1. Introduction

The ability to transmit electromagnetic radiation across arbitrary user-defined geometries is of fundamental importance in numerous applications, including a broad range of information technologies and sensing capabilities. Waveguides, in their various embodiments, offer a simple means for accomplishing this task. At optical frequencies, waveguiding may be realized straightforwardly using a wide variety of dielectric structures in planar and fiber form. However, as one moves to longer wavelengths, particularly in the far-infrared, fewer waveguide embodiments have been well characterized. Given the relative sophistication in generating and detecting coherent THz radiation at present, the design and implementation of useful guided-wave structures is of increasing interest. This is particularly true for THz radiation in the form of broadband pulses, which are readily available through the use of ultrafast laser systems.

In recent years, a number of different waveguide geometries, based on dielectric and metal waveguide architectures, have been fabricated and characterized for broadband THz applications. In the former case [1–5], waveguides based on traditional geometries, as well as microstructured fibers, have been pursued. A limitation that has hindered greater exploration in this direction is the fact that a large fraction of the suitable growth materials exhibit non-negligible absorption and dispersion throughout the THz frequency range. Metal waveguides offer a simple means for confining long wavelength electromagnetic radiation. Given the high conductivity of metals at these wavelengths, propagation losses can be relatively small. With this in mind, the propagation properties of broadband THz pulses have been examined using a number of different metallic waveguide structures [6–9]. Among these structures, the most straightforward metallic waveguides utilize a simply connected domain, such as a cylindrical or rectangular waveguide. However, according to waveguide theory, such geometries exhibit a cutoff frequency and can cause significant pulse distortion [10]. One specific geometry, the parallel plate metal waveguide, has been shown to be well suited for broadband THz applications [7]. This structure allows for nearly distortion-free, low loss propagation of broadband THz pulses and exhibits a mode pattern that enables simple coupling into and out of the device. The utility of this geometry has been extended recently by embedding nonlinear media within the waveguide to allow for broadband generation of THz radiation [11,12]. Such a capability is crucial for the creation of active guided-wave THz devices.

Recently, Wang and Mittleman showed that a cylindrical metal wire allows for low loss, low distortion guided-wave propagation of broadband THz pulses [13]. Several theoretical and experimental studies have further investigated the propagation characteristics of this simple waveguide structure at THz frequencies [14,15]. The basic demonstration is based on a proposal that Sommerfeld made in the late nineteenth century, in which he showed that a single cylindrical conductor of finite conductivity could support a guided wave mode [16]. The dominant propagating mode is a radially symmetric transverse magnetic wave, often referred to as a Sommerfeld wave [16,17]. This idea was validated in a number of studies designed for millimeter wave frequencies nearly half a century ago [17–19]. It should be noted that the Sommerfeld wave is very weakly guided by the metal wire. This has placed limitations on potential applications at microwave frequencies and may do so at THz frequencies. As with all waveguide geometries, a fundamental issue that requires careful consideration is that of coupling electromagnetic radiation to the relevant waveguide mode. At microwave frequencies, a variety of different horn structures have been developed to launch such a wave on the cylindrical conductor [19, 20], while the more recent THz studies have utilized either a wire in close proximity to the wire waveguide [13] or simply used a radially symmetric photoconductive antenna to directly generate the requisite field pattern [14].

In this submission, we demonstrate a simple, yet new, technique for coupling freely propagating THz radiation to a single cylindrical metal wire that involves milling grooves into the wire. The technique is based on recent work that we have done in examining enhanced transmission through a single subwavelength aperture [21,22]. In that work, we fabricated rectangular cross-section annular grooves around a subwavelength aperture. We found that each groove was able to couple the incident THz radiation to a propagating surface wave. By using multiple grooves, multiple oscillations, delayed in time from one another in accordance with the groove separation, would coherently superpose. More recently, we showed that by altering the cross-sectional parameters, the amplitudes of the individual oscillations could be controlled, allowing for complex temporal pulse shaping capabilities [23]. The relationship between this earlier work and the present demonstration is shown graphically in Fig. 1(a). Here we consider a sheet of metal with an array of linear grooves milled into the surface. Aside from the groove geometry, the pattern is identical to what we have previously explored. If we roll the sheet about the axis perpendicular to the groove length, we will have a solid cylindrical metal conductor with circumferentially milled grooves that should allow for coupling of THz radiation. In general, multiple grooves will give rise to narrow band excitation on the wire, although a single groove could be used for broadband excitation. In this initial proof of principle demonstration, the grooves are equally spaced and of uniform depth, although as mentioned above, more complex groove patterns should allow for arbitrary pulse shape excitation.

2. Experimental details

We fabricated circumferentially milled grooves into the middle of 10 cm long sections of 1 mm diameter stainless steel wire. Four different samples were fabricated: the first with 1 groove, the second with 3 grooves, the third with 8 grooves, and the fourth with no grooves. The last sample was used for reference purposes. The rectangular cross-section grooves were 500 μm wide and 100 μm deep, with a center-to-center spacing of 1 mm. A photograph showing a segment of the wire with 3 grooves is shown in Fig. 1(b).

 

Fig. 1. Properties of the grooves milled into the cylindrical metal wire (a) The relationship between a large area metal film with inscribed linear grooves and a cylindrical wire with circumferentially milled grooves. Using the former sample, with slightly different groove patterns [21,22], we showed that each groove was able to couple the incident THz radiation to a propagating surface wave. By using multiple grooves, multiple oscillations, delayed in time from one another in accordance with the groove separation, would coherently superpose. If we roll the sheet about the axis perpendicular to the groove length, we will have a solid cylindrical metal conductor with circumferentially milled grooves that should allow for coupling of THz radiation. (b) Photograph of a section of the 1 mm diameter stainless steel wire containing 3 milled grooves.

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Fig. 2. Schematic diagram of the experimental setup. The emitter was oriented so that the resulting THz radiation was polarized in the plane of the schematic diagram and parallel to the wire length. The fiber-fed photoconductive detector was offset from the center of the wire by approximately 3 mm in order to measure the radially polarized THz electric field. The wire length, from the excitation region to the end (near detector), was approximately 5 cm.

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The experimental setup for generating, coupling, and detecting THz radiation is shown in Fig. 2. A mode-locked Ti:sapphire laser operating at 820 nm with a repetition rate of 89 MHz was used as the optical source. The optical pump beam, with an average power of 100 mW, was used to generate THz pulses from a photoconductive emitter. The emitter was oriented so that the resulting THz electric field was polarized parallel to the length of the wire. An off-axis paraboloidal mirror was used to collect and collimate the THz radiation. A high resistivity silicon cylindrical lens with a focal length of 25 mm was used to focus the THz radiation along the axis perpendicular to the wire length and was normally incident on the wire. A fiber-fed photoconductive detector was situated approximately 5 mm beyond the end of the wire waveguide, with the receiver offset from the center of the wire by approximately 3 mm. For the results discussed below, the detector was placed 3 mm to the left of the wire in the plane of the optical and THz beams and oriented to detect horizontally polarized THz pulses. As discussed below, the detector was placed in different positions surrounding the wire to ensure that the measured wave was radially polarized, which would correspond to the Sommerfeld wave [13,14].

3. Experimental results and discussion

We initially measured the properties of the THz pulse incident on the wire by replacing the wire and cylindrical lens with the photoconductive detector. Figure 3(a) shows the measured time-domain THz waveform in this experimental configuration, demonstrating that a single cycle THz pulse was incident on the wire. The small oscillation, approximately 20 ps after the main pulse, was due to reflections within the emitter. Figure 3(b) shows the corresponding amplitude spectrum. After replacing the lens and wire, we measured the time-domain waveforms corresponding to the THz radiation coupled onto the wire via the milled grooves and radiated from the end of the cylindrical wire waveguide for the four different wire samples described above.

Figure 4(a) shows the observed THz waveforms radiated from the wires with 0, 1, 3, and 8 grooves, respectively, and detected by a laterally offset photoconductive detector. For a normally incident electromagnetic wave, symmetry requires that the radiation coupled by each groove lead to equal amplitude counter-propagating pulses. In the waveforms presented in Fig. 4(a), only the surface wave contributions that propagate initially towards the detector fall within the measured temporal window. It is apparent from the data that grooves are required to couple THz radiation onto the wire. As we noted above, the incident THz radiation is polarized parallel to the wire. The polarization direction in this excitation scheme is important, since incident radiation polarized perpendicular to the wire will not excite the requisite surface waves. This can be understood if one considers the requirements for excitation of surface waves using normally incident radiation on a metal sheet inscribed with an array of linear grooves or slits [24].

We have shown previously that each groove couples a large fraction of the incident THz pulse in the form of a surface wave oscillation [22]. Furthermore, there is a one-to-one correspondence between the number of grooves and the number of oscillations in the measured time-domain waveform. This is consistent with observations using similar structures in enhanced transmission measurements [22]. Multiple grooves, therefore, lead to the excitation of a narrowband THz pulse. The center frequency and linewidth of this excitation depend upon the groove spacing and number of grooves, respectively. This is clearly demonstrated from the amplitude spectra, shown in Fig. 4(b), computed from the temporal waveforms in Fig. 4(a).

 

Fig. 3. (a) Measured time-domain waveform of THz pulse incident on the wire. The waveform was measured by replacing the cylindrical lens and wire with the photoconductive detector (b) Corresponding normalized amplitude spectrum.

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Although the y-axes for Figs. 3 and 4 use the same arbitrary unit scales, it is important to note that no inference of coupling efficiency can be made from comparing these two figures. There are a number of reasons why it is difficult to estimate the coupling efficiency based on the results. First, completely different experimental geometries were used in measuring the different waveforms. The spatial distribution of the THz electric field incident on the photoconductive detector was fundamentally different between the reference measurement (Fig. 3) and the waveguide measurement (Fig. 4). Second, the coupling process may initially excite numerous modes to differing extents, leaving only the radially polarized wave after 5 cm of propagation, as shown below. Finally, we measure only a fraction of the radially polarized wave that radiated from the wire, by virtue of laterally offsetting the detector. With that said, we believe that the amplitude of the coupled THz pulses can be significantly increased with improved focusing of the THz beam. We estimate that the 1/e beam width along the focus axis, perpendicular to the wire, was approximately 3 mm at 0.3 THz (λ = 1 mm).

 

Fig. 4. (a) Measured time-domain THz waveforms for THz pulses coupled to a 1 mm diameter stainless steel wire with eight grooves (red trace), three grooves (blue traces), one groove (green traces), and no grooves (black trace). Broadband THz radiation is coupled to the wire via multiple periodically spaced grooves. The rectangular cross-section grooves are 500 μm wide and 100 μm deep with a center-to-center spacing of 1 mm. The waveforms have been offset from the origin for clarity (b) Corresponding normalized amplitude spectra using the same color scheme noted above.

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Fig. 5. Measured time-domain THz waveforms for THz pulses coupled to a 1 mm diameter stainless steel wire with 3 grooves for two different detection points. The blue trace is the data shown in Fig. 4(a) with the photoconductive detector located 3 mm to one side of the wire center. The black trace corresponds to the observed waveform taken with the detector placed 3 mm to the other side of the wire center. The inversion of the observed waveform with the change in the detector position demonstrates clearly the radial polarization of the wave.

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In order to more clearly understand the polarization properties of the THz pulses radiated from the cylindrical wire and measured by the photoconductive detector, we measured the time-domain properties of the THz waveform for two different detector positions: 3 mm to the left of the wire center and 3 mm to the right of the wire center. These two waveforms are shown in Fig. 5. The two waveforms are clearly related through a simple sign inversion, demonstrating that the polarization direction is reversed between these two positions. This is consistent with earlier results reported by Wang and Mittleman [13]. As we noted above, measurements at different positions surrounding the wire demonstrate clearly that the radiated THz pulse is radially polarized.

4. Conclusion

In conclusion, we have demonstrated a simple, yet new, approach for coupling freely propagating broadband THz radiation to a single cylindrical metal wire using grooves fabricated directly into the wire. The approach is based loosely on our earlier work in which annular grooves were used to increase the transmission through subwavelength apertures. As in our earlier work, we found that each groove was able to couple the incident THz radiation to a propagating surface wave. Thus, by varying the number of grooves and the groove separation, both the linewidth and center frequency can be manipulated. In this initial proof of principle demonstration, the grooves are equally spaced and of uniform depth. However, the groove-to-groove separation and the cross-sectional parameters of the individual grooves are not required to be uniform. Careful control of both parameters should allow for arbitrarily shaped THz pulses to be launched on the waveguide.