1. Introduction

The understanding of surface electromagnetic waves (SEW) began as early as 1899 with Sommerfeld’s calculations of ground-plane propagation of radio waves over a flat earth [1]. Sommerfeld’s student, Zenneck, later formulated a solution of Maxwell’s equations for a general inhomogeneous plane wave propagating over a flat lossy surface [1]. This so-called Zenneck wave, and its close counterparts, the axial cylindrical surface wave (sometimes called the Sommerfeld-Goubau wave) and the radial cylindrical surface wave, have since been studied and implemented in many applications spanning a wide frequency range. Notable examples include a 14 mile single-conductor V.H.F. transmission line over McDonald Pass in Montana U.S.A. [1], microwave dielectric absorption measurements [2], infrared studies [3], and THz axial cylindrical wave generation [4]. More recently Zenneck waves, particularly those on metallic surfaces, have come to be better known as surface plasmon polaritons (SPPs) and are beginning to attract considerable attention due to their role in optical transmission through sub-wavelength aperture arrays, thin-film guided-wave spectroscopy, and non-linear interactions [5, 6]. Monochromatic terahertz (THz) measurements of SPPs began at least as early as 1977 with Miller and Begley’s et al. work on SEWs guided by various metallic [7] and non-metallic [8, 9] surfaces. However, broadband SPP studies using ultrafast THz systems [10, 11, 12, 13, 14] are a recent development.

One of the challenges of utilizing broadband THz SPPs is finding an efficient means of coupling free-space THz to the guided SPP mode. This task requires increasing the wave vector of the free-space THz to match that of the SPP. Recent work has shown highly efficient coupling by the use of metallic gratings [10]. However, this method suffers from rapid decoupling and monochromaticity. Edge-diffraction methods using razors have also been explored [12] with success. In this work, we expand on our initial demonstration [11] of broadband THz SPP (or SEW) coupling using a two-prism arrangement. In particular, we show that coupling to the SPP mode occurs by both the edge-diffraction and hump-coupling mechanisms. Although previous work reports prism coupling via the attenuated total reflection (ATR) method [14] over semiconductor surfaces, we do not observe this mechanism on our metal guides. We estimate coupling and decoupling efficiencies of greater than 3.5% for our experimental configuration. Further, we demonstrate qualitative spectroscopy of plastic tape samples adhered to the metal guiding structure. These measurements are also used to elucidate the relative importance of the aforementioned coupling mechanisms.

2. Experiment and Analysis

The basic experimental setup, shown in Fig. 1(a), is a THz time-domain spectroscopy system very similar to that found in previous work [15]. THz generation and detection is performed via photoconductively switched dipole antennas, and travels from the emitter to the detector by way of silicon collimating lenses and confocal paraboloidal mirrors. The SPP coupling apparatus is centrally placed between the paraboloids and consists of two high-resistivity (> 10⁴ Ω-cm) silicon prisms and a polished metal guiding surface. As indicated by the red lines in Fig. 1(a), THz radiation enters the coupling prism, is totally reflected by the slanted face, and then propagates to the prism-metal gap at close to the critical angle, θ_C = 17.01°. The prism-metal gaps are adjustable but for most experiments were set between 0.5 mm and 1.0 mm. The THz is p-polarized with respect to the guiding surface, but s-polarized measurements were also obtained by rotating the orientation of the emitter and detector antennas by 90°. The THz can also be made to clip the bottom corner of the prism by slight re-positioning of the SPP apparatus, as indicated by the green lines in Fig. 1(a).

This overall design accommodates two possible coupling mechanisms by which free-space THz can be converted to a SPP: attenuated total reflection (ATR) and edge-diffraction (aperture) coupling at the prism corner. In ATR, radiation incident on the prism-metal gap at angles greater than θ_C creates an evanescent field that extends out from the silicon prism surface. This field satisfies the SPP wave vector matching condition for an air-filled gap above a non-magnetic guide at the incidence angle

where n_p is the prism index (equal to 3.418 over the THz bandwidth) and ε_m is relative permittivity of the metal guiding structure, which is on the order of -10⁵ at THz. For the present configuration θ_M approximately equals θ_C = arcsin(1/n_p). Having matched wave vectors, the SPP mode can extract energy from the evanescent field. Though our experimental arrangement was designed to accommodate ATR coupling, we will show that this mechanism is not observed.

In edge-diffraction (or aperture) coupling, free-space THz illuminates an aperture defined by a diffracting edge situated near the SPP metal guiding structure. The aperture causes a perturbation in the translational symmetry for the THz issuing from the aperture (essentially a near-field effect), thereby creating an increase in the field wave vector [16]. In this way, the SPP guided mode can be excited. Once coupled to the metallic surface (a flat polished brass surface in Fig. 1(a)) the SPP travels approximately 6.3 cm where it is then decoupled by the inverse process. Thin material samples can be adhered to the metal surface to investigate their effect on SPP propagation. Metal blocks (labeled ‘Free-space blocks’ in Fig. 1(a)) were placed between the prisms to prevent direct coupling of free-space radiation. Additional metal blocks were placed between the paraboloidal mirrors and the prisms to block THz radiation, which extended beyond the entrance/exit regions on the prism faces. The placement of all of these blocks was tested to ensure that they had no effect on the SPP signal. Furthermore, we found that most of the blocks were unnecessary. For example, either one of the two free-space blocks could be removed without affecting the SPP data.

As will be shown, however, the metal blocks did not fully prevent free-space coupling between the prisms. For this reason, other arrangements, one of which is shown in Fig. 1(b), were investigated. This arrangement utilized a polished copper surface in the ‘over-the-horizon’ configuration [17], where free-space signals are reflected into an undetectable directions. This cleans up the SPP signals, which are otherwise partially obscured by free-space signals that travel at about the same speed, c. This over-the-horizon configuration also introduces another possible coupling mechanism, previously referred to as hump coupling [17], where free-space radiation is coupled into the surface wave mode by the alteration of the electric field in the vicinity of the curved metallic guide.

 

Fig. 1. THz prism coupling arrangements. Thick black lines indicate metal blocks. Thin black boxes represent tape samples adhered to guide surfaces. (a) flat brass guide, (b) humped copper guide, (c) truncated humped copper guide, (d) no-line-of-sight guide.

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Figure 2 shows the time-domain signals and spectra obtained from the setups depicted in Figs. 1(a) and 1(b). In Figs. 2(a) and 2(b) the red curves show the time-domain SPP signals obtained on the bare metal guides, while the black curves (shifted +3nA for clarity) show the signals obtained when the SPPs propagated through 19 mm of 50 μm thick Scotch® tape adhered to the center of the metal surface. The blue waveform shows a free-space reference obtained by altogether removing the SPP apparatus from the system. For visual clarity, this reference is shifted by -1 nA. It was also shifted nearly +700 ps to account for the additional path length introduced by the SPP apparatus. All of the waveforms shown are amplitude-scaled by the color-coded multiplier shown in the figure. Figures 2(a) and 2(b) show the most obvious effect of the tape sample in the form of a positively chirped ringing.

Figures 2(a) and 2(b) present one piece of evidence that the THz radiation is indeed coupling to a surface wave. The SPP data for the flat brass guide (black waveform in Fig. 2(a)) reveals a sharp signal feature, labeled ‘free-space’ occurring before the onset of the chirped portion of the detected waveform. This feature is not affected by the presence of the tape, indicating that it is a free-space signal. This insensitivity to the tape sample is expected when coupling to the surface mode does not occur. However, the chirped portion of the signal reveals a strong dependence on the presence of the tape, which is consistent with surface wave coupling.

Figures 2(a) and 2(b) also show the effectiveness of the over-the-horizon method in blocking direct free-space coupling between prisms. Specifically, the free-space feature is eliminated in the over-the-horizon configuration (Fig. 2(b)) and the entire detected waveform is affected by the tape sample. We note that this over-the-horizon arrangement was also used to measure SPP coupling for s-polarized radiation, wherein coupling to the SPP mode should not occur. The resulting SPP signal was approximately two orders of magnitude smaller in comparison to coupling with p-polarized radiation. This is consistent with the fact that the THz system is not purely linearly polarized. It is generally accepted that photoconductive switch based THz systems generate and/or detect a cross-polarized field component on the order of a few percent as large as the component polarized along the dipole [18].

The chirp in the SPP signals in Figs. 2(a) and 2(b) can be understood in terms of waveguiding effects. Previous THz work with plastic ribbon waveguides [19] has shown that high-frequency components, being more strongly bound within the plastic ribbon, experience a higher effective index of refraction in propagation through the guide. A similar effect occurs for SPPs. Specifically, high-frequency components are more tightly bound to the metal guide [6], and are more strongly influenced by the thin tape sample. This produces a greater effective index for high-frequency SPP components, thus reducing their velocity and creating a positive chirp.

Spectra for these waveforms, obtained by numerical Fourier transform, are shown in Figs. 2(c) and 2(d). In the case of the flat brass guide, the modulated appearance of the spectra in Fig. 2(c) demonstrates the effect of the interference between the SPP wave and the free-space wave traveling directly between prisms. However, aside from this interference, and some obvious losses occurring at frequencies greater than 250 GHz, the addition of the tape sample to the guide does not greatly affect the overall bandwidth of the received signal. The humped copper guide behaves quite differently. From the red waveform in Fig. 2(d) it is clear that the bare-metal SPP experiences a largely frequency independent loss when compared to the free-space reference shown in blue. The smooth SPP spectrum verifies the clean broadband coupling to the SPP mode in this arrangement. Of more interest, however, is the effect of the tape sample. In this case there is actually a strong enhancement of detected energy below about 450 GHz, and a similarly strong attenuation of detected energy above 450 GHz.

 

Fig. 2. Prism SPP coupling data. Red waveforms represent bare guide measurements, black waveforms represent SPP measurements with tape sample adhered to guide. Blue waveform shows free-space reference with no SPP apparatus. Color-coded multipliers indicate amplitude scaling for plots. (a) and (c) are flat brass guide measurements, (b) and (d) are humped Cu guide measurements. Black and blue waveforms in (a) and (b) are shifted for visual clarity.

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To determine the cause of this behavior additional measurements were performed in which tape samples were placed at different locations, shown by the blue lines on the guiding structure in Fig. 1(b). Specifically, we moved the tape from the apex of the hump to either side of it. All the measurements are shown in Figs. 3(a) and 3(b), plotted on the same scale as Fig. 2 for comparison, and are vertically and/or horizontally shifted for visual clarity. The red waveform shows the measurement without the tape sample and is shifted -7 ps. The black waveform (shifted +3 nA) shows the case when the tape sample was placed at the apex of the hump. The blue and green waveforms were obtained when the tape sample was placed on either side of the apex. The blue waveform is shifted -2 nA. All of the tape measurements show a large loss above 450 GHz, regardless of the tape position. Therefore, we believe the loss above 450 GHz is simply due to absorption within the tape sample. We note that this effect is not observed in the tape experiments using the flat brass guide, as seen in Fig. 2(c), which is indicative that the spectral weight observed above 450 GHz in Fig. 2(c) is due to free-space THz transmitting past the edges of the metal blocks and not due to SPP guiding. Re-positioning the tape on the hump did, however, result in a great reduction of signal enhancement below 450 GHz, as shown in Figs. 3(a) and 3(b). For this reason, we believe the low-frequency enhancement phenomenon is caused by waveguiding effects within the tape. Due to the curvature of our guide, energy is tangentially shed as the wave travels over the outside curved surface. However, when a dielectric layer (tape) is applied to the metal guide, it increases the surface reactance, which confines the SPP more closely to the surface [1]. Since the wave is more tightly confined over the curvature of the guide, shedding is reduced and the detected signal is enhanced. As the tape is moved farther from the apex, it does not guide the mode over as much of the shedding (i.e. curved) region. In this case the observed signal enhancement is greatly reduced. Finally, we point out the existence of a small free-space signal preceding the chirped SPP signal in Fig. 3(a). Only against the background of the weaker chirped SPP signals does this free-space signal finally become apparent. It’s effect is also seen as more obvious interference fringes in the spectra of Fig. 3(b).

 

Fig. 3. SPP prism coupling data. Red waveforms represent bare guide measurements. Black waveforms show measurements with tape applied to the hump apex. Blue and green waveforms show measurements with tape applied to sides of the hump. (a) measurements on humped Cu guide of Fig. 1b, (c) measurements of truncated Cu guide of Fig. 1c, (b) and (d) are the respective amplitude spectra of (a) and (c). Waveforms are shifted for visual clarity. Color-coded multipliers indicate amplitude scaling for plots.

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To determine the actual coupling mechanisms occurring in these arrangements, a section of metal was removed from underneath the coupling prism, as shown in Fig. 1(c). A section of guide could also be removed from under the decoupling prism, with equal results. Surprisingly, coupling to the SPP mode still worked, and signals obtained in this configuration are shown in Figs. 3(c) and 3(d). By removing the section of guide, the possibility of ATR coupling was eliminated and the possibility of edge-diffraction coupling was either eliminated or reduced. Therefore, coupling likely occurred by either edge-diffraction at the cut-off boundary of the guide, or by the only remaining mechanism, hump coupling. But, since the signals of Figs. 3(c) and 3(d) were reduced in strength from those measured in configuration of Fig. 1(b) and since hump coupling is not possible in the flat guide arrangement of Fig. 1(a), it is clear that hump coupling is not the only active coupling mechanism in our experiments.

The remaining options for the normally configured system are edge-diffraction and ATR coupling. Theoretical calculations indicate that ATR coupling would be extremely sensitive to the prism-metal gap, the THz wavelength, and the angle of THz incidence on that gap. In fact, ATR coupling sensitivity increases with the increasing conductivity of metals at decreasing frequencies to the extent that only an extremely small fraction of THz photons could possibly satisfy the momentum matching condition. We do not observe this great sensitivity indicating that ATR is not active, but that edge-diffraction at the prism corner is the most likely remaining coupling mechanism. This prism edge-diffraction mechanism was also found to occur in various two-prism SPP measurements in the infrared regime [16, 20]. For the chirped SPP signals shown in Figs. 3(c) and 3(d) the SPP propagated through only 9.5 mm of tape which reduced the duration of chirped ringing in comparison to Fig. 2(b) and 2(c) where the SPPs propagated through 19 mm of tape. This reduced duration chirp effect for shorter tape samples was also observed on the arrangement of Fig. 1(b), and further verifies successful coupling to the surface wave mode.

In another effort to unravel the coupling mechanisms we eliminated any line-of-sight between the prisms by implementing the configuration shown in Fig. 1(d): a polished, gently curved copper surface with approximately 16 cm of path length between the prisms. The SPP signals obtained in this configuration were an order of magnitude smaller, which is due in part to the difficult alignment of this arrangement and the longer curved path over which energy can be shed. As before, SPP propagation was confirmed by applying a tape sample to the SPP path and observing the resulting chirp effect. Changing the position of the tape along this guide had no effect for prism-metal gaps upto about 1.5 mm. But it was found that as the metal-prism spacing was increased, the detected signal increased in amplitude and arrived earlier in time. This counter-intuitive result is consistent with a THz path comprised of two free-space legs and one short portion of travel as a surface wave on the guide. This situation is illustrated in Fig. 1(d) by the blue lines.

As the prism-metal gaps are increased, the free-space THz emerging from the bottom of the prism can travel a greater distance before it encounters the curved path at which point hump coupling to the SPP occurs. It then travels a short distance, decouples again to free-space via the hump curvature, and finally is directed to the detector by the decoupling prism. Therefore, increasing the prism gap actually decreases the total propagation distance, resulting in earlier signal arrival. And since there is less guided travel over the lossy curved path, the detected signal is also stronger. This phenomenon was further verified by strategic application of tape samples along the metal path. These measurements are shown in Fig. 4 for the fixed prism gaps of about 8 mm. Clearly, the tape only affected the signal when it was placed directly on the apex (position ‘C’) of the hump, as shown in Fig. 1(d). However, when the tape was placed in position ‘L’ or ‘R’ it had no effect and the signal was no different from that obtained by the bare guide. Waveforms in Fig. 4 are shifted, from bottom to top, in increments of 2.5 ps and 1.5 nA for visual clarity. Finally, due to the large gaps used for this measurement, the line-of-sight between the prisms became an increasing factor. This is evident in the free-space component, labeled ‘free-space’ in Fig. 4, preceding the chirped portion of the black waveform.

To estimate the coupling efficiency, we used our largest SPP signal shown in Fig. 2(b) to calculate the overall received energy and then compared it to the energy in a free-space reference measurement obtained by removing the SPP apparatus. Accounting only for Fresnel losses at a single face each of the coupling and decoupling prisms, we estimate a minimum coupling and decoupling efficiency of approximately 3.5%. This estimate does not account for many factors including Joule losses, spreading losses in the unguided dimension, and energy shedding from the curvature of the SPP path. Nevertheless, we measure a resulting signal-to-noise ratio as high as 400, indicating a potentially useful configuration for spectroscopy applications. Theoretical estimates of the surface wave launching efficiency have been performed for monochromatic radiation issuing from an aperture or slot placed direcly above a guiding surface. These estimates indicate possible coupling efficiencies of greater than 90% for metallic apertures, but also depend greatly on the ratio of the aperture size and location to wavelength [1]. For broadband THz pulses, these ideal conditions cannot be simultaneously satisfied for all frequencies.

 

Fig. 4. Tape position dependence on no-line-of-sight Cu guide with fixed 8 mm prism-metal gaps. Green waveform (shifted -2.5 ps and -1.5nA), blue waveform (not shifted), and black waveform (shifted +5 ps and +3 nA) show surface wave measurements with tape at position ‘R’, position‘L’, and position ‘C’, respectively. Red waveform (shifted +2.5 ps and +1.5 nA) shows measurement with no tape sample.

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To further study the coupling mechanisms, we applied tape samples to the humped guide of Fig. 1(b) at various locations directly under the prisms, indicated by the black line under the right-hand prism in the figure. This addition affected the coupling if the tape was within 1 cm of the prism corner. This sensitivity indicates that THz is not only emanating directly from the prism corner, but also may be coupling to a guided mode between the prism and metal surface and then transforming to a surface wave upon reaching the aperture defined by the prism corner. This effect has already been observed in infrared work [16], and suggests that a flared parallel plate waveguide, described by Barlow et al.[21] may be the optimal configuration for broadband THz SPP coupling. Of related interest is previous THz parallel plate waveguide work [22] showing that two-dimensional, or planar, quasi-optics can be integrated into guiding structures for the purpose of controlling waves in the ‘unguided’ dimension. This has also been demonstrated at microwave and optical frequencies for SPPs [23, 24] suggesting the possibility of greatly focusing THz SPP energy, which could potentially increase the sensitivity of THz based SPP spectroscopy systems.

While our work makes heavy use of humped or curved surfaces, we note that the definition of a Zenneck wave (or equivalently SPP) is restricted to non-radiative modes. Since energy shedding occurs as our surface waves travel over outside curves, these waves cannot strictly be called SPPs. However, it is clear that curved surfaces can be used to block free-space interference signals and assist in coupling into a SEW. Such an SEW then becomes a non-radiative SPP when it reaches a flat portion of guide. This suggests another interesting configuration where only inside curves are used to guide the surface wave. In this case, loss due to energy shedding cannot occur and, in fact, the surface wave only becomes more evanescent [21]. This would produce an even stronger field enhancement at the guiding surface, especially in regions where the curvature becomes quite sharp. Additionally, line-of-sight issues between coupling and decoupling apparatuses would be eliminated.

3. Conclusion

In conclusion, we have demonstrated the use of silicon prisms for broadband THz coupling to SPP modes. Our data is consistent with edge-diffraction and hump coupling to SPP modes. We find no evidence for ATR coupling. Coupling and decoupling efficiencies of at least 3.5% have been obtained. These can probably be increased by optimization of the experimental arrangement. We have also described arrangements in which THz SPP energy can be more efficiently coupled, and even concentrated, for optimization of sensitive applications such as thin-film spectroscopy. The implementation of these ideas is currently in progress.