies of other higher order resonances are far above 0.75 THz, so their SP excitations at 0.75 THz are weak enough to be ignored. In the following analysis, only the SPs excited by the fundamental and the second-order resonances are considered.
4. THEORETICAL ANALYSIS OF THE SSR-PAIR SYSTEM
Taking advantage of the electromagnetically induced transparency (EIT) effect in metamaterials [40,41], coupled resonant slit-pairs that can asymmetrically excite SPs were recently demonstrated . The essence is introducing a dark mode coupling mechanism, where the basic unit is composed of two artificial resonant elements, a radiative bright one that couples strongly with the incidence and a dark one that couples weakly with the incidence, and then the unit possesses EIT-like resonances due to near-field Fano-type coupling between the bright and dark elements [42,43]. Considering the SSR-pair depicted in Fig. 3(a), under -polarized incidence, the fundamental resonance of the top-right SSR () can be directly excited and acts as a bright mode ; meanwhile, although the bottom-left SSR () cannot be directly excited at its fundamental resonance, it can couple with , giving rise to a resonance and acting as a dark mode . The corresponding transmission spectra of such a single SSR-pair are illustrated in Supplement 1, Section 2, where the cross-polarization resonance peak around 0.75 THz confirms the near-field coupling effect. On the contrary, under the -polarized incidence, the above mode roles exchange, with acting as the bright mode and acting as the dark mode . In addition, the second-order resonances of and can be respectively excited by the - and -polarized incidences, providing minor contributions to the SP excitations at 0.75 THz, which are represented as and , respectively. In this configuration, for an arbitrary incident polarization , the SSR-pair system can be theoretically described by applying the coupled-mode equations [40,44–46]:
According to Eq. (1), every resonance mode can be solved, where we have
Actually, the modes here are the calculated result when or . To analyze the SP excitations, for and , we define the SP fields that propagate along the gap direction as and , respectively, where is the fitting coefficient to normalize the SP excitations from the resonance modes ; then the SP fields along the other directions can be described by and , as discussed previously. Similarly, for , the SP field that propagates along one arm direction can be defined as , and then the SP field along the opposite direction will be due to the phase difference. Based on this, Fig. 3(a) schematically illustrates the overall SP response of an SSR-pair under an arbitrary polarization incidence, where the SP fields from different resonance modes at the four directions are synthetically considered in the unit of the SSR-pair. The subscript and superscript of the inset represent the SP propagating direction and SSR number, respectively. The corresponding expressions can be found in Supplement 1, Section 3.
Next, we consider the SSR-pair array depicted in Fig. 3(b). At the point of observation, , which is located on the side of the SSR-pair array, the SP field can be calculated as a superposition result of the excited SPs from each SSR-pair by using the 2D Huygens–Fresnel principle [23–27,29,47]:1(c)] are integrated as . Similarly, the SP fields at lines , , and are integrated as , , and , respectively. Therefore, SP excitations under an arbitrary polarization incidence can be obtained, , with representing the incident polarization state.
Based on the above discussion, SP excitations of the SSR-pair array under the -polarized, -polarized, LCP, and RCP incidences are mainly studied. According to the derivations from Eq. (1), we found that SP excitations can be well described solely by . The corresponding SP excitations under polarization, LCP, and RCP can be simply expressed as , , and , respectively, where is a matrix that represents to the mirror operation (see the Supplement 1, Section 4):
Based on this, we appropriately select the unit elements by simulation. With the overall performance taken into consideration, eventually, the corresponding simulated amplitude spectra of are illustrated as solid lines in Figs. 3(c)–3(f). It can be seen that is strongly suppressed at resonance frequency, and is the strongest, while and have similar amplitude. Meanwhile, the simulated phase spectra of are illustrated as the solid lines in Figs. 3(g)–3(j). The phase difference between and at resonance frequency is . Both the amplitude and phase results satisfy the prescribed requirements well. The corresponding theoretical fitted amplitude and phase spectra using Eqs. (1) and (3) agree well with the simulations, as represented by the dashed lines in Figs. 3(c)–3(j), which shows good effectiveness of the coupled-mode theory. Furthermore, the simulated and theoretical amplitude spectra in the case of the LCP incidence are illustrated by the solid and dashed lines, respectively, in Figs. 4(a)–4(d). It can be seen that the amplitude of is strongly suppressed around 0.75 THz, whereas the amplitude of becomes the largest, corresponding to destructive and constructive interference as defined by Eq. (5), respectively. Similarly consistent results can also be obtained in the case of the RCP incidence, as shown in Figs. 4(e)–4(h), where the and correspond to the interferences defined by Eq. (6). Both the simulated and theoretical results verify the viability of our design strategy.
5. EXPERIMENTAL VERIFICATION
To further experimentally verify our proposed design, we fabricated the metasurface using conventional photolithography and metallization processing. Figure 5(a) illustrates a scanning electron micrograph image of one fabricated SSR-pair unit, which is made from a 200-nm-thick aluminum film patterned on a 2-mm-thick quartz substrate. A scanning near-field terahertz microscope system was applied to characterize the sample . The working principle is the same as that of the traditional terahertz time-domain spectroscopy. The main difference is that the terahertz detector here was replaced with a near-field photoconductive-antenna-based probe. The detection beam of the system was coupled into a 2-m-long optical fiber to enable a movable probe. Before coupling into the fiber, a pre-dispersion compensation grating pair was employed to suppress the pulse stretching effect in the fiber.
Figure 5(b) illustrates a simple schematic of the measurement. The incident terahertz beam was collimated with a spot size of 5 mm diameter, which was large enough to cover the whole excitation area. The linear polarization was achieved using a metallic grid polarizer. The measured amplitude and phase spectra of are illustrated by circles in Figs. 3(c)–3(j), agreeing well with the corresponding simulated and theoretical results in the frequency range of interest. The circular polarizations were achieved using the combination of a grid polarizer and a quarter-wave plate. The measured amplitude spectra of and are illustrated by the circles in Fig. 4, which also agree well with the corresponding simulated and theoretical results. To more clearly show the asymmetric excitation performance, the SP-field distributions were scanned under the -polarized, -polarized, LCP, and RCP incidences, respectively. During the scan, the probe was placed approximately 50 μm above the sample surface, and the scanning range was , the same as that in the simulation. The measured -field-amplitude distributions at 0.75 THz are illustrated in Figs. 5(c)–5(f), and it can be found that the excited SPs toward each direction agree well with the corresponding simulations. The presented experimental results clearly confirm the proposed four-level polarization-controlled asymmetric excitation of SPs.
6. SP EXCITATION UNDER ARBITRARY INCIDENT POLARIZATION
To take an insight into the proposed metasurface, we perform simulation studies of the SP excitation under arbitrary incidences. It can be found from Eqs. (1) and (3) that the polarization information of the incidence can be fully encoded in the amplitudes and relative phases of the excited SPs. Figures 6(a)–6(d) illustrate the SP amplitudes of the excited SPs toward the , , , and directions at 0.75 THz as a function of polarization parameters and . Here, the incident polarization state is expressed as 
It can be seen in Figs. 6(a)–6(d) that the SP excitations are different from each other, and interestingly, the SP excitation toward the and directions has an opposite trend with that of the and directions, respectively, which can be attributed to the mirror-symmetric configuration of our design. The -polarization, -polarization, LCP, and RCP are the special polarization states, in that each can suppress the SP excitation of a specific direction, as we demonstrated above. Apart from these, continuous tuning of the excitation can be achieved by changing the incident polarization state. For example, if one rotates the angle of the incident linear polarization (see the excitation when or ), the SP excitations toward the and directions are nearly constant, while the SP excitations toward the and directions can be flexibly tuned. In contrast, it can be seen from the SP excitations marked by the white squares that the SP excitations toward the and directions are nearly constant, while the SP excitations toward the and directions can be flexibly tuned. Such versatile tunability is particularly attractive in designing polarization-controlled plasmonic devices or polarization sensing devices.
We show that the excitations of SPs by a metasurface consisting of a coupled SSR-pair system completely depend on the polarization states of the incident light. The proposed design would therefore achieve four-level polarization-controlled asymmetric SP excitation. The flexibility from encoding the polarization information into the SPs, in conjunction with dynamic polarization modulation techniques, may open a gateway toward integrated plasmonic circuitry with electrically reconfigurable functionalities. Furthermore, based on the universal coupled-mode theory, the proposed design scheme is applicable to the broad electromagnetic spectrum.
National Key Basic Research Program of China (2014CB339800); National Natural Science Foundation of China (NSFC) (61420106006, 61422509, 61427814, 61605143); Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (IRT13033); National Science Foundation (NSF) (ECCS-1232081).
We thank Veronic E. Tremblay for her advice on optimizing the writing.
See Supplement 1 for supporting content.
1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
2. V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37(8), 728–738 (2012). [CrossRef]
3. Y. Fang and M. Sun, “Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits,” Light Sci. Appl. 4, e294 (2015).
4. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
5. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329, 930–933 (2010).
6. S. Kawata, Y. Inouye, and P. Verma, “Plasmonics for near-field nano-imaging and superlensing,” Nat. Photonics 3, 388–394 (2009).
7. F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
8. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008).
9. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
10. I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficiency of local surface plasmon polariton excitation on ridges,” Phys. Rev. B 78, 115115 (2008). [CrossRef]
11. H. Kim and B. Lee, “Unidirectional surface plasmon polariton excitation on single slit with oblique backside illumination,” Plasmonics 4, 153–159 (2009). [CrossRef]
12. X. Li, Q. Tan, B. Bai, and G. Jin, “Experimental demonstration of tunable directional excitation of surface plasmon polaritons with a subwavelength metallic double slit,” Appl. Phys. Lett. 98, 251109 (2011). [CrossRef]
13. F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013). [CrossRef]
14. F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007). [CrossRef]
15. A. Baron, E. Devaux, J.-C. Rodier, J.-P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11, 4207–4212 (2011). [CrossRef]
16. L. Wang, T. Li, L. Li, W. Xia, X. G. Xu, and S. N. Zhu, “Electrically generated unidirectional surface plasmon source,” Opt. Express 20, 8710–8717 (2012). [CrossRef]
17. H. Liao, Z. Li, J. Chen, X. Zhang, S. Yue, and Q. Gong, “A submicron broadband surface-plasmon-polariton unidirectional coupler,” Sci. Rep. 3, 1918 (2013). [CrossRef]
18. X. Huang and M. L. Brongersma, “Compact aperiodic metallic groove arrays for unidirectional launching of surface plasmons,” Nano Lett. 13, 5420–5424 (2013). [CrossRef]
19. P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017). [CrossRef]
20. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012). [CrossRef]
21. A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, “Efficient unidirectional polarization-controlled excitation of surface plasmon polaritons,” Light Sci. Appl. 3, e197 (2014). [CrossRef]
22. S.-Y. Lee, K. Kim, S.-J. Kim, H. Park, K.-Y. Kim, and B. Lee, “Plasmonic meta-slit: shaping and controlling near-field focus,” Optica 2, 6–13 (2015). [CrossRef]
23. T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011). [CrossRef]
24. E.-Y. Song, S.-Y. Lee, J. Hong, K. Lee, Y. Lee, G.-Y. Lee, H. Kim, and B. Lee, “A double-lined metasurface for plasmonic complex-field generation,” Laser Photon. Rev. 10, 299–306 (2016). [CrossRef]
25. S. Xiao, F. Zhong, H. Liu, S. Zhu, and J. Li, “Flexible coherent control of plasmonic spin-Hall effect,” Nat. Commun. 6, 8360 (2015). [CrossRef]
26. X. Zhang, Y. Xu, W. Yue, Z. Tian, J. Gu, Y. Li, R. Singh, S. Zhang, J. Han, and W. Zhang, “Anomalous surface wave launching by handedness phase control,” Adv. Mater. 27, 7123–7129 (2015). [CrossRef]
27. Q. Xu, X. Zhang, Y. Xu, C. Ouyang, Z. Tian, J. Gu, J. Li, S. Zhang, J. Han, and W. Zhang, “Polarization-controlled surface plasmon holography,” Laser Photon. Rev. 11, 1600212 (2017). [CrossRef]
28. J. Yang, X. Xiao, C. Hu, W. Zhang, S. Zhou, and J. Zhang, “Broadband surface plasmon polariton directional coupling via asymmetric optical slot nanoantenna pair,” Nano Lett. 14, 704–709 (2014). [CrossRef]
29. J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013). [CrossRef]
30. B. Chen, J. Yang, C. Hu, S. Wang, Q. Wen, and J. Zhang, “Plasmonic polarization nano-splitter based on asymmetric optical slot antenna pairs,” Opt. Lett. 41, 4931–4934 (2016). [CrossRef]
31. L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013). [CrossRef]
32. J. Yang, S. Zhou, C. Hu, W. Zhang, X. Xiao, and J. Zhang, “Broadband spin-controlled surface plasmon polariton launching and radiation via L-shaped optical slot nanoantennas,” Laser Photon. Rev. 8, 590–595 (2014). [CrossRef]
33. F. Huang, X. Jiang, H. Yang, S. Li, and X. Sun, “Tunable directional coupling of surface plasmon polaritons with linearly polarized light,” Appl. Phys. B 122, 16 (2016). [CrossRef]
34. D. Wintz, A. Ambrosio, A. Y. Zhu, P. Genevet, and F. Capasso, “Anisotropic surface plasmon polariton generation using bimodal V-antenna based metastructures,” ACS Photon. 4, 22–27 (2017). [CrossRef]
35. X. Zhang, Q. Xu, Q. Li, Y. Xu, J. Gu, Z. Tian, C. Ouyang, Y. Liu, S. Zhang, X. Zhang, J. Han, and W. Zhang, “Asymmetric excitation of surface plasmons by dark mode coupling,” Sci. Adv. 2, e1501142 (2016). [CrossRef]
36. M. Nazarov and J.-L. Coutaz, “Terahertz surface waves propagating on metals with sub-wavelength structure and grating reliefs,” J. Infrared Millim. Terahertz Waves 32, 1054–1073 (2011). [CrossRef]
37. M. Gong, T.-I. Jeon, and D. Grischkowsky, “THz surface wave collapse on coated metal surfaces,” Opt. Express 17, 17088–17101 (2009). [CrossRef]
38. T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007). [CrossRef]
39. A. Bitzer, A. Ortner, H. Merbold, T. Feurer, and M. Walther, “Terahertz near-field microscopy of complementary planar metamaterials: Babinet’s principle,” Opt. Express 19, 2537–2545 (2011). [CrossRef]
40. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). [CrossRef]
41. J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012). [CrossRef]
42. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961). [CrossRef]
43. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010). [CrossRef]
44. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009). [CrossRef]
45. M. Kang and Y. D. Chong, “Coherent optical control of polarization with a critical metasurface,” Phys. Rev. A 92, 043826 (2015). [CrossRef]
46. H. Zhang, M. Kang, X. Zhang, W. Guo, C. Lv, Y. Li, W. Zhang, and J. Han, “Coherent control of optical spin-to-orbital angular momentum conversion in metasurface,” Adv. Mater. 29, 1604252 (2017). [CrossRef]
47. T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17, 17483–17490 (2009). [CrossRef]
48. Y. Xu, X. Zhang, Z. Tian, J. Gu, C. Ouyang, Y. Li, J. Han, and W. Zhang, “Mapping the near-field propagation of surface plasmons on terahertz metasurfaces,” Appl. Phys. Lett. 107, 021105 (2015). [CrossRef]