1. Introduction

Surface plasmon polaritons (SPPs) are electromagnetic waves propagating along metal-dielectric interfaces, where the collective excitations of surface free electrons in the metal are coupled to form evanescent waves. Recently, plasmonics has been widely studied because the SPPs can overcome the diffraction limit and propagate or be localized in a subwavelength space [1–3]. This feature offers the possibility to realize photonic components with a tiny size and high operation speed. The potential applications include bio-sensing, high density optical data storage and imaging [4–7]. Among these, confined SPPs can help to realize waveguides, which have received extensive attention. For example, at telecommunication wavelengths, different waveguides such as channel plasmon polariton waveguides and dielectric-loaded SPP waveguides with strong confinement and low loss have been investigated [8–11]. However, similar plasmonic waveguides are still lacking at terahertz (THz) frequencies, which are actually of great significance and have many unique advantages. Firstly, there is a broad band in the THz range. It is helpful to transmit a large amount of data at a high speed. Secondly, the wavelength in the THz range is short enough so that most components are available with reasonable dimensions for manipulating and guiding THz beams. Thirdly, due to loose confinement of SPPs in the THz range, the field extends so much into air that it can be easily detected.

Though THz SPP waveguides have great merits, there are two problems that deserve attention. On the one hand, how to detect the guiding THz SPPs directly and simply? In recent years, scanning near-field THz microscopy has attracted a lot of interest, which could be used to measure SPPs successfully [12,13]. On the other hand, apart from a measuring technology, another critical problem to be solved is the confinement of THz SPPs in practical applications. In the optical and near infrared ranges, metals whose permittivity has a small real part and a large imaginary part are treated as a lossy medium. As a result, the surface waves in this range are tightly bound to the surface with a small spatial evanescent extension in the air. However, at THz frequencies, most metals behave as perfect electrical conductors, and hence the surface field extends several millimeters into air such that the surface does not support bound modes of THz surface waves [14]. Different methods such as thin film coating, periodic structures and corrugated surfaces have been adopted to confine and manipulate THz SPPs [15–20]. It has been shown that the SPP fields penetrate into the indentations of periodically corrugated metal structures such as grooves and hole arrays, and then lead to the appearance of confined SPP modes [21–25]. In this case, the geometry of the metal structure has a significant influence on the dispersion relation of the SPP modes. In addition to corrugated metal structures, a thin dielectric layer placed on a bare metal surface also enables a 100-fold reduction in the spatial extent of the evanescent field over a relative broad frequency range [18].

In this letter, we demonstrated a THz SPP waveguide numerically and experimentally. In the proposed structure, metallic cylinders arranged bilaterally in a row (the distance between two neighboring cylinders is much smaller than half of wavelength) to form an effective metal wall and confine the SPPs in the lateral direction. The scheme has the advantage that the cylinders can be placed flexibly in the waveguides. A thin dielectric film of benzocyclobutene (BCB) was covered on the waveguide to reduce the spatial extension of the SPP field. Several types of SPP-based waveguide components with straight, S bend, Y splitter, Mach-Zehnder (MZ) interferometer and sharp bend structures were designed. By adopting the scanning near-field THz microcopy, the amplitude and phase information of the SPPs were recorded. With the proposed designs, we showed that the THz SPPs could be guided and manipulated conveniently, such as shape bending, power separation, etc.

2. Numerical simulations

Figure 1(a) shows the schematic of the waveguide structure with its relevant dimensions. The parameters defined in the illustration are $w=400\text{ μm},d=80\text{ μm},h=150\text{ μm},p=120\text{ μm}$ and the thickness of the dielectric layer t is varied from 50 to 150 μm. Transverse magnetic modes with a dominating y component of the magnetic field are supported at the metal surface. The dispersion curves of these modes in Fig. 1(b) were obtained using the eigen-mode solver of CST Microwave Studio. In the numerical modeling, one unit cell of the periodic structure was considered, using periodic boundary condition and varying phase from 0° to 180° in $\phi$ (with a step of $10°$) along the x direction of propagation. The bottom of the waveguide and cylinders were assumed as perfect electrical conductors. The dispersion relation, i.e., the real part of the propagation constant as a function of frequency, was calculated based on the equation $\text{Re}(k_{\text{x}})=\phi \text{*}\pi /180\text{*}p$. Re(k_x) increased monotonically with frequency. To investigate the effect of the thickness of the dielectric layer on the surface wave propagation, three different thicknesses were considered. The black, red and blue lines in Fig. 1(b) correspond to SPPs supported by structures with dielectric layer thicknesses of 50, 100, 150 μm, respectively. The cutoff frequency (f₀) was about 0.3 THz, implying that only waves with a frequency larger than f₀ were allowed to propagate. The cutoff frequency became smaller when the thickness increased from 50 μm to 150 μm. At the same frequency, Re(k_x)for the 50 μm-thick dielectric layer was smaller than that for 150 μm. When the thickness is increased, the electric field is squeezed inside the region with a higher refractive index. Based on the character of the SPPs, a larger Re(k_x) implies that the field is confined tightly in the waveguide and the field components perpendicular to the direction of propagation have a large decay. Figure 1(c) shows a lateral profile of the magnitude of the main electric-field component (E_z), where a 100 μm thick dielectric layer is considered and the electric field amplitude has been normalized. There is a maximum value of E_z at the bottom of the waveguide and E_z decays exponentially with increasing z. There is a discontinuity of the electric field at the interface between the dielectric layer and air. The E_z field increases by the multiplicative factor ${\epsilon }_{\text{d}}/{\epsilon }_0$ (ε_d andε₀ are dielectric constants of the dielectric layer and air, respectively) [18]. A large part of the electric field is gathered in the middle of the waveguide. The good confinement of a SPP mode is desirable for SPP transmission. To study the effect of different parameters on the dispersion property of the SPP mode, the same simulation method was adopted. The thickness of the dielectric layer was held at 70 μm. The results showed that Re(k_x) was almost unchanged with h increased from 150 μm to 300 μm. In addition to the cylinder height, when the periodic cylinders were replaced by metallic walls with the same height, the dispersion curve was also unaltered. Therefore, the dispersion property of the SPP mode is not sensitive to the size of metal structures, which is a great advantage of the scheme used in this work.

 

Fig. 1 (a) Schematic of waveguide structure with geometrical parameters. (b) Dispersion properties of SPP modes with different dielectric layer thicknesses of 50, 100 and 150 μm. (c) Field distribution of magnitude of electric field component (E_z) for 100 μm-thick dielectric layer.

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In order to achieve two-dimensional integrated optical circuits, components with different functionalities are desired. Based on the periodic structure introduced previously, five components (a straight waveguide, an S-bend, a Y splitter, an MZ interferometer and a sharp bend) based on a planar structure as sketched in Figs. 2(a)–2(f) were designed and simulated using the time domain solver of CST. Bends, which are used for connecting waveguides offset with respect to each other, are very important in integrated optical circuits, because it is often required to properly adjust the separation between adjacent input/output waveguides. Bends are also basic building blocks for Y-splitters and MZ interferometers. These components can be used in switching, modulation, wavelength demultiplexing and power splitting [10, 26]. Straight waveguides are fundamental components in integrated circuits. A 1 × 15 mm²-sized aluminum block with a 0.2 μm thickness was deposited on a silicon substrate. Two rows of metal cylinders with 100 periods were parallelly arrayed within a distance of 480 μm. A 70μm-thick dielectric layer of BCB with a relative permittivity of 2.76 and a loss tangent of 0.022 was coated on the metal film. Due to the lack of a broadband andstrong SPP source at THz frequencies, the narrow band SPPs were excited using periodic gratings. On the metal film, seven-period rectangle-holes with dimensions of 40 μm in the x direction and 380 μm in the y direction were localized in the middle of the parallel cylinder rows. A plane wave was used as the source to excite the SPPs. Periodic gratings were applied to all waveguide structures to facilitate efficient excitation of the SPPs. In all simulations and experiments, the period of the grating was 400 μm corresponding to excited SPPs at a frequency of 0.75 THz. The distribution of the normalized electric filed E_z (z = 50 μm) was obtained from an electric field monitor at 0.68 THz, which is demonstrated in Fig. 2(i). The field was confined in the lateral direction within the waveguide. Besides the straight waveguide, an S-bend with a radius of curvature of R = 911.8 μm was designed based on cosine functions [27]. It is desirable to bring in low additional loss for the connecting section of two straight waveguides offset with respect to each other. There is a lower loss with increasing radius of curvature for a bend [8,23,26]. With low loss taken into consideration, the S-bend with R = 911.8 μm was treated as a basic element for the Y splitter and MZ interferometer. The Y splitter was composed of two mirrored S-bends, and the MZ interferometer two consecutive Y splitters. Using similar simulation procedures, the electric field distributions corresponding to the S-bend, Y splitter and MZ interferometer are displayed in Figs. 2(j)–2(l). As shown in the figures, the SPPs transmitted along the waveguide and did not overflow at the bends. Therefore, the components based on the S-bend accomplished wave separation (the Y splitter) and interference (the MZ interferometer) successfully. In addition to S-bends, sharp bends are also necessary in integrated-optic circuits. Two straight waveguides perpendicular to each other were connected to form a 90°bend [Fig. 2(f)]. However, noticeable SPPs were reflected back by the bend and disturbed the field of propagation [Fig. 2(n)]. As a result, in this structure low transmission was only obtained in numerical calculation. Therefore, as shown in Fig. 2(e), several additional cylinders were put at the corner of the bend and treated as a defect. Ten defect was arranged like a triangle. The distances between two cylinders in the x and y directions were both 120 μm. At the same time, the cylinders on the opposite side were removed to maintain the width of the waveguide and several cylinders were added to avoid wave leaking. The SPPs transmitted through the sharp bend just as a wave was incident on the plane at an angle of 45°and then reflected at the same angle, which is shown in Fig. 2(m). The transmission in this structure was improved.

 

Fig. 2 Planar structures of waveguide components. (a) Straight waveguide. (b) S bend. (c) Y splitter. (d) MZ interferometer. (e) Sharp bend with defects. (f) Sharp bend. (i)–(n) Corresponding electric field distributions of E_z at z = 50 μm.

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3. Experimental results

Based on the numerical simulations, several components including a straight, Y splitter and sharp bend waveguides were fabricated and characterized. To fabricate high-quality waveguide structures, two steps of UV lithography were applied. First, a positive photoresist was spun onto a 4-inchsilicon wafer. The cylinders were patterned by optical lithography, followed by deep reactive ion etching. In the second lithography process, a negative photoresist was employed to form the gratings. A 200-nm-thick Al film metallization of the chips was then conducted in an Al sputter coater. The coverage property of the sputter provided the required Al film quality on the cylinder sidewalls. BCB used as the dielectric layer was injected from the port of waveguide. The wafer was baked at 120°C for five minutes until the gel was solidified. Figure 3 depicts the experimental system used to characterize the surface wave propagation in the plasmonic waveguides. The THz wave was generated by a photoconductive antenna and collimated by a parabolic mirror with a 50.8mm effective focal length. A fiber-coupled THz near field probe with a resolution of 8 μm (TeraSpike TD-800-A-500G) was used as the detector. The sample was put on a specimen holder between the parabolic mirror and the probe. In front of the sample, a THz lens with a 100 mm focal length was used to focus the THz beam at normal incidence onto the gratings. The sample was adjusted such that the direction of the linearly polarized THz wave was perpendicular to the gratings as well as parallel to the propagation axis of the waveguide. Once the SPPs were excited, propagation was detected by the probe placed in close proximity to the waveguide surface. The THz time domain signal was measured by the photocurrent versus time delay. The probe was mounted on a two-dimensional translation stage, which was moved in a fixed step along the x and y directions.

 

Fig. 3 Illustration of experimental setup. The inset show 2D structure of gratings.

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As mentioned above, the parameters of the fabricated waveguide structures were just the same as those employed in the simulations. Figure 4(a) shows a scanning electron microscopy (SEM) image of a part of the straight waveguide. The probe was positioned approximately 200 μm above the surface. The evanescent field of the plasmonic waveguide was sampled point-by-point with a step of 200 μm in the x direction from 0 mm to 4 mm and a step of 100 μm in the y direction from −1 to 1 mm. The normalized power (proportional to |E_z|²) of the straight waveguide was imaged at 0.68 THz [Fig. 4(b)]. The scanning area started with a position in front of the gratings in the x direction, and thus the exciting area was not taken into account. Based on the field amplitude we measured, the horizontal confinement was estimated. Figure 4(c) plots the normalized field amplitude as a function of the y coordinate at x = 2 mm, which shows a full-width at half-maximum of approximately 330 μm. The propagation loss was characterized by the field amplitude along the propagation direction at y = 0 mm. Figure 4(d) plots the amplitude as a function of distance with an exponential fit (red line), which reveals a 1/e propagation length of 5.29 mm. The simulated result represented by the black line with symbols was in good agreement with the experiment. The attenuation of this waveguide obtained from experimental results was estimated to be 1.65 dB/mm.

 

Fig. 4 (a) SEM image of straight waveguide. (b) Near-field image of straight waveguideshowing the normalized power (proportional to |E_z|²) distribution at 0.68THz. (c) Measured amplitude of electric field as a function of ycoordinate. (d) Amplitude attenuation as a function of propagation distance. Reddots represent experimental results. The red line is exponential fit. The black line with squares represents simulated results.

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Figure 5(a) shows an SEM image of the junction of the Y splitter. After the junction, two arms were separated with a distance of 2.3mm. The Y splitter was studied in a similar way by recording the electric field above the surface. The normalized power is exhibited in Fig. 5(b), with a scanning area of 3 × 4 mm². At the junction, the two beams were separated successfully. At the end of the waveguide, the discontinuous waves might be caused by the low power of the SPPs or by scattering due to defects. For a quantitative evaluation of the input and output powers, the normalized data along the lines x = 1 mm and x = 2 mm are shown in Fig. 5(c). The power at each branch was almost the same.

 

Fig. 5 (a) SEM image of Y splitter junction. (b) Normalized power image of Y splitter at 0.68 THz. (c) Input power along the line x = 1 mm and output power along x = 2 mm.

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The last component, i.e., the sharp bend, was also investigated. Figure 6(a) shows an SEM image of the corner of the sharp bend. In this component, the SPPs were deflected by 90 degrees, which is shown in the 4 × 2 mm² scanning area in Fig. 6(b). After the bend, the power of the SPPs became weak. That was caused by high propagation loss, which had also been observed in the straight waveguide. Another reason was that there was still some reflected wave which disturbed the input wave.

 

Fig. 6 (a) SEM image of sharp bend. (b) Normalized power image of sharp bend at 0.68 THz.

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4. Conclusion

In summary, we presented a new structure to confine and manipulate SPPs at THz frequencies. The proposed structure with periodic cylinders arrayed bilaterally on a metal surface and BCB film inside confined SPPs in lateral and vertical directions. The dependence of the dispersion properties on the thickness of the dielectric film was calculated by numerical simulation. Different waveguide components including a straight waveguide, an S-bend, a Y splitter, an MZ interferometer and a sharp bend were designed. To validate the simulations, a straight waveguide, a Y splitter and a sharp bend were fabricated. A near-field scanning system was used to measure and characterize the SPPs. The waveguide realized a horizontal confinement of 330 μm and a propagation length of 5.29 mm. Waveguide components based on this structure accomplished power splitting and wave bending. The performance of the considered waveguides would be further improved by choosing a dielectric layer with a lower loss and by optimizing the geometric structures. For spoof surface plasmon polariton waveguides, the working frequency is determined by the geometric size of the metal structure. The waveguide we proposed was not sensitive to the size of the metallic structure. It was effective for a relative broader frequency range. This demonstration pays a way to realize compact, low cost and integrated circuits at THz frequencies in the future.