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To improve the output power of a photomixer used as a THz source, we propose a four-leaf-clover-shaped antenna structure composed of a highly resonant radiation element and a stable DC feed element. The resonance characteristics of the proposed structure were first investigated on a half-infinite substrate as a simplified radiation environment to reduce the computation time. Based on the antenna characteristics on that half-infinite substrate, the antenna structure was designed to have a maximum total efficiency and a maximum directivity on an extended hemispherical lens. The input resistance of this structure was six times that of a full-wavelength dipole, significantly improving the mismatch efficiency between a photomixer and the antenna. The terahertz output power from this structure is expected to be 2.7 times that of a full-wavelength dipole.
©2010 Optical Society of America
1. Introduction
Terahertz (THz) waves are located between the microwave and infrared regions and have frequencies in the range 0.1–10 THz. THz waves penetrate nonconducting materials as microwaves do, produce high-resolution images as does light, and are strongly attenuated in water, unlike any other spectrum of electromagnetic waves. These interesting properties make THz waves attractive in imaging, spectroscopy, and communication technologies. For example, it is possible to use them to see through the internal structure of opaque objects, analyze a molecular-level mechanism, and transmit radio signals from space. They can also provide much higher data transmission rates than existing microwave or millimeter systems for short-range communications can [1–3].
The commercialization of THz technologies depends on the performance of THz radiation sources, which have been the focus of intense development activity due to recent advances in semiconductor, laser, and superconductor technologies. Many THz sources exist such as a photoconductive antennas [4] and an optical rectification [5] for pulse sources, and photomixers [6], hot-hole lasers [7], free-electron lasers [8], and quantum cascade lasers [9] for continuous wave (CW) sources. However, none of these sources is suitable for real applications due to their inherent weaknesses. Of all the different THz sources, the THz photomixer is considered to be one of the most promising technologies because of its room-temperature operation and frequency-tunable characteristics that can be implemented in compact and low-cost systems [10]. However, a THz photomixer system composed of a photomixer and an antenna produces a relatively low output power, on the order of a few microwatts, and this drawback is caused by two THz photomixing mechanisms. One is the low conversion efficiency of the photomixer from the incident laser to the THz photocurrent. This is related to the transit time and photocarrier lifetime, and it can be overcome by an improvement in the photoconductor [10,11] and the design of the photomixer structure [12]. The other drawback is the low total efficiency of the antenna from the THz photocurrent to the THz wave, which can be overcome by the design of the antenna structure [13–15]. Previous research related to antennas has concentrated on increasing the mismatch efficiency, but we must also pay attention to the radiation efficiency due to the shape of the antenna structure and the reduced conductivity of metal at THz frequencies.
We have improved the low output power of the THz photomixer by using an antenna with high input resistance, optimally designed in terms of the mismatch efficiency, radiation efficiency, and radiation pattern. The proposed antenna was first investigated on a half-infinite substrate to reduce computation time and then was designed to have maximum total efficiency and maximum directivity on an extended hemispherical lens. All results for the analysis were calculated using CST Microwave Studio based on the Finite-Integration Time-Domain technique.
2. Terahertz photomixer antenna
2.1 Photomixer characteristics and its antenna structure
As a CW THz source, the THz photomixer transforms THz beat signals of the incident laser into THz waves through the use of a photoconductor and an antenna. Figure 1 shows the equivalent circuit of the THz photomixer. The photoconductor is represented as a set of photocurrent sources Iphoto, a photoconductance Gphoto, and a capacitance of electrodes Celect connected in parallel, and the antenna is represented as an input admittance Yantenna. The photoconductance Gphoto under photomixing conditions is normally less than (10 kΩ)−1 because of the use of the CW laser as an excitation source, and this phenomenon causes a serious mismatch between the photomixer and the antenna. Therefore, an antenna for a THz photomixer must not only have high radiation efficiency, but also a high input resistance.
Figure 2 shows the proposed THz photomixer structure composed of an antenna as a radiation element and a bias circuit as a DC power supply element. The four-leaf-clover-shaped antenna for full-wavelength resonance has the following design parameters: width Dx, length Dy, gaps Gx and Gy, and line width w. The coplanar stripline bias circuits with photonic bandgap (PBG) cells have the following design parameters: line length Lhigh and space Ghigh for the high-impedance line, line length Llow and space Glow for the low-impedance line, quantity N PBG cells, total bias line length Lbias, and DC pad length px and width py. The metal layer has a conductivity of 1.6 × 107 S/m and a thickness of 0.35 μm, and is placed on a GaAs (εr = 12.9) substrate [16,17].
2.2 Photomixer antenna characteristics on a half-infinite substrate
Except for the radiation patterns, an antenna shows similar resonant characteristics on both a lens substrate and a half-infinite substrate [18]. We thus first investigated the resonant characteristics of the proposed antenna on a half-infinite substrate to reduce computation time. In the antenna design, the total efficiency εtotal, the product of the radiation efficiency εradiation and the mismatch efficiency εmismatch can be written as [19]
Equation (1) will be discussed in detail because it is fundamental to the output power of the photomixer. The reflection coefficient Γ in the mismatch efficiency in Eq. (1) is determined not by the characteristic impedance of the transmission line, but by the photomixer impedance Zphotomixer in
The initial dimensions of the antenna to resonate at around 1.0 THz are as follows: Dx = 36 μm, Dy = 36 μm, Gx = 2 μm, Gy = 2 μm, and w = 3 μm. Each right or left half of the antenna forms a full-wavelength dipole with a total length of approximately 2[(Dx + Dy)−(Gx + Gy) −1.5w] corresponding to 1 λ at about 1.0 THz on the GaAs substrate (see Fig. 4 ). We also investigated the characteristics of an 88 × 3-μm full-wavelength dipole antenna (FWDA) which is directed in the y-direction for the sake of comparison.
It is possible to design DC bias lines that do not cause a considerable change in the characteristics of the proposed antenna at the full-wavelength resonance. A FWDA with DC bias lines suffers from a relatively large variation in resonant characteristics due to current leakage to the DC bias lines [20]. However, the proposed antenna maintains the input impedance and radiation efficiency characteristics shown in Fig. 3 if the DC bias lines are connected to suitable positions of antenna structure. This can be explained using the current density distribution at the full-wavelength resonance, as shown in Fig. 4. Because a minimum current density is formed at the corners a distance of λ/4 from the photomixer source point, it is possible to suppress the AC leakage to DC bias lines. Moreover, PBG cells also function as a choke to prevent leakage of AC current, and the number of PBG cells, N, had a negligibleeffect on the antenna performance in terms of resonance frequency, input impedance, and radiation efficiency when N was greater than 3. In particular, the distance, d, between the antenna and the PBG cells significantly affected the antenna characteristics. Figure 5 shows the input impedance and radiation efficiency as a function of the distance d; a significant change occurs when d = 46 μm, which is about 3/8 λ at the resonance wavelength of λ = 120 μm.
Fig. 3 Characteristics of the proposed antenna before and after attaching DC bias lines (a) Input resistance, (b) radiation efficiency.
Fig. 5 Input resistance and radiation efficiency at a full-wavelength resonance when a distance d between the proposed antenna and PBG cell varies.
The proposed antenna exhibits a high input resistance, which improves the mismatch efficiency between the photomixer and the antenna at full-wavelength resonance. We compared the input resistance characteristics of the proposed antenna and a FWDA at a similar resonance frequency by changing the ratio of length to width (Dy/Dx), as shown in Fig. 6 . This comparison is possible because Dy/Dx does not significantly affect the resonance frequency when the sum of width and length (Dx + Dy) is fixed. The input resistances of the proposed antenna are from 4 to 10 times higher than that of the 246-Ω input resistance of the FWDA. This is because a strong resonance is induced by the four-leaf-clover-shaped structure, the ends of which are folded inward. The effects on the antenna performance due to the variation of antenna parameters Gx, Gy, and w were also investigated. When Gx or Gy increased, the antenna input resistance increased as well, reaching a maximum for a Gx value of about 7 µm or a Gy value of about 6 um, and then decreased as shown in Fig. 7 . However, the radiation efficiency also decreased, reaching a minimum, and then increased as Gx or Gy reached the values above. A balance between these two criteria occurred when either Gx or Gy was small (2 µm) or relatively large (12 µm). However, the radiation direction deviated gradually from the desired z-direction to the undesired x-direction when Gx or Gy increased. On the other hand, the resonant frequencies increased due to the decrease in the total length of the antenna as Gx or Gy increased. In addition, when the antenna line width w (also the width of the high-impedance line of the PBG bias structure) increased from 3 to 5 µm, the resonance frequency, input resistance, and radiation efficiency all increased slightly. However, a further increase in these line widths resulted in degraded radiation patterns, i.e., less radiation in the desired z-direction. In addition, the radiation pattern of the proposed antenna has a relatively high rotational symmetry around the z-axis, and this leads to high Gaussian beam efficiency.
Figure 8 shows the radiation pattern of the proposed antenna compared to that of the FWDA at 1 THz. Almost the same radiation pattern is formed in the free space region of θ < 90° regardless of the structure, and a peak and a null occur near the critical angle of θ = 165° in the substrate region θ > 90° [18]. The proposed antenna can be considered as a loop type antenna, so both the proposed antenna and the FWDA have identical field patterns but with the E-field and H-field interchanged. We performed a parameter study of the maximum of total efficiency focused on the ratio of length to width (Dy/Dx) for an almost fixed frequency. Figure 9 shows the mismatch efficiency and radiation efficiency as a function of the ratio of length to width, Dy/Dx. The proposed structure was set to Gx = 2 μm, Gy = 2 μm, and Dx + Dy = 72 μm; the mismatch efficiency was calculated assuming a photomixer impedance of 10 kΩ. As the ratio of length to width (Dy/Dx) increases, the mismatch efficiency increases, but the radiation efficiency decreases. Due to the tradeoff between the two efficiencies, the total efficiency depicted by the solid line in Fig. 10 has a maximum value of 22.5% at a ratio of 1.06 (Dy = 37 μm, Dx = 35 μm). This is 2.7 times higher than the 8.3% total efficiency of the FWDA indicated by the dotted line in Fig. 10. This indicates that the THz output power could be 2.7 times that of the FWDA. Design parameters for the maximum total efficiency shown in Table 1 were determined for a resonance frequency of 1 THz.
Fig. 8 Radiation patterns of antennas at 1 THz on a half-infinite GaAs substrate (a) x-z plane (b) y-z plane.
Fig. 9 Radiation efficiency and mismatch efficiency at a full-wavelength resonance when a ratio of Dy/Dx varies.
Table 1. Design parameters of the proposed antenna for a maximum total efficiency on a half-infinite GaAs substrate
2.3 Photomixer antenna characteristics on a lens substrate
A lens substrate was designed for a high-directivity radiation pattern based on the proposed antenna structure on the half-infinite substrate. Antennas on a flat substrate of finite thickness generally suffer from a large decrease in directivity and radiation efficiency because the total internal reflection effects produce a substrate mode loss. However, a lens substrate can eliminate the total internal reflection and increase the directivity of the radiation pattern by beam focusing [21]. In this design, we used an extended hemispherical lens, as shown in Fig. 11 , to increase the directivity by adjusting the thickness of the flat substrate while maintaining the hemispherical lens at a fixed size [22]. A hemispherical lens made of silicon (εr = 11.7) was attached to a GaAs flat substrate because silicon has a permittivity close to that of GaAs, can be easily processed into a lens, and has low dielectric losses. A λ/4-thick matching layer made of plexiglass (εr = 3.4) was used for suppression of reflected waves from the internal lens surface and to improve the coupling between the Si and GaAs [23].
We investigated the radiation pattern of the antenna in general and the directivity of the main beam in the z-axis in particular, as shown in Fig. 12 , by changing the ratio of the substrate thickness to the radius of the hemisphere, T/R. We used hemisphere radii R of 2.5, 3.5, and 4.5 λ at a resonance wavelength of 300 μm in free space, and a ratio of substrate thickness to radius (T/R) in the range 0.3–0.5. The results for the proposed antenna and the FWDA are shown by solid and broken lines, respectively. The higher directivity of the main beam can be achieved with a larger hemisphere radius. In addition, the substrate thickness for maximum directivity became more distinct as the radius of the hemisphere became larger. For the proposed antenna, the maximum directivity of the radiation pattern was 23.7 dBi at a ratio of T/R = 0.41, 26.2 dBi at T/R = 0.40, and 28.2 dBi at T/R = 0.40 for hemisphere radii of 2.5, 3.5, and 4.5 λ, respectively. For the FWDA, the maximum directivity of the radiation pattern was 23.7, 26.5, and 28.4 dBi at the almost the same ratio of T/R = 0.38 for radii of 2.5, 3.5, and 4.5 λ, respectively. The directivities of FWDA are not shown for ratios greater than T/R = 0.44 because a null region of the radiation pattern appears in the z-axis. Thus, the proposed structure and the FWDA have similar radiation patterns with maximum directivity on the substrate structure with same hemispherical lens, but a slightly larger T/R is required for the proposed structure. These results indicate that the maximum directivity can be achieved when the shape of the extended hemispherical lens is close to that of an elliptical lens. In addition, an antenna structure on the substrate also affects the maximum directivity [23].
Fig. 12 Directivities of antennas on lens when a ratio of substrate thickness to radius of hemisphere T/R varies.
Figure 13 shows a comparison of the radiation patterns for a hemisphere radius of 4.5 λ at 1.0 THz in the x–z and y–z planes. In the x–z pattern, the half-power beamwidths (HPBWs) were 6.9° and 5.6°, the side lobe levels (SLLs) were less than –21.0 dB and –13.5 dB, and the front-to-back (F/B) ratios were 22.2 dB and 27.1 dB for the proposed antenna and the FWDA, respectively. In the y–z pattern, the HPBWs were 5.6° and 7.0°, the SLLs were less than –13.4 dB and –27.9 dB, and the F/B ratios were 22.2 dB and 25.2 dB for the proposed antenna and the FWDA, respectively. The HPBW variations in the two principle radiation planes were + 1.3° and –1.4°, respectively, for the proposed antenna and the FWDA.
Fig. 13 Radiation patterns of antennas at 1 THz on an extended hemispherical lens substrate (R = 4.5 λ) (a) x-z plane (b) y-z plane.
We investigated the input resistance of the proposed antenna by changing the T/R ratio for a hemisphere radius of 4.5 λ, and the results are shown in Fig. 14 . The results for T/R values of 0.3, 0.4, and 0.5 are also shown for the same antenna structure on the half-infinite substrate. The rippling at the lens became strong as T/R increased because the routes of internal reflection increased as T/R increased. Nevertheless, the result for T/R = 0.4, where the maximum directivity appeared, was immune to rippling caused by internal reflection. Figure 15 shows the input resistance of the proposed antenna and FWDA on the extended hemispherical lens structure when the maximum directivity occurred. The ratios were T/R = 0.40 and 0.38 for the same hemisphere radius of 4.5 λ. In specific numerical values, the hemisphere radius R was 1350 μm for both antenna structures, and the thicknesses of the flat substrate T were 540 and 513 μm for the proposed antenna and the FWDA, respectively. The peak value of the proposed antenna was six times higher than that of the FWDA at the resonance frequency, and the proposed antenna was more immune than was the FWDA to rippling caused by internal reflection.
Fig. 14 Input resistance characteristics of the proposed antenna when a ratio of substrate thickness to radius of hemisphere T/R varies (R = 4.5 λ).
Fig. 15 Input resistance characteristics of the proposed antenna and a full-wavelength dipole antenna on an extended hemispherical lens substrate (R = 4.5 λ).
3. Conclusion
We have proposed a four-leaf-clover-shaped structure as a THz photomixer antenna. Compared with the well-known results for a FWDA, the proposed antenna has a much higher input resistance, a stable DC bias line design, and a radiation pattern with high rotational symmetry in the z-axis. The proposed antenna was investigated on a half-infinite substrate to simplify calculation, and it was then designed to have a maximum total efficiency and a maximum directivity on an extended hemispherical lens. A slightly thicker lens was required for maximum directivity for the proposed antenna than for the FWDA, and the directivities of both structures were very similar. However, the input resistance of the proposed structure was six times greater than that of the FWDA at the resonance frequency and showed a significant improvement over the dual-dipole and dual-slot antennas [13], and the half-wavelength folded dipole antenna [14]. This significantly improves the mismatch efficiency between the photomixer and the antenna. The THz Yagi-Uda antenna designed on a thin GaAs membrane [15] is also a good reference for the sake of comparison with an impedance of approximately 3000 Ω at 0.636 THz. However, it is better suited to some other application due to its end-fire radiation pattern. From a radiation efficiency perspective, the THz output power from the proposed structure should be 2.7 times that of the FWDA. Therefore, the application of the proposed antenna to THz photomixer design will be a major step in solving the output power problem.
Acknowledgements
This work was supported by National Research Foundation of Korea Grant funded by the Korean Government (grant code: 2009-0083512).
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