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In this paper, transmission characteristics of the fundamental mode (TE10) of Parallel-Plate Dielectric Waveguide (PPDW) at 0.4-1.0 THz (1 THz = 1012 Hz) are studied. The investigation results show PPDW with virtually low attenuation and remarkable simple structure is a promising candidate as THz transmission medium. Then, a novel broadband coaxial probe to PPDW transition is designed. Although coaxial probe excitation has been used in microstrip lines and rectangular waveguides in microwave, millimeter-wave frequency domain, the present study shows that it is also an effective method to excite the PPDW at THz frequency. As the investigation results show, the return loss of coax-PPDW transition is better than 20 dB from 0.45 THz to 0.75 THz, and the insertion loss is as low as 0.18 dB, which will have wide potential application in the terahertz regime.
©2010 Optical Society of America
1. Introduction
The interest in THz technology [1] has strongly increased in the recent years with diverse applications in the fields of biotechnology [2], spectroscopy [3], imaging [4] and security [5].Terahertz wave bridges the gap between the microwave and optical regimes and offers significant scientific and technological potential in many fields. However, wave guiding in this intermediate spectral region still remains a challenge. Neither conventional metal waveguides for microwave, nor dielectric fibers for visible and near-infrared radiation can be used to guide terahertz wave over a long distance, owing to the high loss from the finite conductivity of metals or the high absorption coefficient of dielectric materials in this frequency region. THz transmission line is a key component of THz systems and devices. Comparably efficient THz wave guiding structures are still under investigation.
In an attempt to meet the compelling need for useful THz waveguides, various guides have been demonstrated within the last few years. The most promising studies have reported dispersionless propagation in parallel-plate waveguides by R. Mendis [6,7]. But in this case the electromagnetic field distribution fills the entire cross-sectional area of the waveguide causing unacceptable high radiation loss. The H-guide, originally proposed by Tischer [8], is a hybrid waveguide with a dielectric strip embedded between the parallel plates. The two parallel plates’ separation of H-guide is made much larger than half a wavelength. This guide has low conduction loss in the plates for wave modes with the electric field strength predominantly parallel to the plates [9].However, the H-guide itself is unsuitable for THz wave integrated circuits, because the radiation loss caused by its semi-open type structure is fairly large, too. As we known, if two parallel plates are separated by a distance smaller than half a wavelength. Electromagnetic waves with the electric field parallel to the plates cannot propagate between them because of their cutoff properties [10]. The nonradiative dielectric (NRD) guide, developed by Yoneyama [11] to eliminate radiation while maintain the low transmission loss nature of dielectric waveguide, is regarded as a promising waveguide for millimeter-wave and THz circuits applications [12,13]. The different between NRD-guide and H-guide is that the parallel plates’ separation of NRD-guide is less than half a wavelength. Waves in NRD-guide will be suppressed in the air region, while will freely propagate in the dielectric strip for the wavelength is shortened to remove the cutoff state. However, both the H-guide and NRD-guide choose to use the higher order modes of the parallel-plate structure. These higher order modes have cutoff behavior, and would require thick parallel-plate separation for operation, which greatly limits its practical applications. Therefore, a parallel-plate dielectric waveguide (PPDW) has been proposed to solve this problem [14,15].The guiding mode of PPDW is the fundamental TE10 mode, which supports an electric field across the parallel plates, and the power are almost entirely confined within the dielectric strip without radiating or leaking into the parallel plate [14].This fundamental mode of PPDW eliminating the cutoff state, allows the use of physically thinner (smaller a) waveguides, which is a desirable feature for THz integrated circuits applications [15]. Hence, we propose to use PPDW as an efficient guiding medium in THz frequency region.
Although the transmission characteristics of PPDW in low microwave frequency range and coax-PPDW transitions at 2-3 GHz have been studied and designed [14,15], the properties of PPDW in THz region still remain unknown. In this paper, the theoretical and simulation investigation of a PPDW and its transition at THz frequency will be presented. In part 2, the propagation characteristics of PPDW, such as effective permittivity, transmission loss and core power confinement factor at 0.4-1.0 THz will be discussed. The investigation results show PPDW is a low loss and simple structure THz transmission line. As we know, how to design an efficient transition is very important to the future application of PPDW. Although coaxial probe excitation has been used in microstrip lines and rectangular waveguides in microwave frequency domain, the present study shows that it is also an effective method to excite the PPDW at THz frequency. Based on the theoretical analysis and numerical field simulation, an efficient broadband Coaxial Probe to PPDW transition at 0.4-0.8 THz frequency band is designed in part 3. The coaxial probe is simply placed at the center of the dielectric strip with the outer conductor is connected with the upper metal plate. However, the inner probe is inserted into the center dielectric strip apart from the below metal certain distance. This is in distinct contrast to “the center conductor of the probe connected to the opposite metal plate”, which appeared already in the ref [14,15].
2. Transmission characteristics of PPDW
The PPDW consists of a rectangular dielectric strip embedded between two parallel metallic plates. As is shown in Fig. 1 .(a), the center dielectric strip of height a and width b extends indefinitely in the axial (z) direction. The center strip relative dielectric constant εr is bigger than the outside region relative dielectric constant εs. Here, we choose silver (conductivity σ = 6.1 × 107 S/m) and glass (εr = 5.5, tanδ = 0.001) as the materials of Parallel Plates and the center dielectric strip of PPDW, respectively. Because the waveguide is placed in the air, so the outside dielectric εs = 1. The width of silver plate is 300μm, the length of this waveguide is 1,000μm, and a = 100μm, b = 100μm. The TE10 mode (PPDW mode) is the fundamental mode of propagation in the PPDW and will be analyzed below.
Fig. 1 (a) Cross-sectional view of PPDW, PPDW dimensions: a = 100μm, b = 100μm, εr = 5.5, εs = 1, σ = 6.1 × 107; (b) PPDW TE10 mode electric field Ey normalized amplitude distribution in the xy-plane at 0.7 THz frequency. The red curve is calculation result by using formula (1), and the blue curve is simulation result by using HFSS (the same below).
Using the coordinates described in Fig. 1.(a), the TE10 mode of the PPDW has only one component of the electric field Ey and two components of magnetic fields Hx and Hz, and Hx and Hz can be derived by Ey. Solving the Helmholtz equations for the TE10 wave with the boundary conditions, the field component Ey (at -a/2<y<a/2) can be derived:
WhereThe unknown coefficient A will be determined by the excitation, k0 is the free space wavenumber, and β is the propagation constant of the PPDW mode. The electric field Ey normalized amplitude distribution is calculated by using formula (1) at z = 0 plane at 0.7 THz frequency, and electromagnetic simulation has been performed by commercial software Ansoft HFSS for comparison, shown in Fig. 1.(b).
Matching the tangential fields at x = b/2 yields the dispersion relation:
Where εeff = (β/ k0)2 is the effective permittivity of the PPDW. Therefore, the εeff -f and εeff–b diagrams for theTE10 mode computed by Eq. (4) and simulated by HFSS are shown in Fig. 2 .(a).We can see that εeff increases with the increases of frequency and the width b.Fig. 2 (a) Dispersion curves (the εeff -f and εeff–b) for the fundamental PPDW mode (TE10 mode);(b) The Г–f and Г–b diagrams for the fundamental PPDW mode (TE10 mode). Where, PPDW dimensions: a = b = 100μm, εr = 5.5, εs = 1, σ = 6.1 × 107 for εeff –f and Г–f diagrams; PPDW dimensions: a = 100μm, εr = 5.5, εs = 1, σ = 6.1 × 107 and f = 0.7 THz for εeff –b and Г–b diagrams.
The PPDW core power confinement factor, another important quantity, is defined as fraction of power guided in the waveguide:
Therefore, the Г–f and Г–b diagrams for theTE10 mode computed by Eq. (5) and simulated by HFSS are shown in Fig. 2(b). We can see that Г increases with the increases of frequency and center strip width b. This property allows us use a wider strip width b for higher power confinement.All calculation results shown in Fig. 1(b) and Fig. 2 are consistent with the simulation results well. These imply that we may use HFSS to simulate the transmission characteristics of PPDW and design coaxial-PPDW transition accurately. The following analysis is based on HFSS field simulations.
To further study the power confinement characteristics, we compare the electric field distribution of PPDW and the parallel-plate waveguide with the same silver plates dimensions at 0.7 THz. It is obviously shown in Fig. 3 , the field of PPDW across the parallel plates and the field confinement is quiet better than it in parallel-plate waveguide. After propagating a short distance (1 mm), the waves in parallel-plate waveguide decline a lot for its large radiation, while waves in PPDW almost keep unchanged without radiating outside the waveguide.
Fig. 3 (a).Electric field distribution of PPDW at 0.7 THz frequency; (b).Electric field distribution of parallel-plate waveguide at 0.7 THz frequency.
As we know, the total transmission loss αt, consisting of conductor loss αc, dielectric loss αd, and radiation loss αr. In order to calculate αc, αd, and αr, we assume using ideal glass (tanδ = 0) and PEC to replace the materials of the center strip and parallel plates of PPDW, respectively.
Where, αt, αt case 1, αt case 2 can be obtained by the HFSS simulation. Then, αc, αd, and αr can be generated from the solutions to Eq. (6).As is shown in Fig. 4 (a), both αc and αd increase with the increases of the frequency. However, αr decreases as the frequency increases, which is because both εeff and Г increase as the frequency (Fig. 2). The radiation los αr (smaller than 0.01dB/mm) can be ignored at frequency higher then 0.7 THz. The lowest total loss of PPDW is only 0.284dB at 0.65 THz. As is shown in Fig. 4(b), we change the width b of PPDW while remaining other parameters unchanged at different THz frequency. The loss decreases with the increases of b, which is also caused by the increase of εeff and Г (Fig. 2). Especially at lower frequency, increases b has more obvious impact for its power confinement.Fig. 4 (a) Comparison of the frequency characteristics of total transmission loss αt, conductor loss αc, and dielectric loss αd and radiation loss αr of PPDW; (b)Comparison of the total transmission loss αt as a function of the width b of PPDw at 0.4, 0.6,0.8 THz.
3. Coaxial probe to PPDW transition
In this part, a novel broadband coaxial probe to PPDW transition is designed and analyzed. As is shown in Fig. 5 , the coaxial probe is simply placed at the center of the dielectric strip with the outer conductor is connected with the upper metal plate. The inner probe is inserted into the center dielectric strip acting as a radiating antenna to excite the TE10 mode of PPDW apart from the below metal plate certain distance c. Short-circuit plates are placed inside the parallel plates to create short-circuit stubs for the PPDW. The stub lengths s is chosen so as to give an open circuit at the location of the coaxial probe at the frequency of interest.
The electric field at the center of the waveguide across the parallel plates, shown in Fig. 3(a), can be used to define the voltage of the PPDW. The characteristic impedance can be defined as [14]:
Where V is the peak voltage and P is the average power propagating down the waveguide. By tuning the inner radius r0 and outer radius r1 of coaxial probe, distance c and stub lengths s, we can match the PPDW impedance with the input impedance of transition. Here, a back-to-back coaxial probe to PPDW transition is designed with the dimension parameters c = 46μm, s = 60μm, r0 = 5μm and r1 = 25μm.In order to analyze the insertion loss of the coax-PPDW transition, the loss of PPDW is simulated for comparison. Figure 6 (a) shows that PPDW has a good transmission performance with insertion loss less than 0.4 dB, and return loss greater than 30 dB in 0.4-1.0 THz range. That is to say, the average loss is as low as 0.1 dB/λg. Although the back-to-back coax-PPDW transitions do no has a good transmission performance at frequency greater than 0.8THz (Fig. 6(b)), which is because the stub lengths s = 60μm of short-circuit plates is no longer acting as an open circuit for the coaxial probe and causing some reflection. Of course, we can improve the properties in this higher than 0.8THz frequency range just by shortening the s.
Fig. 6 (a) Reflection and transmission parameters of PPDW; (b)Reflection and transmission parameters of coax-PPDW transition. Where, PPDW dimensions: a = 100μm, b = 100μm, εr = 5.5, εs = 1, σ = 6.1 × 107;
The back-to-back coax-PPDW transitions insertion loss is less than 0.7 dB, and return loss greater than 20 dB for almost whole 0.45-0.75 THz band. Compared with than the straight PPDW (Fig. 6(a)), the back-to-back coax-PPDW transitions causing 0.36dB more insertion loss on average in 0.45-0.75 THz frequency range, owning to two coaxial probes’ insertion loss at the two ports, which equivalently only 0.18 dB insertion loss per coax-PPDW transition. Although the return loss decreases, it is still quite good for many THz circuits and systems applications. From this comparison, we can conclude that coaxial probe excitation is an effective method to excite the PPDW at THz frequency.
4. Conclusion
In this paper, transmission characteristics of PPDW at 0.4-1.0 THz are studied. Then a novel broadband coax-PPDW transition is demonstrated, which shows that coaxial probe excitation is a simple and efficient method to excite the PPDW. Comparative analysis between the back-to-back transition and straight PPDW shows that every transition insertion loss is just as low as 0.18 dB. This coaxial probe excitation of PPDW may open a way to many other applications in the THz frequency domain.
Acknowledgement
The work is supported by a key lab fund from National Key Laboratory of Monolithic Integrated Circuits and Modules (9140C1401010901) and a youth fund from University of Electronic Science and Technology of China.
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