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This paper reports an experimental and simulation study of a tapered parallel-plate waveguide (TPPWG) to improve THz coupling to the plate separation gap. The flat- and round-type TPPWG without any silicon lens is compared to the parallel-plate waveguide (PPWG) with a plano-cylindrical silicon lens. The spectrum amplitudes of the input-side TPPWG and the input- and output-side TPPWG both having a 3° slop angle increased about 56% and 103% at 1 THz when compared to that of the PPWG. Since the input- and output-side TPPWG had almost no impedance mismatch to the propagating THz wave, coupling to the waveguide could be improved twice compared with the PPWG.
©2010 Optical Society of America
1. Introduction
In recent years, there has been increased interest in understanding the guided-wave propagation of terahertz (THz) radiation and efficient broadband coupling between guiding and freely propagating THz waves. THz waveguides for single-mode coupling, such as circular and rectangular metals [1,2], single-crystal sapphire fibers [3], coplanar and single metal wires [4–7], coaxial cables [8], and parallel-plate waveguides (PPWGs) [9,10] have been demonstrated. When THz waves propagate into a material in the waveguides, such as crystal sapphire of fibers or Teflon of coaxial cables, there is absorption loss by the material. Also, when the THz waves propagate on a metal surface, such as metal wires, the guiding property is very weak.
Among these waveguides, PPWG has been used in spectroscopy [11], sensing [12], the super-prism effect [13], and Bragg resonances [14]. All these PPWG applications have used the transverse-electromagnetic (TEM) mode, which offers many advantages such as very low absorption, negligible group-velocity dispersion, and no cutoff frequency [9,10]. To achieve the TEM mode, the air gap between the two parallel plates must be less than 100 μm if the bandwidth is about 3 THz, which is also the cutoff frequency of the TM2 mode.
Because the plate separation is very small, plano-cylindrical silicon lenses are attached to the input and output side of the PPWG to create a line focus and to propagate the THz wave to the air. Because of the high refractive index of the silicon (n = 3.412), however, about 30% THz beam is reflected from each lens. Consequently, there is about a 50% total loss from the two silicon lenses. This reflection loss induces a low coupling efficient. Recently, large plate separation at a scale of a few millimeters has been studied to achieve the transverse-electric (TE1) mode without using silicon lenses [15]. A high THz energy concentration in a hundred-micron plate separation of the PPWG is still attractive, however, for many useful applications.
To concentrate freely propagated electromagnetic beams, tapered-structure waveguides were used in the microwave [16,17] and X-ray [18] regions. Recently, numerical simulations have shown that micro-nano-size tapered waveguides can concentrate THz energy and improve the spatial resolution and the signal-to-noise ratio [19]. Also, THz quantum cascade laser operating with a micro-TEM-horn emitter antenna has been demonstrated [20,21]. An adiabatically compressed parallel-plate metal waveguide was used to enhance the sensitivity of waveguide THz time-domain spectroscopy [22]. In this paper, a TPPWG without silicon lenses is reported as having a higher THz coupling efficient than PPWG, using experimental and theoretical calculations.
2. Measurement and Simulation
The waveguides were set up in the middle of two parabolic mirrors similar to those in previous studies [1,2,4,10]. All the waveguides used in this research were made of aluminum. Also, a computer numerical controlled end mill was used to make tapered structures of the waveguides. Because of the size of the plano-cylindrical silicon lens (15 mm (width) × 9.1 mm (height) of plano surface) that was positioned at the input and output of the PPWG, a 10 mm (width) × 5 mm (height) rectangular aperture was inserted about 2 cm before the waveguides during the entire experiment. The rectangular aperture keeps the same input cross section to the waveguides. The incoming THz beam was vertically polarized, and the waveguides were horizontally set up to achieve the TEM mode with 100 μm plate separation. All the waveguides that were used in the experiment had the same flat plate dimensions of 30 mm (width) × 30 mm (length). The high-resistivity plano-cylindrical silicon lens of the input side formed a line focus to the incoming THz beam along the plate separation. Since the 1/e amplitude of the line focus at the beam waist was about 200 μm [9], the entire THz beam could not couple to the waveguide gap. Moreover, there was a reflection loss from the silicon lens surface.
To prevent reflection loss and to concentrate the THz beam on the air gap of the plate separation, the structure of the input side of the PPWG was changed into a tapered structure (a one-sided TPPWG), as shown in the inset in Fig. 1(a) . The incoming THz beam was guided by the tapered structure and naturally formed a line focus to the air gap, as did the plano-cylindrical silicon lens. The five different slop angles of the tapered part—i.e., 20°, 15°, 10°, 5°, and 3°—were used to get the THz pulses. Therefore, the opening angle of the TPPWG was twice the slop angle, and the length of the tapered part increased with the decrease in the angle to retain the input cross-section
Fig. 1 (a) Measured THz pulses of the TPPWG with different slop angles, and dotted THz pulses for the PPWG. (b) Corresponding amplitude spectra for the THz pulses. The inset shows the amplitude ratios of the PPWG and the 3° TPPWG.
Figure 1 (a) and (b) show the measured THz pulses and their spectra for the TPPWG and the PPWG. The peak-to-peak amplitude of the THz pulse at the 3° slop angle was 1,380 pA, which was about three times bigger than that of the 20° slop angle. The peak-to-peak amplitude of the PPWG was 788 pA, similar to that of the 10° TPPWG. The spectrum bandwidth extended to almost 4 THz for both waveguides. Moreover, the spectrum of the PPWG was similar to that of the 10° TPPWG. The inset in Fig. 1(b) shows the amplitude ratio between the PPWG and the 3° TPPWG. The spectrum amplitude of the 3° TPPWG at 1 THz increased about 60%, unlike that of the PPWG. As the slop angle of the TPPWG decreased, the amplitudes of the THz pulses were enhanced. Had the slop angle been smaller than 3°, the measured THz pulse would have been enhanced more. In such a case, however, the length of the TPPWG would dramatically increase to retain the cross-section for the input THz beam.
When the input THz beam carried out incidence on one edge of the two tapered surfaces, the incidence angle decreased with the increase in the number of reflections from the two tapered surfaces. When the incidence angle approached a critical angle, the reflected THz beam could not go forward. The input THz beam was inserted, however, at the same time between the two edges of the tapered surfaces. The most incidence THz field was strongly distributed between the two edged surfaces to obtain the TM mode, and was guided to the propagation direction along the tapered surfaces. Because the space between the two tapered surfaces continuously decreased with the THz beam propagation until 100 μm (the air gap of
the plate separation), the higher TM order modes were cancelled and only the TM0 (TEM) mode remained. Finally, the TEM THz beam was propagated to the parallel plate gap. Therefore, coupling to the plate gap by the tapered structure was more efficient than the plano-cylindrical silicon lens.
When the THz beam was propagated on the metal surface, the discontinuous boundary surface engaged its reflection [14]. The discontinuous boundary between the tapered and flattened surfaces also engaged the THz reflection. To reduce the reflection, the discontinuous boundary made a continuously changing surface (round) with an 80mm-diameter circular arc, wherein the area of the flat surface kept identical to that of the TPPWG. If the circular arc is getting large, the length of the waveguide should be dramatically long to keep the same input cross section. Therefore, the 80mm-diameter arc round taper was chosen to optimize waveguide length and to remove the discontinue boundary.
In this study, the magnitude of electric field propagation of 10° TPPWG with and without a round taper was calculated via FDTD numerical simulation, as shown in Fig. 2 . The linearly polarized THz pulses, wherein central frequency was 1 THz, were modeled as a plan wave with a magnitude of electric field that was incidence in perpendicular to the beam propagation. The waveguide blocks are defined as perfect electrical conductors with a mesh size of 1 × 1 μm. Because of the limited computer memory size, the width of both opened tapers was only 1.71mm. However, the important round part was covered in the simulation. The reflected THz field from the discontinuous boundary was stronger than that of the continuous boundary (round). The figures show that the strong main magnitude of THz fields were in the parallel plate gap and went forward, and that the reflected THz waves were in the tapered area and went towards the backward direction. To clearly show the reflected THz beam, the maximum magnitude of the field bar was shown as only 120. Therefore, the THz field in the parallel plate gap was saturated with the maximum magnitude. The maximum magnitude of THz field in the parallel plate gap without the saturation were 292 and 276 for the round and non-round TPPWG, respectively. Because of the continuous boundary (the round tapered surface), the THz field coupling to the parallel plate gap was bigger than that of the discontinuous boundary, and it had a small reflection loss.
Fig. 2 Calculated input-side magnitude of THz field distribution. (a) 10° non-round TPPWG. (b) 10° round TPPWG with an 80mm-diameter circular arc.
The measured THz pulses and spectra of the 10° round TPPWG and the 10° non-round TPPWG are shown in Fig. 3 . The peak-to-peak THz pulse of the round TPPWG increased about 15%. The spectrum of the 10° round TPPWG was also enhanced in the measured bandwidth. The inset in Fig. 3(b) shows the spectra ratio. The round TPPWG was enhanced by about 13% at the 1THz frequency. The spectrum of the round TPPWG improved in the high frequency range. Only the 10° round and non-round TPPWGs were measured because the smaller tapered slop angle, especially 3°, had almost the same THz field in simulation for the round and non-round TTPWG.
Fig. 3 (a) Measured THz pulses for the 10° round TPPWG (upper pulse) and the 10° non-round TPPWG (lower pulse). The inset shows the comparison of the pulses. (b) Corresponding amplitude spectra for the THz pulses. The inset shows the amplitude ratio.
Figure 4 shows the magnitude of THz field propagations to the air by the output tapered structure at a 10° angle. The continuous propagating magnitude of THz field shows by a snapshot every 1.25 mm period to the propagation direction. The THz field was well guided by the tapered surfaces in the inner area, in the same way the input side was. After this, much of the THz field was propagated to the open air at the same speed. There was only a slight refraction at the edge of the tapered structure. Because the output tapered structure operated as a cylindrical silicon lens, the output-side silicon lens of the TPPWG was replaced by the tapered structure. Therefore, the coupling of two-sided TPPWG will be enhanced by the structure since no silicon lenses are needed.
Fig. 4 Calculated the magnitude of THz field propagations to the air by the output tapered structure at a 10° angle. The magnitude of THz field shows by a snapshot every 1.25 mm period.
Figure 5 (a) compares the PPWG with the cylindrical silicon lens and the one-sided and two-sided TPPWGs with a 3° slop angle. The THz pulses obtained by the waveguide were time shifted for comparison. All the waveguides had 100- μm plate separations and lengths of 30-mm, 90-mm, and 180-mm total, in order to retain the THz input cross-section. The peak-to-peak THz amplitude of the two-sided and one-sided TPPWGs improved by 138% and 38%, respectively, compared to the PPWG. Since the two-sided TPPWG had almost no impedance mismatch between the freely propagating wave and the guided wave, most of the freely propagating THz wave coupled in and out of the TPPWG gap. The reference pulse shown in the upper pulse in Fig. 5(a) was obtained by removing the waveguides. In other words, the THz beam went through an aperture only. The reference spectrum had the biggest amplitude, as shown in Fig. 5(b).
Fig. 5 Comparison of the PPWG and the one-sided and two-sided TPPWGs with 3° slop angles. (a) Measured THz pulses. The measured reference pulse is shown in the upper pulse. (b) Corresponding amplitude spectra for the THz pulses. (c) The amplitude ratios of reference × α and the measured spectra. The inset shows the amplitude ratios of the PPWG and the two-sided TPPWG.
The frequency-dependent absorption for the TEM mode is given in the following equation [23]:
wherein dis the gap between the parallel plates, ℜis the characteristic resistance, and ζis the intrinsic impedance of the medium (air). The calculated absorption constant was 0.092 cm−1 at the 1 THz frequency. When the THz pulse was propagated to the parallel plate area (3 cm long) with the 100- μm air gap, a 13% attenuation loss at the 1THz frequency was observed. The dashed spectrum in Fig. 5(b) shows the new reference spectrum for the measured frequency range with neglected the attenuation loss by the 3 cm long parallel plate area.Therefore the new reference spectrum indicates 100% coupling to the waveguide. When the attenuation loss is neglected, the two-sided TPPWG, the one-sided PPWG, and the PPWG recorded a coupling of 56%, 42%, and 27% at 1 THz, respectively as shown in Fig. 5(c). The inset figure shows the improved ratio with the use of the two-sided TPPWG over PPWG. Coupling of the two-sided TPPWG improved the measured frequencies by over 100%, unlike the cylindrical silicon used in the PPWG. It is expected that the strong THz signal will be useful for many PPWG applications including sensing and spectroscopy.3. Conclusions
In conclusion, this paper suggested a new type of TPPWG and compared the characteristics of THz beam coupling to the plate separation gap with those of the PPWG. Because the plano-cylindrical silicon lens used in the PPWG had a high index of refraction in the THz frequency, each of the silicon lenses had a 30% reflection loss on the surface. The two-sided (input and output) TPPWG, however, had basically no impedance mismatch for the freely propagating wave. Its coupling efficient also doubled compared to that of the PPWG, while the TPPWG easily aligned the waveguide block. However, the THz signal of the PPWG was very sensitive in the alignment of the silicon lens. It is hoped that the suggested new type of TPPWG will be used in many other THz waveguide applications.
Acknowledgments
This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean Government (MEST) (R11-2008-095-01000-0) and from MKE (The Ministry of Knowledge Economy), Korea, under the ITRC (Information Technology Research Center) support program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA-2009-C1090-0903-0007).
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