Abstract

In this paper, a novel broadband 3dB directional coupler with very flat coupling based on bridged parallel plate dielectric waveguide (PPDW) is proposed and demonstrated. In the uniform coupling section, a bridge structure between the two PPDWs is employed to obtain accurate coupling value and achieve a broadband coupling. It is found that this new type of coupling structure exhibits excellent performance at terahertz frequencies. In order to achieve strong isolation between the adjacent ports and reduce the power reflection in all ports, two quarter-circle bend arms are introduced as the curved transition sections to connect the uniform coupling section. For this bridged coupler, it only needs the value of the uniform coupling length as short as 400μm to achieve a broadband 3dB coupling. In this case, the coupler’s average return loss is greater than 28dB, average isolation is better than 27dB and average coupler loss is only 0.9dB, over a percentage bandwidth of 12.5% at 1THz. Compared to the conventional PPDW coupler, the bridged PPDW coupler shows significantly greater bandwidth (about 4.2 times), compact and mechanically stable with a much shorter uniform coupling length (reduced about 61%), which may have potential applications for terahertz integrated circuits and systems.

© 2011 OSA

I. Introduction

Terahertz (THz) technology [1] has received considerable attention in recent years due to its great potential in many scientific and technological fields, such as spectroscopy [2], imaging and security [35]. THz radiation is located in the frequency range of 0.1~10 THz, thus bridging the gap between the microwave and optical regimes. Together with the rapid development of THz radiation sources [5] and detectors [6], considerable progress in THz waveguiding has been achieved within the last few years [7]. Examples include the metal wire waveguides [8,9], parallel-plate waveguides [10,11], photonic-crystal fibers [7,12,13], dielectric-lined metallic waveguides [14,15], polymer tubes [16,17], the plastic porous fibers and plastic Bragg fibers [1820]. In parallel with these investigations, a parallel plate dielectric waveguide (PPDW) was proposed in our previous study as an efficient guiding medium for developing terahertz-wave integrated circuits and systems [21].

As we know, one of the frequently used components for integrated circuits and systems is the directional coupler, which can distribute power at a specified ratio between two waveguide branches. The nonradiative dielectric (NRD) guide is a hybrid waveguide with a dielectric strip embedded between two metal plates [22], which configuration is similar to the PPDW (shown in Fig. 1 ). The existing conventional parallel directional couplers based on NRD guide or metal-insulator-metal plasmonic waveguide mainly use a method that decides the coupling value by adjusting the distance and the coupling length between the two dielectric guides [23,24]. However, this method is not easy to adjust to an exact coupling value and has a drawback of narrow bandwidth. The size of this conventional coupler is very large in comparison with the wavelength in terahertz-wave range. In addition, according to the previous study [21,25], the NRD-guide has a characteristic of cutoff behavior by using the higher order modes. This would greatly limit its practical applications for requiring higher parallel-plate separation in operating. However, by choosing the fundamental TE10 mode as the guided mode, the PPDW eliminates the cutoff state, allows physically thinner parallel-plate separation and confines almost entire power within the dielectric strip without radiating outside of the parallel plate, which are desirable features for THz integrated circuits applications. In this paper, in order to achieve strong coupling, a novel bridged PPDW directional coupler is proposed. In its uniform coupling section, a rectangular dielectric strip is used as a bridge to connect the coupled parallel PPDWs. By optimizing the sizes of the bridge, the coupling coefficient is largely enhanced, which results in an extremely compact coupler compared to the conventional configuration. Moreover, the degree of coupling of this PPDW coupler can be changed not only by controlling the spacing of coupled guides, but also by changing the sizes and material of the bridge. Therefore, the existence of such a bridge makes it easy to reach various and accurate coupling values and achieve a broadband coupling.

 

Fig. 1 (a) Cross-sectional view of the PPDW; (b) 3D view of the PPDW

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In previous study by Nielsen et al. [26], a broadband fiber directional coupler for terahertz radiation has been demonstrated. In this study, a novel high performance 1THz broadband 3dB directional coupler will be presented. The THz wave transmission characteristics of PPDW will be briefly introduced in section II. Subsequently, this directional coupler based on bridged PPDW will be designed and analyzed in section III. The frequency-dependent characteristics of this bridged coupler will be obtained and compared to those of the conventional coupler. Finally, some concluding remarks will be given in Section IV.

II. THz transmission characteristics of PPDW

The PPDW consists of a rectangular dielectric strip (height a and width b) embedded between two parallel metallic plates, which schematic diagrams are shown in Fig. 1(a, b). In order to achieve mode guidance, the center strip’s 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) as the material of parallel plates and silicon (εr = 11.9, tanδ = 0.0001) as the material of center dielectric strip, and this waveguide is placed in the air (outside dielectric ε s = 1). Meanwhile, we assume the separation distance a = 80μm, the strip’s width b = 40μm, the width of silver plate is w = 200μm and the length of this waveguide is l = 1,000μm.

According to previous studies [21], the field component Ey of PPDW is mentioned below

Ey(x)={Aeγs(x+b/2)                                                           <xb/2A[cos[γr(x+b/2)]+γsγrsin[γr(x+b/2)]]   b/2xb/2A[cos(γrb)+γsγrsin(γrb)]eγs(xb/2)                    b/2x<
where the unknown coefficient A will be determined by the excitation. The transverse distribution constants γr and γs are related to the propagation constant (β), frequency (ω) and properties of the medium (μ and ε), by the following equations

γr=k02εrβ2,γs=β2k02εsandk0=ωε0μ0

Therefore, the normalized electric field distribution of component E y at 1 THz frequency for the fundamental TE10 mode can be obtained from Eq. (1, 2). As shown in Fig. 2(a) , the guided mode field has a cosine distribution in the core strip and decays exponentially on either side to rapidly become negligible. This waveguide can confine most of the power within the dielectric strip without radiating outside of the parallel plate. The PPDW has an outstanding transmission performance at THz frequencies. From Fig. 2(b), it is found that the PPDW’s average insertion loss is less than 0.32dB (0.08dB/λg) and the return loss is greater than 38dB in frequency range of 0.9THz to1.2THz.

 

Fig. 2 (a) Normalized electric field distribution for the TE10 mode of PPDW at 1THz; (b) Reflection and transmission parameters of PPDW in 0.9~1.2THz

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III. High performance coupler design and analysis

A conventional coupler can be constructed by simply placing two guides close to each other (spaced by a distance d), whose coupling mechanism is due to the interaction of exponentially decaying fields between the two waveguides. The cross-sectional view of the uniform conventional PPDW coupling section is shown in Fig. 3 (a). Although the degree of coupling is sensitive to the spacing and length of this section, it is still not trivial to a strong coupling just by controlling the spacing and the length. In order to achieve strong coupling, a uniform bridged PPDW coupling section is proposed, and its cross-sectional view is shown in Fig. 3(b). In this structure, a rectangular dielectric strip (width d and height c) is used as a bridge to connect the coupled parallel PPDWs.

 

Fig. 3 (a) Cross-sectional view of the uniform conventional PPDW coupling section; (b) Cross-sectional view of the uniform bridged PPDW coupling section

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Due to the cross-sectional symmetry of the uniform structures, it is possible to describe the fields of the coupling sections as a superposition of the even and the odd modes. For the uniform unbridged PPDW coupling section, the phase constants β even and β odd are determined by employing the method in [27,28], where the fields of the coupling section are calculated by using the TE10 mode field components. For the uniform bridged PPDW coupling section, the phase constants β even and β odd are obtained from a full-vectorial modal analysis based on the finite element method. Assuming the PPDW is lossless and is matched in every port, and then, in order to transfer the total power of the incident wave from Port 1 to Port 4, the length L of the PPDW must be

L=πβeβo

The uniform coupling length of a 3dB directional coupler is

L3dB=π2(βeβo)=L2

The scattering parameters as a function of the length l of the coupling section between the ports, as defined in Fig. 4 , can be expressed as

 

Fig. 4 (a) Scattering parameters versus coupling length of the conventional PPDW 3dB coupler at 1THz (a = 100μm, b = 100μm, d = 50μm, ε r = 11.9, ε s = 1, σ = 6.1 × 107 S/m); (b) Scattering parameters versus coupling length of the bridged PPDW coupler at 1THz (a = 100μm, b = 100μm, c = 50μm, d = 50μm, ε r = 11.9, ε s = 1, σ = 6.1 × 107 S/m)

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|S21|=|cosβeβo2l|
|S41|=|sinβeβo2l|

The coupling lengths and the scattering parameters of the conventional and the bridged PPDW coupling section as a function of the length l are computed from Eqs. (3)~6). As shown in Fig. 4(a, b), the value of l required for 3dB directional coupling section ( = L 3dB) can be read from the intersection of |S21| and |S31| curves. The L 3dB = 1100μm for the conventional PPDW coupling section and the L 3dB = 475μm for the bridged PPDW coupling section at 1THz frequency, respectively. The size of the uniform conventional coupling section is very large in comparison with the wavelength in terahertz-wave range. By introducing the bridged coupling section, the coupling coefficient is largely enhanced and the uniform coupling length is reduced about 625μm (56.8%), which results in an extremely compact coupler compared to the conventional configuration. Moreover, the existence of such abridge makes it easy to reach various and accurate coupling values and achieve a broadband coupling. Obviously, this interesting feature can be used to make the design process of bridged coupler very flexible. The degree of coupling of this bridged PPDW coupler can be changed not only by controlling the spacing of coupled guides, but also by changing the sizes and material of the bridge.

In order to achieve strong isolation of the adjacent ports and guide a smooth flow of energy into/out of the coupling region, it is necessary to introduce curved transition sections to connect the uniform coupling section. Figure 5 (a) shows the schematic diagrams of the bridged PPDW 3dB directional coupler with curved transition sections to be discussed here. Two quarter-circle bend arms (the inner radius r = 50μm) are used for the curved transition sections to reduce the reflection. Considering the coupling effect of the connecting bend arms in determining the overall coupling, the uniform coupling section must be reduced. Therefore, in order to obtain the desire coupling level in the design of a bridged PPDW 3dB directional, the length of the uniform coupling section is reduced from 475μm to 400μm, making the effective coupling length l eff = L 3dB. Similarly, the uniform coupling section is reduced from 1100μm to 1025μm in the design of the conventional 3dB directional coupler. In this case, Compared to the conventional coupler, the uniform coupling length of the bridged coupler is reduced approximately 61% (decreased from 1025μm to 400μm). Figure 5(b) shows the normalized magnitude of Poynting power vector distribution, obtained from a full-vectorial modal analysis based on the finite element method, for this bridged PPDW coupler at 1THz. It is found that the unit THz signal power of fundamental TE10 mode incidents from Port1 and transfers its power equally to Port2 and Port4 without coupling to Port3.

 

Fig. 5 (a) The bridged PPDW 3dB directional coupler structures used here with two quarter-circle bend connecting arms; (b) Normalized magnitude of Poynting power vector distribution for this bridged PPDW coupler at 1THz (a = 80μm, b = 40μm, c = 50μm, d = 50μm, r = 50μm, l = 400μm,ε r = 11.9, ε s = 1, σ = 6.1 × 107 S/m)

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The numerical calculated results of both the conventional PPDW coupler and the bridged PPDW coupler are presented for comparison. Figure 6 (a) shows the frequency characteristics of the conventional PPDW coupler. From the frequency range of 1.025THz to1.055 THz, the unbridged coupler’s average return loss (S11) is over 30dB, average isolation (S31) is about 28dB, and average coupler loss (S21 and S41) is 0.9 dB, over a percentage bandwidth of 3% at 1THz. Figure 6(b) shows the frequency characteristics of the bridged PPDW coupler. From the frequency range of 0.975THz to1.100THz, the bridged coupler’s average return loss (S11) is over 28dB, average isolation (S31) is better than 27 dB, and average coupler loss (S21 and S41) is 0.9 dB, over a percentage bandwidth of 12.5% at 1THz. Although comparing to the conventional coupler, the return loss and the isolation level of the bridged coupler are a little bit smaller during the bandwidth frequency region, it still satisfies the practical requirements. The major reason for this deterioration is due to the extra mismatch introduced by the bridge coupling section for the bridged coupler; meanwhile, this mismatch can be reduced by optimizing the sizes and material parameters of bridge section. The average coupler loss of the bridged couplers is the same level as the conventional coupler (0.9 dB), both of which is composed of the insertion loss of the total length of PPDW in the couplers and some scattering losses caused by the curved arms. Most importantly, it is found that the bandwidth of the bridged coupler is 4.2 times broader (increased about 9.5%), while it’s uniform coupling length much shorter (reduced about 61%) than the conventional one. Obviously, the bridged PPDW directional coupler exhibits more compact, mechanically stable than the conventional coupler. In addition, the existence of such a bridge makes it easy to reach the required degree of coupling and achieve a broadband coupling not only by controlling the spacing of coupled guides, but also by changing the sizes and material of the bridge. From the comparison above, it can be concluded that this type of bridged PPDW directional coupler has excellent performance and it may have potential applications for Terahertz integrated circuits and systems.

 

Fig. 6 (a) Frequency characteristics for the conventional PPDW coupler with two quarter-circle bend connecting arms with the uniform coupling length l = 1025μm; (b) Frequency characteristics for the bridged PPDW coupler with two quarter-circle bend connecting arms with the uniform coupling length l = 400μm

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IV.Conclusion

In this paper, the transmission characteristics of PPDW at 0.9~1.2THz have been studied. Then a novel terahertz broadband, compact and mechanically stable 3dB directional coupler with two quarter-circle bend connecting arms based on bridged PPDW coupler at 1THz has been designed and analyzed. For this bridged coupler, it only needs the value of the uniform coupling length as short as 400μm to achieve a broadband 3dB coupling. In this case, the coupler’s average return loss is greater than 28dB, average isolation is better than 27dB and average coupler loss is only 0.9dB, over a percentage bandwidth of 12.5% at 1THz. Comparative analysis between this type of bridged coupler and the conventional coupler shows that the bridged one has excellent performance with significantly broader bandwidth, shorter coupling length, compact and mechanically stable structure. The investigation results show this type of coupler is useful component and it may have potential applications for Terahertz integrated circuits and systems.

Acknowledgement

The work has been supported in part by a key lab fund from the National Key Laboratory of Monolithic Integrated Circuits and Modules, a fund (Grant No. 9140A01020209DZ0203) and a Fundamental Research Funds for the Central Universities (Program No. 103.1.2 E022050205). The authors would like to acknowledge the enlightening discussion with Dr. Xiaofan Yang and Dr. Xiong Xu at University of Electronic Science and Technology of China.

References and links

1. P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50(3), 910–928 (2002). [CrossRef]  

2. B. Clough, J. Liu, and X.-C. Zhang, ““All air-plasma” terahertz spectroscopy,” Opt. Lett. 36(13), 2399–2401 (2011). [CrossRef]   [PubMed]  

3. M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, K. J. Ahn, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Near field imaging of terahertz focusing onto rectangular apertures,” Opt. Express 16(25), 20484–20489 (2008). [CrossRef]   [PubMed]  

4. V. P. Wallace, E. MacPherson, J. A. Zeitler, and C. Reid, “Three-dimensional imaging of optically opaque materials using nonionizing terahertz radiation,” J. Opt. Soc. Am. A 25, 3120–3133 (2008). [CrossRef]  

5. R. Degl’Innocenti, M. Montinaro, J. Xu, V. Piazza, P. Pingue, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Differential near-field scanning optical microscopy with THz quantum cascade laser sources,” Opt. Express 17(26), 23785–23792 (2009). [CrossRef]   [PubMed]  

6. C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, S. X. Li, and J. Q. Yao, “Time-dependent theoretical model for terahertz wave detector using a parametric process,” Opt. Express 18(17), 18180–18189 (2010). [CrossRef]   [PubMed]  

7. K. Nielsen, H. K. Rasmussen, A. J. L. Adam, P. C. M. Planken, O. Bang, and P. U. Jepsen, “Bendable, low-loss Topas fibers for the terahertz frequency range,” Opt. Express 17(10), 8592–8601 (2009). [CrossRef]   [PubMed]  

8. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef]   [PubMed]  

9. T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005). [CrossRef]  

10. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001). [CrossRef]   [PubMed]  

11. R. Mendis, “Guided-wave THz time-domain spectroscopy of highly doped silicon using parallel-plate waveguides,” Electron. Lett. 42(1), 19–21 (2006). [CrossRef]  

12. M. Cho, J. Kim, H. Park, Y. Han, K. Moon, E. Jung, and H. Han, “Highly birefringent terahertz polarization maintaining plastic photonic crystal fibers,” Opt. Express 16(1), 7–12 (2008). [CrossRef]   [PubMed]  

13. M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004). [CrossRef]  

14. O. Mitrofanov and J. A. Harrington, “Dielectric-lined cylindrical metallic THz waveguides: mode structure and dispersion,” Opt. Express 18(3), 1898–1903 (2010). [CrossRef]   [PubMed]  

15. B. Bowden, J. A. Harrington, and O. Mitrofanov, “Fabrication of terahertz hollow-glass metallic waveguides with inner dielectric coatings,” J. Appl. Phys. 104(9), 093110 (2008). [CrossRef]  

16. D. Chen and H. Chen, “A novel low-loss Terahertz waveguide: polymer tube,” Opt. Express 18(4), 3762–3767 (2010). [CrossRef]   [PubMed]  

17. D. Chen, “Mode Property of Terahertz Polymer Tube,” J. Lightwave Technol. 28(18), 2708–2713 (2010). [CrossRef]  

18. A. Dupuis, A. Mazhorova, F. Désévédavy, M. Rozé, and M. Skorobogatiy, “Spectral characterization of porous dielectric subwavelength THz fibers fabricated using a microstructured molding technique,” Opt. Express 18(13), 13813–13828 (2010). [CrossRef]   [PubMed]  

19. A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express 16(9), 6340–6351 (2008). [CrossRef]   [PubMed]  

20. A. Dupuis, K. Stoeffler, B. Ung, C. Dubois, and M. Skorobogatiy, “Transmission measurements of hollow-core THz Bragg fibers,” J. Opt. Soc. Am. B 28(4), 896–907 (2011). [CrossRef]  

21. L. Ye, R. Xu, Z. Wang, and W. Lin, “A novel broadband coaxial probe to parallel plate dielectric waveguide transition at THz frequency,” Opt. Express 18(21), 21725–21731 (2010). [CrossRef]   [PubMed]  

22. T. Yoneyama and S. Nishida, “Nonradiative Dielectric Waveguide for Millimeter-Wave Intergrated Circuits,” IEEE Trans. Microwave Theory Tech., vol. MTT-29, no.11, pp. 1188–1192, Nov. (1981).

23. T. Yoneyama, N. Tozawa, and S. Nishida, “Coupling Characteristics of Nonradiative Dielectric Waveguide,” IEEE Trans. Microwave Theory Tech., vol. MTT-31, no. 8, pp. 648–654, Aug. (1983).

24. M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, and X. Luo, “Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide,” Opt. Express 18(20), 21030–21037 (2010). [CrossRef]   [PubMed]  

25. G. K. C. Kwan and N. K. Das, “Excitation of a parallel-plate dielectric waveguide using a coaxial probe-basic characteristics and experiments,” IEEE Trans. Microw. Theory Tech. 50(6), 1609–1620 (2002). [CrossRef]  

26. K. Nielsen, H. K. Rasmussen, P. U. Jepsen, and O. Bang, “Broadband terahertz fiber directional coupler,” Opt. Lett. 35(17), 2879–2881 (2010). [CrossRef]   [PubMed]  

27. K. Solbach and L. Wolff, “The electromagnetic fields and the phase constants of dielectric image lines,” IEEE Trans. Microwave Theory Tech., vol. MTT-26, pp. 266–274, Apr. (1978).

28. K. Solbach, “The Calculation and the Measurement of the Coupling Properties of Dielectric Image Lines of Rectangular Cross Sections,” IEEE Trans. MTT, vol.27, pp.54–58, Jan. (1979).

References

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  1. P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50(3), 910–928 (2002).
    [CrossRef]
  2. B. Clough, J. Liu, and X.-C. Zhang, ““All air-plasma” terahertz spectroscopy,” Opt. Lett. 36(13), 2399–2401 (2011).
    [CrossRef] [PubMed]
  3. M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, K. J. Ahn, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Near field imaging of terahertz focusing onto rectangular apertures,” Opt. Express 16(25), 20484–20489 (2008).
    [CrossRef] [PubMed]
  4. V. P. Wallace, E. MacPherson, J. A. Zeitler, and C. Reid, “Three-dimensional imaging of optically opaque materials using nonionizing terahertz radiation,” J. Opt. Soc. Am. A 25, 3120–3133 (2008).
    [CrossRef]
  5. R. Degl’Innocenti, M. Montinaro, J. Xu, V. Piazza, P. Pingue, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Differential near-field scanning optical microscopy with THz quantum cascade laser sources,” Opt. Express 17(26), 23785–23792 (2009).
    [CrossRef] [PubMed]
  6. C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, S. X. Li, and J. Q. Yao, “Time-dependent theoretical model for terahertz wave detector using a parametric process,” Opt. Express 18(17), 18180–18189 (2010).
    [CrossRef] [PubMed]
  7. K. Nielsen, H. K. Rasmussen, A. J. L. Adam, P. C. M. Planken, O. Bang, and P. U. Jepsen, “Bendable, low-loss Topas fibers for the terahertz frequency range,” Opt. Express 17(10), 8592–8601 (2009).
    [CrossRef] [PubMed]
  8. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
    [CrossRef] [PubMed]
  9. T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005).
    [CrossRef]
  10. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001).
    [CrossRef] [PubMed]
  11. R. Mendis, “Guided-wave THz time-domain spectroscopy of highly doped silicon using parallel-plate waveguides,” Electron. Lett. 42(1), 19–21 (2006).
    [CrossRef]
  12. M. Cho, J. Kim, H. Park, Y. Han, K. Moon, E. Jung, and H. Han, “Highly birefringent terahertz polarization maintaining plastic photonic crystal fibers,” Opt. Express 16(1), 7–12 (2008).
    [CrossRef] [PubMed]
  13. M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004).
    [CrossRef]
  14. O. Mitrofanov and J. A. Harrington, “Dielectric-lined cylindrical metallic THz waveguides: mode structure and dispersion,” Opt. Express 18(3), 1898–1903 (2010).
    [CrossRef] [PubMed]
  15. B. Bowden, J. A. Harrington, and O. Mitrofanov, “Fabrication of terahertz hollow-glass metallic waveguides with inner dielectric coatings,” J. Appl. Phys. 104(9), 093110 (2008).
    [CrossRef]
  16. D. Chen and H. Chen, “A novel low-loss Terahertz waveguide: polymer tube,” Opt. Express 18(4), 3762–3767 (2010).
    [CrossRef] [PubMed]
  17. D. Chen, “Mode Property of Terahertz Polymer Tube,” J. Lightwave Technol. 28(18), 2708–2713 (2010).
    [CrossRef]
  18. A. Dupuis, A. Mazhorova, F. Désévédavy, M. Rozé, and M. Skorobogatiy, “Spectral characterization of porous dielectric subwavelength THz fibers fabricated using a microstructured molding technique,” Opt. Express 18(13), 13813–13828 (2010).
    [CrossRef] [PubMed]
  19. A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express 16(9), 6340–6351 (2008).
    [CrossRef] [PubMed]
  20. A. Dupuis, K. Stoeffler, B. Ung, C. Dubois, and M. Skorobogatiy, “Transmission measurements of hollow-core THz Bragg fibers,” J. Opt. Soc. Am. B 28(4), 896–907 (2011).
    [CrossRef]
  21. L. Ye, R. Xu, Z. Wang, and W. Lin, “A novel broadband coaxial probe to parallel plate dielectric waveguide transition at THz frequency,” Opt. Express 18(21), 21725–21731 (2010).
    [CrossRef] [PubMed]
  22. T. Yoneyama and S. Nishida, “Nonradiative Dielectric Waveguide for Millimeter-Wave Intergrated Circuits,” IEEE Trans. Microwave Theory Tech., vol. MTT-29, no.11, pp. 1188–1192, Nov. (1981).
  23. T. Yoneyama, N. Tozawa, and S. Nishida, “Coupling Characteristics of Nonradiative Dielectric Waveguide,” IEEE Trans. Microwave Theory Tech., vol. MTT-31, no. 8, pp. 648–654, Aug. (1983).
  24. M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, and X. Luo, “Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide,” Opt. Express 18(20), 21030–21037 (2010).
    [CrossRef] [PubMed]
  25. G. K. C. Kwan and N. K. Das, “Excitation of a parallel-plate dielectric waveguide using a coaxial probe-basic characteristics and experiments,” IEEE Trans. Microw. Theory Tech. 50(6), 1609–1620 (2002).
    [CrossRef]
  26. K. Nielsen, H. K. Rasmussen, P. U. Jepsen, and O. Bang, “Broadband terahertz fiber directional coupler,” Opt. Lett. 35(17), 2879–2881 (2010).
    [CrossRef] [PubMed]
  27. K. Solbach and L. Wolff, “The electromagnetic fields and the phase constants of dielectric image lines,” IEEE Trans. Microwave Theory Tech., vol. MTT-26, pp. 266–274, Apr. (1978).
  28. K. Solbach, “The Calculation and the Measurement of the Coupling Properties of Dielectric Image Lines of Rectangular Cross Sections,” IEEE Trans. MTT, vol.27, pp.54–58, Jan. (1979).

2011

2010

O. Mitrofanov and J. A. Harrington, “Dielectric-lined cylindrical metallic THz waveguides: mode structure and dispersion,” Opt. Express 18(3), 1898–1903 (2010).
[CrossRef] [PubMed]

D. Chen and H. Chen, “A novel low-loss Terahertz waveguide: polymer tube,” Opt. Express 18(4), 3762–3767 (2010).
[CrossRef] [PubMed]

A. Dupuis, A. Mazhorova, F. Désévédavy, M. Rozé, and M. Skorobogatiy, “Spectral characterization of porous dielectric subwavelength THz fibers fabricated using a microstructured molding technique,” Opt. Express 18(13), 13813–13828 (2010).
[CrossRef] [PubMed]

C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, S. X. Li, and J. Q. Yao, “Time-dependent theoretical model for terahertz wave detector using a parametric process,” Opt. Express 18(17), 18180–18189 (2010).
[CrossRef] [PubMed]

K. Nielsen, H. K. Rasmussen, P. U. Jepsen, and O. Bang, “Broadband terahertz fiber directional coupler,” Opt. Lett. 35(17), 2879–2881 (2010).
[CrossRef] [PubMed]

M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, and X. Luo, “Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide,” Opt. Express 18(20), 21030–21037 (2010).
[CrossRef] [PubMed]

L. Ye, R. Xu, Z. Wang, and W. Lin, “A novel broadband coaxial probe to parallel plate dielectric waveguide transition at THz frequency,” Opt. Express 18(21), 21725–21731 (2010).
[CrossRef] [PubMed]

D. Chen, “Mode Property of Terahertz Polymer Tube,” J. Lightwave Technol. 28(18), 2708–2713 (2010).
[CrossRef]

2009

2008

2006

R. Mendis, “Guided-wave THz time-domain spectroscopy of highly doped silicon using parallel-plate waveguides,” Electron. Lett. 42(1), 19–21 (2006).
[CrossRef]

2005

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005).
[CrossRef]

2004

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004).
[CrossRef]

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[CrossRef] [PubMed]

2002

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50(3), 910–928 (2002).
[CrossRef]

G. K. C. Kwan and N. K. Das, “Excitation of a parallel-plate dielectric waveguide using a coaxial probe-basic characteristics and experiments,” IEEE Trans. Microw. Theory Tech. 50(6), 1609–1620 (2002).
[CrossRef]

2001

Adam, A. J. L.

Ahn, K. J.

Bang, O.

Beere, H. E.

Beltram, F.

Bowden, B.

B. Bowden, J. A. Harrington, and O. Mitrofanov, “Fabrication of terahertz hollow-glass metallic waveguides with inner dielectric coatings,” J. Appl. Phys. 104(9), 093110 (2008).
[CrossRef]

Chen, D.

Chen, H.

Cho, M.

Clough, B.

Das, N. K.

G. K. C. Kwan and N. K. Das, “Excitation of a parallel-plate dielectric waveguide using a coaxial probe-basic characteristics and experiments,” IEEE Trans. Microw. Theory Tech. 50(6), 1609–1620 (2002).
[CrossRef]

Degl’Innocenti, R.

Désévédavy, F.

Dubois, C.

Dupuis, A.

Goto, M.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004).
[CrossRef]

Grischkowsky, D.

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005).
[CrossRef]

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001).
[CrossRef] [PubMed]

Han, H.

Han, Y.

Harrington, J. A.

O. Mitrofanov and J. A. Harrington, “Dielectric-lined cylindrical metallic THz waveguides: mode structure and dispersion,” Opt. Express 18(3), 1898–1903 (2010).
[CrossRef] [PubMed]

B. Bowden, J. A. Harrington, and O. Mitrofanov, “Fabrication of terahertz hollow-glass metallic waveguides with inner dielectric coatings,” J. Appl. Phys. 104(9), 093110 (2008).
[CrossRef]

Hassani, A.

Hu, C.

Jeon, T.-I.

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005).
[CrossRef]

Jepsen, P. U.

Jiang, C. Y.

Jung, E.

Kang, J. H.

Kim, D. S.

Kim, J.

Kwan, G. K. C.

G. K. C. Kwan and N. K. Das, “Excitation of a parallel-plate dielectric waveguide using a coaxial probe-basic characteristics and experiments,” IEEE Trans. Microw. Theory Tech. 50(6), 1609–1620 (2002).
[CrossRef]

Lee, J. W.

Li, S. X.

Lin, W.

Liu, J.

Liu, J. S.

Luo, X.

MacPherson, E.

Mazhorova, A.

Mendis, R.

R. Mendis, “Guided-wave THz time-domain spectroscopy of highly doped silicon using parallel-plate waveguides,” Electron. Lett. 42(1), 19–21 (2006).
[CrossRef]

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001).
[CrossRef] [PubMed]

Mitrofanov, O.

O. Mitrofanov and J. A. Harrington, “Dielectric-lined cylindrical metallic THz waveguides: mode structure and dispersion,” Opt. Express 18(3), 1898–1903 (2010).
[CrossRef] [PubMed]

B. Bowden, J. A. Harrington, and O. Mitrofanov, “Fabrication of terahertz hollow-glass metallic waveguides with inner dielectric coatings,” J. Appl. Phys. 104(9), 093110 (2008).
[CrossRef]

Mittleman, D. M.

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[CrossRef] [PubMed]

Montinaro, M.

Moon, K.

Nielsen, K.

Ono, S.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004).
[CrossRef]

Park, H.

Park, Q. H.

Piazza, V.

Pingue, P.

Planken, P. C. M.

Pu, M.

Quema, A.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004).
[CrossRef]

Rasmussen, H. K.

Reid, C.

Ritchie, D. A.

Rozé, M.

Sarukura, N.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004).
[CrossRef]

Seo, M. A.

Siegel, P. H.

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50(3), 910–928 (2002).
[CrossRef]

Skorobogatiy, M.

Stoeffler, K.

Sun, B.

Takahashi, H.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004).
[CrossRef]

Tredicucci, A.

Ung, B.

Wallace, V. P.

Wang, C.

Wang, K.

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[CrossRef] [PubMed]

Wang, K. J.

Wang, Z.

Xin, X.

Xu, J.

Xu, R.

Yao, J. Q.

Yao, N.

Ye, L.

Zeitler, J. A.

Zhang, J.

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005).
[CrossRef]

Zhang, X.-C.

Zhao, Z.

Appl. Phys. Lett.

T.-I. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86(16), 161904 (2005).
[CrossRef]

Electron. Lett.

R. Mendis, “Guided-wave THz time-domain spectroscopy of highly doped silicon using parallel-plate waveguides,” Electron. Lett. 42(1), 19–21 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50(3), 910–928 (2002).
[CrossRef]

G. K. C. Kwan and N. K. Das, “Excitation of a parallel-plate dielectric waveguide using a coaxial probe-basic characteristics and experiments,” IEEE Trans. Microw. Theory Tech. 50(6), 1609–1620 (2002).
[CrossRef]

J. Appl. Phys.

B. Bowden, J. A. Harrington, and O. Mitrofanov, “Fabrication of terahertz hollow-glass metallic waveguides with inner dielectric coatings,” J. Appl. Phys. 104(9), 093110 (2008).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

M. Goto, A. Quema, H. Takahashi, S. Ono, and N. Sarukura, “Teflon Photonic Crystal Fiber as Terahertz Waveguide,” Jpn. J. Appl. Phys. 43(No. 2B), L317–L319 (2004).
[CrossRef]

Nature

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[CrossRef] [PubMed]

Opt. Express

K. Nielsen, H. K. Rasmussen, A. J. L. Adam, P. C. M. Planken, O. Bang, and P. U. Jepsen, “Bendable, low-loss Topas fibers for the terahertz frequency range,” Opt. Express 17(10), 8592–8601 (2009).
[CrossRef] [PubMed]

R. Degl’Innocenti, M. Montinaro, J. Xu, V. Piazza, P. Pingue, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Differential near-field scanning optical microscopy with THz quantum cascade laser sources,” Opt. Express 17(26), 23785–23792 (2009).
[CrossRef] [PubMed]

O. Mitrofanov and J. A. Harrington, “Dielectric-lined cylindrical metallic THz waveguides: mode structure and dispersion,” Opt. Express 18(3), 1898–1903 (2010).
[CrossRef] [PubMed]

D. Chen and H. Chen, “A novel low-loss Terahertz waveguide: polymer tube,” Opt. Express 18(4), 3762–3767 (2010).
[CrossRef] [PubMed]

A. Dupuis, A. Mazhorova, F. Désévédavy, M. Rozé, and M. Skorobogatiy, “Spectral characterization of porous dielectric subwavelength THz fibers fabricated using a microstructured molding technique,” Opt. Express 18(13), 13813–13828 (2010).
[CrossRef] [PubMed]

C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, S. X. Li, and J. Q. Yao, “Time-dependent theoretical model for terahertz wave detector using a parametric process,” Opt. Express 18(17), 18180–18189 (2010).
[CrossRef] [PubMed]

M. Cho, J. Kim, H. Park, Y. Han, K. Moon, E. Jung, and H. Han, “Highly birefringent terahertz polarization maintaining plastic photonic crystal fibers,” Opt. Express 16(1), 7–12 (2008).
[CrossRef] [PubMed]

A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express 16(9), 6340–6351 (2008).
[CrossRef] [PubMed]

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, K. J. Ahn, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Near field imaging of terahertz focusing onto rectangular apertures,” Opt. Express 16(25), 20484–20489 (2008).
[CrossRef] [PubMed]

M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, and X. Luo, “Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide,” Opt. Express 18(20), 21030–21037 (2010).
[CrossRef] [PubMed]

L. Ye, R. Xu, Z. Wang, and W. Lin, “A novel broadband coaxial probe to parallel plate dielectric waveguide transition at THz frequency,” Opt. Express 18(21), 21725–21731 (2010).
[CrossRef] [PubMed]

Opt. Lett.

Other

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Figures (6)

Fig. 1
Fig. 1

(a) Cross-sectional view of the PPDW; (b) 3D view of the PPDW

Fig. 2
Fig. 2

(a) Normalized electric field distribution for the TE10 mode of PPDW at 1THz; (b) Reflection and transmission parameters of PPDW in 0.9~1.2THz

Fig. 3
Fig. 3

(a) Cross-sectional view of the uniform conventional PPDW coupling section; (b) Cross-sectional view of the uniform bridged PPDW coupling section

Fig. 4
Fig. 4

(a) Scattering parameters versus coupling length of the conventional PPDW 3dB coupler at 1THz (a = 100μm, b = 100μm, d = 50μm, ε r = 11.9, ε s = 1, σ = 6.1 × 107 S/m); (b) Scattering parameters versus coupling length of the bridged PPDW coupler at 1THz (a = 100μm, b = 100μm, c = 50μm, d = 50μm, ε r = 11.9, ε s = 1, σ = 6.1 × 107 S/m)

Fig. 5
Fig. 5

(a) The bridged PPDW 3dB directional coupler structures used here with two quarter-circle bend connecting arms; (b) Normalized magnitude of Poynting power vector distribution for this bridged PPDW coupler at 1THz (a = 80μm, b = 40μm, c = 50μm, d = 50μm, r = 50μm, l = 400μm,ε r = 11.9, ε s = 1, σ = 6.1 × 107 S/m)

Fig. 6
Fig. 6

(a) Frequency characteristics for the conventional PPDW coupler with two quarter-circle bend connecting arms with the uniform coupling length l = 1025μm; (b) Frequency characteristics for the bridged PPDW coupler with two quarter-circle bend connecting arms with the uniform coupling length l = 400μm

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

E y ( x ) = { A e γ s ( x + b / 2 )                                                             < x b / 2 A [ cos [ γ r ( x + b / 2 ) ] + γ s γ r sin [ γ r ( x + b / 2 ) ] ]     b / 2 x b / 2 A [ cos ( γ r b ) + γ s γ r sin ( γ r b ) ] e γ s ( x b / 2 )                      b / 2 x <
γ r = k 0 2 ε r β 2 , γ s = β 2 k 0 2 ε s and k 0 = ω ε 0 μ 0
L = π β e β o
L 3 dB = π 2 ( β e β o ) = L 2
| S 21 | = | cos β e β o 2 l |
| S 41 | = | sin β e β o 2 l |

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