In this study, the coupling properties of a conical copper wire waveguide were investigated in the terahertz (THz) frequency range using theoretical simulations and experiments. Because a conical wire tip has a smaller tip diameter than a cylindrical wire tip, it has a greater THz field density than a cylindrical wire tip. The measured THz pulse increased 4.5 times upon contact with the 30µm-diameter conical wire tip compared with the THz pulse when a 500µm-diameter cylindrical wire tip was used. This result agrees well with that of theoretical simulations such as high-frequency structure simulation (HFSS), which is based on the finite element method.
©2008 Optical Society of America
In the late 19th century, Sommerfeld published a paper on wave propagation along an infinitely long cylindrical wire . It was the first published paper on field propagation on a conductive wire. In 1950, Goubau published a paper on the applicability of non-radiating surface waves to transmission lines . Twelve years later, King and Wiltse theoretically analyzed surface wave propagation on coated or uncoated metal wires at millimeter wavelengths . For about 50 years, these research topics have not interested scientists. Recently, however, many researchers and scientists have redescribed surface wave propagation on a cylindrical conductor (the Sommerfeld wave) in the terahertz (THz) frequency range [4–12]. D. Grischkowsky et al. conducted many other kinds of surface wave propagation researches [10–15]. The higher conductivity of a metal wire gives the Sommerfeld wave minimal attenuation and group velocity dispersion. Metal wire waveguides are an interesting research topic for applications in THz imaging and spectroscopy [16–18]. Also, wave propagation has a weak guidance property due to the small electric field in the metal wire [12, 19, 20]. There is no guided propagation on a perfect conductor, as there is no field distribution in the conductor [19, 21]. When the generated THz pulses were coupled with the cylindrical conductor (wire), only the dominant transverse-magnetic surface wave mode (TM01: the Sommerfeld wave) was propagated along the wire. Because all the higher modes had very high attenuations, they vanished almost immediately after they were coupled with the wire. The wire diameter was an important factor in the characterization of the THz propagation [5, 18, 22].
Recently, a conical wire tip was used to launch a THz pulse on a metal wire waveguide [9, 12, 18,19]. F. A. Hegmann, et al., investigated the photoconductive antenna characteristics of a metal tip coupled with an air-propagated THz pulse . A photoconductive dipole antenna on a silicon-on-sapphire (SOS) receiver was located on a cylindrical wire tip to detect the surface wave mode [12, 19]. Because the system did not have a silicon lens on its receiver chip, it detected the THz field at a certain point. In this paper, the detected THz intensity was improved by replacing the cylindrical wire tip of the dipole antenna of the receiver chip with a conical wire tip. In recent researches, numerical simulations of field distributions on a cylindrical wire were performed [8, 9]. S. A. Maier, et al., simulated the dispersion relationship of surface plasmon polaritions propagated along a cylindrical wire and a conical wire with a periodic array of radial grooves, using finite difference time domain (FDTD) . J. A. Deibel, et al., simulated the THz emission from tapered wire waveguide, using a finite element method (FEM) model . In this study, FEM simulations of the field distribution in the conical wire are presented using high-frequency structure simulation (HFSS) software. The simulation results show that the field intensity near the conical wire tip was much bigger than that near the cylindrical wire tip. This agrees well with the experimental results. The enhanced THz signal will be useful in THz sensing, THz imaging, and THz spectroscopy.
2. Experimental setup
The THz waveguide system is based on the photoelectronic generation and detection of a beam of subpicosecond THz pulses. In this study, an SOS transmitter and receiver chips were used to generate and detect THz pulses, because SOS is a strong and optically transparent material. The excitation laser beam travels by air, but the detection laser beam is guided by optical fibers, as shown in Fig. 1(a). Therefore, the receiver part of the THz waveguide system can freely move without laser beam adjustment.
The transmitter chip consisted of coplanar 10µm-wide, 20mm-long metal lines with a 30µm separation, and two dipole antennas separated by a 5µm gap, as shown in Fig. 1(b). The dipole antenna structure allowed easy alignment of the laser beam and the copper wire tip. Because the dipole antenna gap was only 5 µm, the DC voltage bias was 10 V. The 6.3mW laser excitation beam was focused on the 5µm gap of the biased dipole antenna, at which the antenna faced the copper wire tip. Because SOS is an optically transparent material, the laser beam was able to pass through the SOS and arrive at the dipole antenna gap. Commercial copper wires with a diameter of 500 µm were used in this study, and the 18.5cm-long copper wire was cut into two pieces, W1 and W2, as shown in Fig. 1(a). The two flat, cut ends of each wire faced each other, with a 150µm air gap between them. Figure 1(b) shows the dipole antenna of the transmitter chip that came in contact with the conical copper wire tip (wire W1), the diameter of which was about 30 µm. Because the conical wire tip was located close to the emitter source, the generated THz pulses were directly coupled with the wire without any silicon lens [8, 9, 12, 17].
The receiver chip had the same structure as the transmitter chip, except for a 50µm separation between the two metal lines, as shown in Fig. 1(c). The 50µm separated dipole antenna was shorter than that of used in Ref . The short dipole antenna detected a smaller THz signal and a wider THz spectrum than the long dipole antenna. The 500µm-diameter cylindrical copper wire tip (wire W2) was located beside the dipole receiver antenna so it could detect the propagated THz Sommerfeld wave. To detect the THz signals, the dipole antenna directed the THz field direction in the known TM01 mode. The Sommerfeld wave that was launched from the transmitter chip was propagated through the two wires and ended up at the receiver chip. Because the air gap between the two wires was only 150 µm, the THz pulses were easily coupled with the minimized coupling loss from wire W1 to wire W2. Also, the receiver-side copper wire W2 could be replaced with any kind of wire structure without adjusting the transmitter part and the laser beams, because the fiber coupling receiver part allowed flexibility of movement. In this research, the THz field intensities of the 500µm-diameter cylindrical wire tip and the 30µm-diameter conical wire tip were compared for the same receiver chip with a fixed transmitter chip and wire W1. The two cut wires were supported by two tightly fitted 3mm-thick Teflon disks that were well positioned to ensure the wires’ optimal coupling. To protect the transmitter and receiver dipole antennas, the chips were covered with a 15µm-thick polyethylene insulation tape.
3. Field simulations
In this study, electric fields were calculated with an HFSS numerical field simulation. The THz Sommerfeld wave is an electric field in the cylindrical wire, as in the experimental situation. When the number of selected meshes was few, the results varied according to the distance from the surface. Therefore, approximately 80,000 meshes were used, and the calculation loop was used several times until the results converged less than 0.5% compared to previous calculation results. The wire waveguide was modeled in three dimensions (3D). The 3D simulation domain was bounded by a 9mm-diameter and 10mm-long cylindrical tube, with the wire model located in the center. The outer boundary of the wire is defined as a perfect electrical conductor (PEC) because the attenuation loss of copper wire can be disregard in the THz frequency range . In this simulation, the plan wave is excited on the circular input face of the cylindrical tube. The outer wall of the domain assumed an absorbing boundary condition to minimize any back reflections on the wire. The absorption coefficient of the outer wall was bigger than -80 dB.
The wire model had a 4mm-long, 500µm-diameter cylinder with a 6mm-long, 30µm-diameter conical tip. Therefore, the diameter gradually decreased from 500 µm to 30 µm. Because the attenuation of the copper wire was very small , the field simulation of the 10mm-long copper wire was sufficient compared with the experimental results for the geometric structure of the wire tip to the receiver. Figures 2(a) and 2(b) show the magnitude of the field distribution using the 0.15THz frequency. The simulation shows horizontal (xz plane) and vertical (yz plane) field distributions near the wire to confirm the field intensity variation along the wire tip. Because the diameter of the conical tip was small compared with that of the cylindrical wire, the guided electric field along the wire was concentrated around the conical tip. Therefore, the field intensity around the 30µm tip was stronger than that on the cylindrical body surface.
Figure 3 shows the definitions of radial distance (R) and tip diameter (D) and the calculations of field distribution on copper wire. Figure 3(a) shows the field intensity at the end of the conical wire tip, at 1 µm, 30 µm, and 60 µm radial distances, with different tip diameters. The solid line is a fitting curve for the simulation results. The figure shows that the field intensity exponentially increased with decreases in the tip diameter D. The field intensities at the 500µm-diameter tip are almost same at a radial distance of 1 µm, 30 µm, and 60 µm. However the field intensity at the 30µm-diameter tip, as shown by the dashed line, increased by about 9.6 and 4.2 times at a radial distance of 1 µm and 30 µm, respectively, compared with the field intensity at the 500µm-diameter tip. This comparison is important because the receiver dipole antenna in this study’s experimental setup was located at a 30µm radial distance (R=30µm) from the surface of 30µm-diameter tip (D=30µm). The field distribution on the cylindrical copper wire was already measured with the radial distance away from the wire (y direction) using the 0.15THz central frequency . The field intensity in the air exponentially decreased as the radial distance increased. The results of this study’s simulation also show this situation. Figure 3(b) shows the field distribution with the radial distance for the 30µm-diameter tip. The field intensity dramatically decreased with increases in the radial distance. Therefore, a smaller tip diameter and radial distance results in a higher field intensity.
The THz field density at the cylindrical wire tip depended on the tip diameters of the wire. The large tip diameter had less field density on the surface than the small tip diameter when their input fields were the same. Therefore, an attempt was made to compare the cylindrical wire tip and the conical wire tip with the same input THz field. Figures 4(a) and 4(b) show the field distribution near the tips of the 10mm-long, 500µm-diameter cylindrical wire tip and the 4mm-long cylinder with the 6mm-long, 30µm-diameter conical wire tip, respectively. The 2D images (xy plane) of the simulated spatial field distribution have symmetrical patterns. Red indicates high intensity and blue indicates low intensity. The figure shows that the field distributions around the conical tip were much stronger than those around the cylindrical tip. As explained from Fig. 3, the field intensity 30 µm above the conical tip surface was 4.2 times bigger than that at the cylindrical tip. Because the receiver dipole antenna gap in this study was located about 30 µm above the wire tips in the experimental measurement, there was concern over this comparison in the field simulation.
The THz Sommerfeld waves in the cylindrical and conical tips of the dipole receiver antenna were measured to compare their THz field intensities. Because of the fiber-coupled photoconductive receiver, wire W2 could be replaced with another wire without any change in the transmitter parts and the laser detection beam. The THz Sommerfeld wave generated from the transmitter chip was propagated using the copper wires W1 and W2, as explained in the Experimental Setup section. First, the 9cm-long, 500µm-diameter cylindrical wire W2 was measured with fixed wire W1. Then the cylindrical wire was replaced with the conical wire. The wire tips were located about 30 µm beside the dipole antenna gap (R=30µm), as shown in Fig. 5(a). Because the direction of the THz Sommerfeld wave was from the wire tip surface to the air, the dipole antenna was directed towards the wire tip surface. The measured peak-to-peak amplitudes of the cylindrical and conical tips were 20 pA and 89 pA, respectively as shown in Fig. 5(b). They increased by about 4.5 times, which was slightly more than the results of the simulation, because an exact 30µm separation between the tips’ surfaces and the dipole antenna gap could not be made. The field intensity near the wire surface was very sensitive. The THz field distribution decreased according to the a/r relationship, as shown in Ref. 12, wherein a is the radius (in this study, 250 µm) of the wire and r is the distance from the center of the wire to the dipole antenna gap. Also, the field intensity near the tip surface dramatically decreased with the increase in the radial distance, as shown in Fig. 3(b). The simulation and measurement values differed by only 7%, however, which is an acceptable result. The full width half maximum of the pulses increased from 1.11 ps to 1.66 ps for the cylindrical tip and the conical tip, respectively. Therefore, the low-frequency components of the conical wire tip were bigger than those of the cylindrical wire tip, as shown in Fig. 5(c). Because there were reflections from the SOS chip, the wire tip, the thin insulation film, the Teflon, etc., the reflected THz pulses appeared after the main THz pulse. Therefore, a fast Fourier-transform was made only on the main THz pulses. The spectrum band limit was very narrow compared to the standard THz time-dome spectroscopy system  because the high-frequency THz components were lost to the coupling between the copper wire and the transmitter chip. The maximum spectrum peak for the cylindrical wire tip was located at 0.15 THz, similar to previous measurements [12, 19]. Although a fiber-coupled receiver chip and a fixed transmitter chip were used, the system was not a perfect linear system. The conical wire tip had a bigger THz signal and a bigger spectrum, however, than the cylindrical wire tip.
This paper presented the results of a study on the characteristics of a copper wire waveguide in the THz frequency range, through theoretical simulations and experiments. Using a conical wire with a 30µm-diameter tip, the measured THz pulse increased by about 4.5 times compared with the THz pulse when a 500µm-diameter cylindrical wire tip was used, because the THz field density from the conical tip increased, unlike that from the cylindrical tip. This result agrees well with the theoretical simulations via HFSS. The theoretical simulations showed that the smaller the tip diameter of the conical wire was, the bigger the field intensity around the tip was. When the conical wire tip diameter was 1 µm, the field intensity increased by about 9.6 times compared with the field intensity at the 500µm-diameter cylindrical wire tip. This means it can be detected dramatically big THz Sommerfeld wave by a conical waveguide without any optoelectric change.
The authors thank Professor D. Grischkowsky for supplying the SOS photoconductive chips and Professor D. K. Park for his helpful comments on this simulation. This work was supported in part by the University Fundamental Research Program of the Ministry of Information & Communication, and by the Korea Science and Engineering Foundation under Grant No. KOSEF 2007-8-1158.
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