1. Introduction

Surface waves (SWs), the transmission modes of electromagnetic waves which are bounded at a metal/dielectric interface, have found promising applications in ultrasensitive biosensors [1], high-resolution microscopy [2], and all-optical devices [3]. SWs-based photonic integrated circuits [4] appear to be of great promise because they own the potential to carry optical signals [5,6] and miniaturize electronics [7], which can play a significant role in information processing [8] and energy transfer [9,10]. Among varieties of ways to control the SWs, metallic antenna array metasurface have been proposed as a rather ideal modal to engineering the propagation of SWs at will by tuning subwavelength interval and spatially varying geometric parameters (for instance, antenna dimension, orientation and shape) [11–13]. In particular, metasurface has attracted considerable attention in terahertz (THz) frequency range [14], because THz SWs have unique advantages [15], including enhancing the interactions between light and THz-sensitive materials or molecules [16], and the strong abilities to inspect non-destructively [17].

In the achievement of on-chip photonic integrated circuits based on subwavelength waveguides, it is necessary to effectively control guided waves (GWs) and SWs simultaneously. However, most of the recent works are limited to using specific metasurfaces to convert propagating waves to SWs [13,18]. Moreover, they dealt with SWs signals via numerical simulations [19] or far-field analysis [20]. To realize energy transfer from GWs to SWs, finding an efficient approach to combining metasurface and optical waveguides appears great promise, especially in THz frequency range. As a result, a lithium niobate (LN) subwavelength planar waveguide can be adopted, where the generation, propagation, detection, and control of THz signal can be fully integrated in one sample [21]. This on-chip platform has been analyzed from dispersion relations, polarization mode transmission, and transmission losses [22], which builds up a bridge between the LN slab and other optical or optoelectronic devices. Nevertheless, in these works, the optical power is confined in the waveguide, which cannot be effectively manipulated [23]. Therefore, the composite structure of LN waveguide and metasurface is designed to link GWs and SWs in this paper, which provides a new way for the development of flexible and compact plasmonic circuits operating at THz frequencies.

In this work, we presented a novel THz integrated platform which could be used for the conversion from GWs to SWs via coupling of a LN subwavelength waveguide and metasurface antennas. The conversion process and transmission of the THz electric field (E-field) were directly observed using time-resolved phase contrast imaging. Based on the temporal evolution, the dispersion relation was extracted and analyzed to demonstrate the characteristics of SWs, possessing particular behaviors compared with the guided modes of the bare LN slab. These results were in good agreement with numerical simulations. Meanwhile, by analyzing the E-field distributions of the antennas, we demonstrated that the SWs were induced by the collective oscillation of the antenna array. The simulated maximum coupling efficiency was around 62.6%. This work builds up a bridge linking GWs and SWs on an on-chip platform in THz range, which would open a door for strong light-matter interaction and THz surface integrated devices.

2. Experiment setup

As schematically shown in Fig. 1(a), the metasurface antenna array was fabricated on the surface of LN slab (11 mm × 10 mm × 0.05 mm) via UV photolithography of a positive photoresist followed by the deposition of a 100 nm gold layer using magnetron sputtering. Figure 1(b) shows an optical microscope image of the metasurface with the characteristic parameters. The length of antenna is l = 70 µm. The gap between symmetric antennas is w = 30 µm (|y| < 15 µm). The period and width of the antenna are d = 12 µm, a = 6 µm, respectively. The above parameters of the hybrid structure (the metasurface antenna array and LN subwavelength waveguide) have been optimized by using 3D finite-difference time-domain (FDTD) simulations according to analysis [24].

 

Fig. 1 (a) The experimental geometry. 800 nm pump beam (red) is line-focused orthogonally into 50 μm thick LN slab to generate counterpropagating THz waves (black solid curve), one of which then encounters the hybrid structure. (b) Microscope image of a sample. Detailed designed parameters d, a, l and w are fixed as 12 µm, 6 µm, 70 µm and 30 µm, respectively. (c) Schematic diagram of the pump-probe setup. The focal lengths of the lenses are f₁ = 10 cm and f₂ = 15 cm, respectively. The sample is imaged into the CCD camera through lens group. The phase plate is placed in the Fourier plane of the first lens. The 400 nm probe branch (blue) illuminates the whole sample at normal incidence.

Download Full Size | PDF

A Ti: sapphire regenerative amplifier (800 nm central wavelength, 120 fs pulse duration, 1 kHz repetition rate, 500 µJ) is separated into a pump beam (with 90% of total energy, red beam) and a probe beam (with 10% of total energy, blue beam) to achieve a standard ultrafast pump-probe detection, as shown in Fig. 1(c). The y-polarized pump beam is tracked through a mechanical delay line and line-focused into the LN slab by a cylindrical lens (focal length is 20 mm) to produce a linearly polarized THz waves based on optical rectification [25]. Noticing that the polarization of the pump beam, the THz E-fields generated and the long axis of antenna are aligned to the optical axis of the LN crystal axis in Fig. 1(a). A time- and space-dependent change of LN refractive index is induced by the electro-optic effect due to the propagation of THz waves. The probe branch is frequency-doubled to 400 nm by a BBO crystal, spatially filtered to minimize high order scattering noise, and then expanded to illuminate the whole sample. The phase of expanded probe beam is modulated immediately after the sample imparting a corresponding shift, which is proportional to the refractive index [26].

However, the collecting camera is sensitive only to intensity. It is essential to convert the phase information into a spatially varying intensity. We accomplish this by imaging the sample with phase contrast imaging technique [26]. The sample is imaged onto the CCD camera through a 4f system. The phase plate is placed on the Fourier plane of the first lens. We fabricate the phase plate via a double sided fused silica within optical flat (1 mm-thickness, surface area 25 $\times$ 25 mm²). A 222 $\pm$ 5 nm silicon dioxide layer (with refractive index 1.45 at 400 nm) is spin-coated onto the substrate followed by removing a 35 $\times$ 35 µm² area in the center of the plate using electron beam lithography. This leads to a phase plate with an extremely flat surface which is transparent in the visible with a central recessed square, (l/4 for the 400 nm probe wavelength). The temporal resolution is 120 fs, which is determined by the probe pulse duration, and is about several-tenths of the THz waves duration. The system achieves an imaging resolution as small as 3 µm, which is about one tenths of the THz waves wavelength in LN crystal, providing an extra fine spatial resolution. By changing the time delay between the arrival of the pump and probe pulses on the sample, a full spatiotemporal evolution of THz wave is extracted from the image sequence.

3. Result and analysis

3.1 Temporal evolution and dispersion relation

In our experiment, when the THz GWs encounters the hybrid structure, the optical power transfers onto the surface and forms SWs via coupling between the waveguide and metasurface at special frequency bands. Emphatically, parts of the electric fields of the SWs still immerse into LN waveguide which can be detected by the phase contrast imaging method. Through extracting the intensity information from the image recorded at each time delay, we collapse the signals into a row vector along the y direction and display the collapsed row vectors in time order along the vertical axis to generate a space-time mapping [27]. Figures 2(a) and 2(b) show the space-time plots for the LN subwavelength waveguide decorated with antenna array, which are retrieved from the slot region (|y| < 15 µm) by experiment and simulations. In these images, conversion, dispersion and reflection processes are all clearly shown. In Fig. 2(c), the t-x mapping extracted from the bare LN subwavelength waveguide is used as a reference.

 

Fig. 2 (a) and (b) The space-time plots of the hybrid structure with the image intensity showing THz E-field, which suggest the results of SWs propagating in the gap (|y| < 15 µm) from experiment and numerical simulations. (c) The space–time plot of the bare LN subwavelength waveguide as a reference. Two black dashed lines are the metasurface edges in Figs. 2(a)-2(c). These plots are divided into three regions: incidence (Inci.) and reflection region (Refl.), metasurface region (Meta. region) and transmitted region (Tran.). (d)-(f) The dispersion curves of excited modes are obtained from experiment and numerical simulation by performing 2D Fourier transform of the region between two dashed lines in Figs. 2(a)-2(c). In Figs. 2(d)-2(f), the black dashed curves: theoretically calculated the first two dispersion curves of the waveguide modes (${\text{TE}}_0{\text{andTE}}_1$) for a bare 50 µm-thick LN slab. White lines: light line in air.

Download Full Size | PDF

In order to interpret more clearly the properties of propagating modes in the sample, some extra marks: incidence (Inci.) and reflection region (Refl.), metasurface region (Meta. region) and transmitted region (Tran.) are added to the Fig. 2(a). The wiggles in Inci. indicate the mode in LN, and the reflection wave caused by the edge of Meta. region can be clearly resolved as well. However, Meta. region includes two hybrid modes [I and II in the Fig. 2(d)] covering broadband THz frequency. The SWs mode (plasma mode) cannot be clearly resolved in t-x plot. The appearance of wiggles is due to the mismatching of group velocity and phase velocity in the subwavelength waveguide associated with the structural dispersion.

With the spatiotemporal data, the frequency information of the waves in the gap can be straightforward acquired and analyzed. Figures 2(d)-2(f) show the corresponding dispersion diagrams of the experiment and the numerical simulation which are obtained by performing a 2D Fourier transform of the space-time plot.

The black dashed lines show the first two TE waveguide modes (TE₀ and TE₁) for a bare 50 µm-thick LN slab [22]. Here, the hybrid structure supports two distinct types of modes (labelled as I and II, respectively). For the type I (0.15 ~0.33 THz), the propagation constant $k_x$ is larger than that in the stand-alone LN GWs at the same frequency, indicating the formation of the SWs and strong field confinement in the direction perpendicular to the interface. The formation of SWs can also be confirmed in Fig. 3(a), where electric fields lay mostly on the top of the hybrid structure. Moreover, the slight curvature of the dispersion line of SWs means the existence of a cut-off frequency which is co-determined by the antenna length, orientation, period and waveguide thickness [24,28]. Meanwhile, the antenna array can be used to achieve broadband device performance, because of an inverse relation between device dimension and their working bandwidth [29].

 

Fig. 3 (a-b) and (c-d) The E-field intensity maps are recorded in the symmetrical plane (y = 0 plane) of the hybrid structure at f = 0.27 THz and 0.43 THz, respectively. Rectangular dashed frame and two black dashed lines indicate the locations of the antenna array and the LN subwavelength waveguide. The relative intensity |E| at the center of the gap (blue line) and the middle line (y = 0, z = 0) in the LN waveguide (red line) are shown in the Fig. 3(b) and 3(d). (e) Simulated coupling efficiency from the mode of stand-alone LN subwavelength waveguide to the SWs. (f) The field confinement in the SWs over the guided mode. The maximal field enhancement of the upper panel is 5 times relative to the lower. The black dashed line is the boundary of the cross section of the planar waveguide.

Download Full Size | PDF

However, for the type II, the wavevector, located between the black (TE₀) and white dashed lines, is smaller than that of the stand-alone LN GWs at the same frequency, which indicates that the optical power is still in the waveguide. The numerical simulation agrees well with the experiment. Meanwhile, a part of branch II (within the white dash ring) below the black dashedline (TE₁) appears in the simulation. Unfortunately, it cannot be detected in experiment because this mode is too weak. At higher frequency (about 0.7 THz), given that the excitation of antennas is weak, the energy is confined in the waveguide. The discrepancy in the dispersion curves of simulations and experiment comes from the different spectra of light sources.

3.2 E-field intensity calculations and antennas excitations

To show the spatial distribution of electric fields of the modes, we select two characteristic frequencies as representatives to study above phenomena. The field intensity distribution defined as |E| in the symmetrical plane of the structure (y = 0 plane) is calculated by FDTD simulation. Figure 3(a) and 3(b) (f = 0.27 THz in type I), compared with Fig. 3(c) and 3(d) (f = 0.43 THz in type II), show clearly that the electric fields are confined to the surface via coupling between the LN subwavelength waveguide and metasurface. The transmission loss of SWs is very small as shown in Fig. 3(b), and the lifetime could reach about 98.04 ps (see Appendix). Then, we consider the energy coupling efficiency from the initial waveguide mode to the SWs mode through numerical simulation. To that end, we define the coupling efficiency $\eta =p_1/p_0$, where $p_1$ and $p_0$ are the power flow of SWs and of the bare LN waveguide, respectively [30]. Figure 3(e) shows the variation of the coupling efficiency with frequency, and the maximum of $\eta$ is about 62.6% at 0.33THz. Figure 3(f) shows the field confinement in the SWs over the GWs. The maximal electric field between closed terminals of antennas (the upper panel) is enhanced 5 times than the stand-alone waveguide (the lower panel).

To further clearly understand the mode supported by metasurface, the field profiles and phase diagrams with the antenna metasurface are investigated in detail in Fig. 4. Figures 4(a)-4(d) show y and z components of E-field from top-view of the antenna array at 0.27 and 0.43 THz, respectively. At type I (f = 0.27 THz), the $E_y$ component has the same orientation while the $E_z$ component is oriented into the opposite direction at the terminals, demonstrating thedipolar excitation of each antenna. In further, this dipolar excitation can be verified by the phase profiles of the $E_z$ component in Fig. 4(e). The electric fields are enhanced at both ends of the excited antenna and the phase lag of each antenna is π. Moreover, the lateral coupling between antennas can be realized through near-field interactions as long as the separation between antennas is within the subwavelength scale. Along the antenna array, there is π phase shift always for the electric fields between adjacent antennas, which is similar to dipolar exactions along the x axis. Due to the collective effect, the antenna array behaves as a waveguide associated with stable k-vector in Fig. (e). In brief, we demonstrate that the SWs are formed by the collective oscillation of the metasurface antenna array. In contrast, the plasmonic antennas array does not confine the optical power onto the surface at 0.43 THz. Neither the $k_x$ is stable, i.e. phase mismatching at the surface, as Figs. 4(b) and 4(d) show, nor the antenna array forms a collective oscillation. The antenna array does not behave as a waveguide and each antenna oscillates individually in Fig. 4(f). In brief, we demonstrate that the SWs are formed by the collective oscillation of the metasurface antenna array.

 

Fig. 4 (a)-(d) Top view maps of the y and z components of the E-field in the midplane of the antenna array at f = 0.27 THz (up row) and 0.43 THz (down row), respectively. The dashed frames are the boundaries of the antenna array. (e) and (f) Phase profiles along the propagation direction extracted from both side of the single antenna. Red line is inner side of antenna at y = 15 µm, and blue line is outer side at y = 85 µm.

Download Full Size | PDF

4. Conclusion

The conversion from THz GWs to SWs is realized through coupling of a LN subwavelength waveguide and metallic metasurface antennas. This LN subwavelength waveguide serves as an all-feature THz integrated platform and all dynamic processes, including THz generation, propagation and mode conversion are visualized by a time-resolved imaging system in the experiment. We demonstrated the formation of SWs through the comparison between the dispersion curves of GWs and SWs, which is confirmed via the analysis of spatial electric field distribution of the modes at different frequencies. The experimental results are reproduced very well by simulations. Our findings may find applications for strong light-matter interactions and efficient energy control of the subwavelength waveguide. Meanwhile, since LN crystal possesses large electro-optical and nonlinear coefficients, it is believed that the proposed platform offers a promising approach for developing more robust and complex THz functional devices and is thus useful in THz integrated plasmonic circuits.

Appendix

The appendix includes: (1) Details of theoretical simulation, (2) Discuss the role that the separation (g) and the antenna dimension (l) play for the formation of SWs.

1. Details of theoretical simulation

The geometry of our model is shown in the Fig. 5, where the LN waveguide, antenna array and the dipole sources are clearly shown. The numerical calculations are performed by using the commercial FDTD Solutions software, in which the parameters of materials and input source are needed. To make it more clearly, the parameters of materials, the excitation sources and the simulation settings are given in detail as following.

 

Fig. 5 The perspective, top (XY), front (XZ), and left (YZ) view of the simulation model are provided. The red dielectric waveguide is a 50 μm thick LN waveguide. The optical axis of LN, long axis of the antenna and the polarization directions of dipoles are along the y direction. A column of dipoles with an interval of 4 μm is set inside the waveguide to produce the THz waves.

Download Full Size | PDF

1.1 Physical parameters of LN and Au

LN is characterized by the dielectric tensors ${\epsilon }_{xx}(w)={\epsilon }_{zz}(w)={\epsilon }_{\perp }(w)$ and${\epsilon }_{yy}(w)={\epsilon }_{\parallel }(w)$, where the $\perp$ and $\parallel$ stand for THz waves polarization perpendicular or parallel to the optic axis. The dielectric function will be characterized as [31],

(3)$${\epsilon }_{\parallel }(w)={\epsilon }_{\infty \parallel }+\frac{w_{TO\parallel }^2({\epsilon }_{0\parallel }-{\epsilon }_{\infty \parallel })}{w_{TO\parallel }^2-w^2-iw{\Gamma }_{\parallel }},$$

(4)$${\epsilon }_{\perp }(w)={\epsilon }_{\infty \perp }+\frac{w_{TO\perp }^2({\epsilon }_{0\perp }-{\epsilon }_{\infty \perp })}{w_{TO\perp }^2-w^2-iw{\Gamma }_{\perp }}.$$

Where $w_{TO}$ is the resonance frequency of the lowest transverse optic phonon mode, ${\epsilon }_0$ and ${\epsilon }_{\infty }$ are the dielectric constants in low and high frequency limits, ${\Gamma }_{\parallel }$ and ${\Gamma }_{\perp }$are the phenomelogical damping terms. The constants in Eqs. (2) and (3) are given in Table 1.

Table 1. Physical constants for THz waves in LN.

View Table

On the other hand, the Au antenna array patterned on the top surface of the LN waveguide is assumed to be perfect electric conductor (PEC), which is valid at THz frequencies because Au has conductivity at the order of 10⁷ S/m.

1.2 Column of dipoles as excitation source

In our experiments, the THz waves are excited in LN crystal waveguide via ultrafast laser pulses. However, because the production of THz waves is a complicate multi-physics process, it is not so easy to simulate it using FDTD. As a result, a column of y-polarized dipoles (50 dipoles with an interval of 4 μm), locating inside the LN waveguide, is used as the excitation source in the simulations. The reason why dipoles can be used to mimic the pulse excitation can be understood as follows. In LN crystal, niobium ions are slightly above the centers between two oxygen planes, and lithium ions are slightly above the oxygen planes. This structure lacks inversion symmetry and shows spontaneous polarization along the optical axis. When the incident electric field of pump light is parallel to the optical axis, the oscillations of niobium and lithium ions along the optical axis would exist, which is similar to a series dipoles polarized along the optical axis and produce the THz waves.

1.3 Simulation setting

The dimensions of the simulation region along x, y and z axes are set to 6 mm, 0.6 mm and 0.8 mm, respectively. Perfectly matched layer absorbing boundary conditions are used at all boundaries of the simulation domain. Moreover, the maximum mesh steps are set to 2 µm, 3 µm and 10 nm along the x, y and z axes respectively. Convergent results can be obtained because the mesh sizes are smaller than the corresponding minimum size of construction.

2. Discussion: Role that separation (g) and antenna dimension (l) play

Figure 6(a)-6(d) show the dispersion relation of the SWs calculated with FDTD, with gap (g) ranging from 5 to 50 μm at a fixed antenna length l = 70 μm. One can see that there is no obvious change on saturated frequency of the SWs dispersion relation, but the amplitude levels of the wavevector components after Fourier transformation alter a lot. This effect can be attributed to strong electric field distribution in the gap. In further, the propagation length of SWs can be considered as follows. It is worth noting the losses of propagating SWs mainly originate from the energy dissipation in LN waveguide, as a result, the portion of the SWs immersed in the waveguide is a critical factor. Figure 6(e) indicates the electric intensity distribution of the SWs along the thickness of waveguide (z axis) at the symmetrical plane (y = 0). The degree of field confinement of SWs depends on g. The area of the mode field in the waveguide is proportional to the transmission loss. As a result, one can find that the optimal outcome occurs when the gap is about 30 μm. The maximum lifetime of SWs could reach $1/\Delta f\approx 99.01ps$ as shown in the Fig. 6(f).

 

Fig. 6 (a-d) The effects of different gap (g) on the dispersion relation of SWs mode. The width of the SWs mode,$\Delta f$, gives an estimate of the lifetime of the SWs. $1/\Delta f\approx 65.8ps$when $g=5\mu m$. The blue dash line is light line in air. (e) The electric intensity distribution of the SWs along the thickness of waveguide (z axis) at the symmetrical plane (y = 0) with varying g. The dash lines are the boundaries of the planar waveguide. (f) The blue solid line indicates the integration of the electric field immersed in the waveguide. The black solid line provides an estimate of the lifetime of the SWs.

Download Full Size | PDF

Next, the parameter l dependent properties of SWs are shown in Figure 7. In contrast to the change of g, the dispersion relations of SWs change a lot as l = 50, 70 and 90 μm. Considering that dipolar resonance of each antenna and their near-field coupling are the prerequisites for the formation of the SWs, it is easy to understand that the collective modes alter a lot after the change of the dipolar resonance of single antenna. In further, the SWs frequencies saturate at different frequencies which are positively relative to the resonances of the antenna.

 

Fig. 7 (a-c) The influence of different antenna length (l) on the dispersion relation of SWs mode. The blue dash line is light line in air.

Download Full Size | PDF

Funding

National Natural Science Foundation of China (61378018, 11574158); Fundamental Research Funds for the Central Universities; the 111 Project (B07013); the Program for Changjiang Scholars and Innovative Research Team in University (IRT 13R29).

References

1. L. Wu, J. Guo, H. Xu, X. Dai, and Y. Xiang, “Ultrasensitive biosensors based on long-range surface plasmon polariton and dielectric waveguide modes,” Photon. Res. 4(6), 262–266 (2016). [CrossRef]  

2. M. G. Somekh, S. Liu, T. S. Velinov, and C. W. See, “High-resolution scanning surface-plasmon microscopy,” Appl. Opt. 39(34), 6279–6287 (2000). [CrossRef]   [PubMed]  

3. J. Chen, Z. Li, S. Yue, and Q. Gong, “Highly efficient all-optical control of surface-plasmon-polariton generation based on a compact asymmetric single slit,” Nano Lett. 11(7), 2933–2937 (2011). [CrossRef]   [PubMed]  

4. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef]   [PubMed]  

5. J. Du, S. Liu, Z. Lin, J. Zi, and S. T. Chui, “Guiding electromagnetic energy below the diffraction limit with dielectric particle arrays,” Phys. Rev. A 79(5), 51801 (2009). [CrossRef]  

6. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008). [CrossRef]  

7. P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nat. Photonics 3(5), 283–286 (2009). [CrossRef]  

8. T. Goto, Y. Katagiri, H. Fukuda, H. Shinojima, Y. Nakano, I. Kobayashi, and Y. Mitsuoka, “Propagation loss measurement for surface plasmon-polariton modes at metal waveguides on semiconductor substrates,” Appl. Phys. Lett. 84(6), 852–854 (2004). [CrossRef]  

9. J. Shi, M. H. Lin, I. T. Chen, N. Mohammadi Estakhri, X. Q. Zhang, Y. Wang, H. Y. Chen, C. A. Chen, C. K. Shih, A. Alù, X. Li, Y. H. Lee, and S. Gwo, “Cascaded exciton energy transfer in a monolayer semiconductor lateral heterostructure assisted by surface plasmon polariton,” Nat. Commun. 8(1), 35 (2017). [CrossRef]   [PubMed]  

10. M. Février, P. Gogol, A. Aassime, R. Mégy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12(2), 1032–1037 (2012). [CrossRef]   [PubMed]  

11. R. Tellez-Limon, M. Fevrier, A. Apuzzo, R. Salas-Montiel, and S. Blaize, “Theoretical analysis of Bloch mode propagation in an integrated chain of gold nanowires,” Photon. Res. 2(1), 24–30 (2014). [CrossRef]  

12. B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. 35(9), 1320–1322 (2010). [CrossRef]   [PubMed]  

13. 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(5), 426–431 (2012). [CrossRef]   [PubMed]  

14. M. Lee and M. C. Wanke, “Applied physics. Searching for a solid-state terahertz technology,” Science 316(5821), 64–65 (2007). [CrossRef]   [PubMed]  

15. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]  

16. B. Ng, S. M. Hanham, J. Wu, A. I. Fernández-Domínguez, N. Klein, Y. F. Liew, M. B. H. Breese, M. Hong, and S. A. Maier, “Broadband terahertz sensing on spoof plasmon surfaces,” ACS Photonics 1(10), 1059–1067 (2014). [CrossRef]  

17. D. Zimdars, J. A. Valdmanis, J. S. White, G. Stuk, S. Williamson, W. P. Winfree, and E. I. Madaras, “Technology and applications of terahertz imaging non-destructive examination: inspection of space shuttle sprayed on foam insulation,” Rev. Quant. Nondestruct. Eval. 24, 570–577 (2005). [CrossRef]  

18. J. Wang, S. Qu, H. Ma, Z. Xu, A. Zhang, H. Zhou, H. Chen, and Y. Li, “High-efficiency spoof plasmon polariton coupler mediated by gradient metasurfaces,” Appl. Phys. Lett. 101(20), 201104 (2012). [CrossRef]  

19. S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88(25), 251120 (2006). [CrossRef]  

20. Y. Fan, J. Wang, H. Ma, J. Zhang, D. Feng, M. Feng, and S. Qu, “In-plane feed antennas based on phase gradient metasurface,” IEEE Trans. Antenn. Propag. 64(9), 3760–3765 (2016). [CrossRef]  

21. C. A. Werley and K. A. Nelson, “The LiNbO₃ slab waveguide: a platform for terahertz signal generation, detection, and control,” in Ferroelectric Crystals for Photonic Applications: Including Nanoscale Fabrication and Characterization Techniques, P. Ferraro, S. Grilli, and P. D. Natale, eds. (Springer, 2014), pp. 423–452.

22. C. Yang, Q. Wu, J. Xu, K. A. Nelson, and C. A. Werley, “Experimental and theoretical analysis of THz-frequency, direction-dependent, phonon polariton modes in a subwavelength, anisotropic slab waveguide,” Opt. Express 18(25), 26351–26364 (2010). [CrossRef]   [PubMed]  

23. Q. Wu, Q. Chen, B. Zhang, and J. Xu, “Terahertz phonon polariton imaging,” Front. Phys. 8(2), 217–227 (2013). [CrossRef]  

24. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef]   [PubMed]  

25. J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004). [CrossRef]  

26. Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009). [CrossRef]   [PubMed]  

27. C. Pan, Q. Wu, Q. Zhang, W. Zhao, J. Qi, J. Yao, C. Zhang, W. T. Hill, and J. Xu, “Direct visualization of light confinement and standing wave in THz Fabry-Perot resonator with Bragg mirrors,” Opt. Express 25(9), 9768–9777 (2017). [CrossRef]   [PubMed]  

28. Z. Li, M. H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12(7), 675–683 (2017). [CrossRef]   [PubMed]  

29. M. Mansuripur, “The uncertainty principle in classical optics,” Opt. Photonics News 13, 44–48 (2002).

30. A. Y. Nikitin, P. Alonso-González, and R. Hillenbrand, “Efficient coupling of light to graphene plasmons by compressing surface polaritons with tapered bulk materials,” Nano Lett. 14(5), 2896–2901 (2014). [CrossRef]   [PubMed]  

31. Z. Chen and K. A. Nelson, “Modeling phonon-polariton generation and control in ferroelectric crystals,” Master dissertation (Massachusetts Institute of Technology, 2009).