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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 8460–8472
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Characteristics of bent terahertz antiresonant reflecting pipe waveguides

Chih-Hsien Lai, Teng Chang, and Yi-Siang Yeh  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 8460-8472 (2014)
http://dx.doi.org/10.1364/OE.22.008460


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Abstract

Bending characteristics of the terahertz (THz) pipe waveguides are numerically investigated. Numerical results reveal that the inherent periodic feature of the loss spectrum, resulting from the antiresonant reflection guiding mechanism, is nearly unaffected under bending. However, attenuation constant of the fundamental (HE11) mode becomes polarization dependent for the bent pipe waveguide, and the polarization perpendicular to the bending plane experiences less bending losses. Moreover, unlike the straight case where a larger air-core diameter leads to a smaller attenuation constant, increasing core diameter of the bent pipe waveguide is unable to reduce attenuation constant effectively if the propagation mode is a whispering gallery mode. Finally, behavior of the bent pipe waveguide connected to a straight one is also examined in this work.

© 2014 Optical Society of America

1. Introduction

Terahertz (THz) radiation has received significant attentions due to its increasing applications in biology and medicine, environment monitoring, security, imaging, and communications [1

1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]

5

5. J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010). [CrossRef]

]. To facilitate THz science and technologies, it is essential to develop low-loss and low-cost THz waveguides [6

6. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000). [CrossRef]

16

16. M. Rozé, B. Ung, A. Mazhorova, M. Walther, and M. Skorobogatiy, “Suspended core subwavelength fibers: towards practical designs for low-loss terahertz guidance,” Opt. Express 19(10), 9127–9138 (2011). [CrossRef] [PubMed]

]. The pipe waveguide is a recently proposed hollow structure for THz waveguiding [17

17. C.-H. Lai, Y.-C. Hsueh, H.-W. Chen, Y.-J. Huang, H.-C. Chang, and C.-K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett. 34(21), 3457–3459 (2009). [CrossRef] [PubMed]

,18

18. C.-H. Lai, B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, C.-K. Sun, and H.-C. Chang, “Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding,” Opt. Express 18(1), 309–322 (2010). [CrossRef] [PubMed]

]. It is a simple pipe with a large air core surrounded by a thin dielectric cladding layer, and its guiding mechanism is based on the antiresonant reflection guiding [19

19. M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986). [CrossRef]

]. A commercially available 3-m long Teflon pipe was demonstrated to achieve very low propagation losses, with the attenuation constant well below 0.005 cm−1, under straight condition [17

17. C.-H. Lai, Y.-C. Hsueh, H.-W. Chen, Y.-J. Huang, H.-C. Chang, and C.-K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett. 34(21), 3457–3459 (2009). [CrossRef] [PubMed]

]. Owing to the structure simplicity and excellent performance, after the pioneering Teflon pipe, various pipe waveguides have been reported for THz transmission, being made of silica [20

20. E. Nguema, D. Férachou, G. Humbert, J. L. Auguste, and J. M. Blondy, “Broadband terahertz transmission within the air channel of thin-wall pipe,” Opt. Lett. 36(10), 1782–1784 (2011). [CrossRef] [PubMed]

], polypropylene (PP) [21

21. B. You, J.-Y. Lu, C.-P. Yu, T.-A. Liu, and J.-L. Peng, “Terahertz refractive index sensors using dielectric pipe waveguides,” Opt. Express 20(6), 5858–5866 (2012). [CrossRef] [PubMed]

], chalclgenide glass [22

22. A. Mazhorova, A. Markov, B. Ung, M. Rozé, S. Gorgutsa, and M. Skorobogatiy, “Thin chalcogenide capillaries as efficient waveguides from mid-infrared to terahertz,” J. Opt. Soc. Am. B 29(8), 2116–2123 (2012). [CrossRef]

], and polymethylmethacrylate (PMMA) [23

23. M. F. Xiao, J. Liu, W. Zhang, J. L. Shen, and Y. D. Huang, “THz wave transmission in thin-wall PMMA pipes fabricated by fiber drawing technique,” Opt. Commun. 298-299, 101–105 (2013). [CrossRef]

].

In practical applications, waveguides often suffer bending. Hence it is important to investigate the transmission characteristics of the THz pipe waveguide under bent condition. Attempts have been made experimentally [23

23. M. F. Xiao, J. Liu, W. Zhang, J. L. Shen, and Y. D. Huang, “THz wave transmission in thin-wall PMMA pipes fabricated by fiber drawing technique,” Opt. Commun. 298-299, 101–105 (2013). [CrossRef]

,24

24. J.-T. Lu, Y.-C. Hsueh, Y.-R. Huang, Y.-J. Hwang, and C.-K. Sun, “Bending loss of terahertz pipe waveguides,” Opt. Express 18(25), 26332–26338 (2010). [CrossRef] [PubMed]

] in that bending losses of the bent THz pipe waveguides were measured. However, because the experimental setups comprised both straight and bent sections, according to the waveguide theory, except the bending loss due to a uniform curvature, there would be an additional power loss incurred at the straight-to-bent interface, owing to the mode mismatch between the straight and bent waveguides [25

25. W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14(5), 130–132 (1978). [CrossRef]

]. Therefore, the previously measured results are not “pure” bending losses and thus the bending characteristics of the THz pipe waveguide require further investigation.

In this paper, we aim to numerically investigate the bending characteristics of the THz pipe waveguides. For the study of waveguide bends, one widely used technique is the conformal transformation [26

26. M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975). [CrossRef]

], where the curved waveguide is transformed into an approximate equivalent straight waveguide (ESW) with a modified index profile. An alternative approach is to employ a rigorous formulation derived in a cylindrical coordinate system (CCS) [27

27. S. Kim and A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14(9), 2085–2092 (1996). [CrossRef]

30

30. J. Xiao, H. Ni, and X. Sun, “Full-vector mode solver for bending waveguides based on the finite-difference frequency-domain method in cylindrical coordinate systems,” Opt. Lett. 33(16), 1848–1850 (2008). [CrossRef] [PubMed]

]. It has been shown that the CCS approach is more accurate than the ESW one, especially when the bending radius is small [29

29. K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14(23), 11128–11141 (2006). [CrossRef] [PubMed]

]. In this work, we use the full-vectorial finite-difference frequency-domain (FDFD) mode solver in a local CCS [30

30. J. Xiao, H. Ni, and X. Sun, “Full-vector mode solver for bending waveguides based on the finite-difference frequency-domain method in cylindrical coordinate systems,” Opt. Lett. 33(16), 1848–1850 (2008). [CrossRef] [PubMed]

] to perform the bending analysis. To effectively deal with the leaky modes, the perfectly matched layer (PML) absorbing boundary condition based on the complex coordinate stretching [31

31. F. L. Teixeira and W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7(9), 285–287 (1997). [CrossRef]

] is also incorporated.

2. Structure for numerical modeling

Structure of the bent THz pipe waveguide in the local CCS is shown in Fig. 1(a)
Fig. 1 (a) Structure and (b) cross-section of the bent THz pipe waveguide.
. The bending plane is assumed to be the x-z plane and the bending radius R is measured from the bending center to the point where x = 0. Cross-section of the pipe waveguide is shown in Fig. 1(b). It consists of a large air core with refractive index n1 = 1 and a uniform dielectric cladding layer with refractive index n2. The thickness t of the cladding layer is much smaller than the diameter D of the air core.

Guiding mechanism of the THz pipe waveguide can be described by treating its cladding layer as a Fabry–Perot etalon [18

18. C.-H. Lai, B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, C.-K. Sun, and H.-C. Chang, “Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding,” Opt. Express 18(1), 309–322 (2010). [CrossRef] [PubMed]

]. At the resonant frequencies, transmittance of the cladding is near unity and no THz waves would be confined in the air-core region, causing a large amount of losses. While at the antiresonant frequencies, strong reflection occurs at the core–cladding interface, allowing THz waves to bounce back and forth inside the air-core region with relatively low propagation losses. This guiding mechanism is similar to that of the antiresonant reflecting optical waveguide (ARROW) [19

19. M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986). [CrossRef]

], but is realized with a single-layer cylindrical hollow waveguide structure. Resonant frequencies of the cladding are given by [18

18. C.-H. Lai, B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, C.-K. Sun, and H.-C. Chang, “Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding,” Opt. Express 18(1), 309–322 (2010). [CrossRef] [PubMed]

]
fm=mc2n1t(n2/n1)21,m=1,2,3,
(1)
where c is the speed of light in vacuum and m is an integer.

To simulate the behaviors of the bent THz pipe waveguide, the full-vectorial FDFD mode solver in the local CCS is applied [30

30. J. Xiao, H. Ni, and X. Sun, “Full-vector mode solver for bending waveguides based on the finite-difference frequency-domain method in cylindrical coordinate systems,” Opt. Lett. 33(16), 1848–1850 (2008). [CrossRef] [PubMed]

]. As shown in Fig. 1(a), the computational window is located in the x-y plane, with (x, y) = (0, 0) being the waveguide center. Essentially, the FDFD mode solver is to solve an eigenvalue matrix equation in the form:
[PxxPxyPyxPyy][ExEy]=β2[ExEy],
(2)
where Ex and Ey are transverse components of the electric field and β is the complex propagation constant. Once Eq. (2) is solved, bending loss, in terms of attenuation constant, can be obtained as −2Im(β). In subsequent simulations, the following parameters are assumed: D = 9 mm, t = 0.5 mm, and n2 = 1.4. We primarily investigate the fundamental (HE11) mode in this work.

3. Numerical results

3.1 General characteristics

We first calculate the attenuation spectrum, i.e., attenuation constant as a function of frequency, of the bent THz pipe waveguide. Calculated results for the polarization parallel to the bending plane (x-polarized) and the polarization perpendicular to the bending plane (y-polarized) are both shown in Fig. 2
Fig. 2 Attenuation spectra of the bent and straight THz pipe waveguides. For the bent case, the bending radius R = 200 cm.
. The bending radius is R = 200 cm. Attenuation spectrum of the straight pipe waveguide is also shown for comparison, where the polarization is not defined for the straight case, because attenuation constants of the x- and y-polarized HE11 modes are the same owing to cylindrical symmetry. In Fig. 2, it is noted that two discontinuities (around 300 and 600 GHz, respectively) occur in the attenuation spectrum of the straight pipe waveguide. These discontinuity frequencies are the resonant frequencies predicted by Eq. (1), which can be confirmed by substituting m = 2 and 3 into Eq. (1) and the resultant resonant frequencies are 306 and 612 GHz, respectively. As previously stated, near the resonant frequencies, the cladding is almost transparent and THz waves could hardly be confined in the air-core region. Thus local maximum losses occur. These resonant frequencies make the attenuation spectrum periodic, and such a periodicity is a unique feature of the ARROW-like waveguides. Obviously, the bent pipe waveguide exhibits the same periodic behavior as that of the straight waveguide, in that the two discontinuities in the attenuation spectrum of the bent pipe waveguide also coincide with the resonant frequencies. Hence, simulation results in Fig. 2 reveal that the inherent periodic characteristics of the THz pipe waveguide is nearly unaffected under bending. In addition, as expected, attenuation constants of the bent pipe waveguide are larger than those of the straight one because of the radiationlosses caused by bending. However, it is found that the y-polarized mode suffers less bending losses than the x-polarized one does. The polarization effect on bending will be discussed later.

3.2 Polarization effect

Then, we investigate the polarization effect on bending loss. Calculated attenuation constants for x- and y-polarized modes as a function of bending radius are shown in Fig. 4
Fig. 4 Attenuation constants as a function of bending radius. The frequency is 800 GHz.
. The results are calculated at 800 GHz. Clearly, attenuation constants for both polarizations are almost the same when the bending radius is large, e.g., R = 1000 cm. Actually, if the bending radius approaches infinity, which is the case of straight pipe waveguide, there would be no difference between the attenuation constants of x- and y-polarizations because of the symmetrical geometry under straight condition. When the bending radius decreases, as expected, the attenuation constant of either polarization increases. However, it is found that the attenuation constant of the y-polarized mode is less than that of the x-polarized one, and the difference between the two polarizations is getting obvious with decreasing bending radius. This phenomenon is much different from that observed in the total-internal-reflection-based waveguides, such as the conventional step-index fiber. For the step-index fiber, bending losses of the x- and y-polarized HE11 modes are the same [32

32. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66(3), 216–220 (1976). [CrossRef]

,33

33. R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007). [CrossRef]

]. While for the antiresonant-reflection-based THz pipe waveguide studied here, the y-polarized HE11 mode experiences less bending loss than the x-polarized one does. Similar polarization effect was also observed in the bent hollow-core Bragg fiber [34

34. M. Skorobogatiy, K. Saitoh, and M. Koshiba, “Full-vectorial coupled mode theory for the evaluation of macro-bending loss in multimode fibers. application to the hollow-core photonic bandgap fibers,” Opt. Express 16(19), 14945–14953 (2008). [CrossRef] [PubMed]

], but explanation was not provided. In the following, we explain the polarization-dependent phenomenon occurring in the bent pipe waveguide. The reason for the THz wave to be guided in the air-core region of the pipe waveguide is the partial reflection occurring at the core-cladding interface. The more THz wave the interface reflects, the less power loss the pipe waveguide suffers. As having been seen in Fig. 3, under bent condition, THz wave shifts toward the outer cladding of the pipe waveguide so that there is more amount of THz field existing near the outer cladding. Therefore, reflection occurring at the outer core-cladding interface plays a dominant role in determining the bending loss. When the THz wave is x-polarized (parallel to the bending plane), the wave close to the outer cladding is like a transverse magnetic one (TM-like), i.e., the electric field is perpendicular to the outer core-cladding interface, as shown in the left case of Fig. 3(b). On the contrary, for the y-polarized THz wave (perpendicular to the bending plane), the electric field is parallel to the outer core-cladding interface which makes the wave like a transverse electric wave (TE-like), as shown in the right case of Fig. 3(b). It is well known from the electromagnetic theory that reflection is larger for the TE wave than for the TM wave [35

35. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

]. As a result, the bending loss for the y-polarized HE11 mode is smaller than that of the x-polarized one. In other words, the y-polarization, i.e., the polarization perpendicular to the bending plane, would be more preferred for the THz pipe waveguides when bending is taken into consideration.

3.3 Influence of the air-core diameter

We further study the influence of the air-core diameter by examining the y-polarized mode. Intensity distributions of the bent pipe waveguides with various core diameters are shown in Fig. 5
Fig. 5 Intensity distributions of the straight and bent THz pipe waveguides for different air-core diameters. The frequency is 500 GHz and the bending radius is 200 cm.
, where the cladding thickness is still fixed to 0.5 mm. The frequency is 500 GHz and the bending radius is R = 200 cm. Simulated results for the straight case are also shown for comparison. Clearly, under the same bending condition, the larger core diameter the pipe waveguide has, the more severe deformation the field profile suffers. In Fig. 5, shift ratios of the intensity peak are 3%, 13%, 34%, 51%, and 61% for D = 3, 6, 9, 12, and 15 mm, respectively.

3.4 Considering the straight-to-bent interface

In practical applications, the pipe waveguide might contain a straight section as well as a bent section. When the HE11 mode propagates from the straight one into the bent one, coupling loss will occur due to the mismatch between the field distributions of the straight and bent HE11 modes. Moreover, higher order modes will be excited in the bent section. To study the problem with a straight-to-bent interface, one of the commonly used techniques is the coupled mode theory [34

34. M. Skorobogatiy, K. Saitoh, and M. Koshiba, “Full-vectorial coupled mode theory for the evaluation of macro-bending loss in multimode fibers. application to the hollow-core photonic bandgap fibers,” Opt. Express 16(19), 14945–14953 (2008). [CrossRef] [PubMed]

]. In the following, the coupled mode approach is utilized for further investigation.

For the convenience of discussion, in what follows, the y- and x-polarized HE11 modes in the bent pipe waveguide are denoted as HE11y and HE11x. Under the same bending condition, attenuation constants of the HE11y and HE11x modes are 0.0018 and 0.0022 cm–1, respectively.

4. Conclusion

Appendix

In this appendix, the ESW model [26

26. M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975). [CrossRef]

] is used to estimate the incident angle θi at the outer core-cladding interface for the bent pipe waveguide. Consider the straight case first, and Fig. 11(a)
Fig. 11 (a) Longitudinal cross-section of the straight THz pipe waveguide. (b) Transformed index profile and field distribution of the bend THz pipe waveguide.
depicts the longitudinal cross-section of the straight pipe waveguide. It has been shown that the incident angle θi for the straight pipe waveguide is given by [18

18. C.-H. Lai, B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, C.-K. Sun, and H.-C. Chang, “Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding,” Opt. Express 18(1), 309–322 (2010). [CrossRef] [PubMed]

]:
θi=sin1(Re(β)n1k0),
(6)
where β is the complex propagation constant, n1 is the refractive index of the core, and k0 is the free-space wavenumber.

By using the technique of conformal transformation [26

26. M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975). [CrossRef]

], the bent pipe waveguide can be represented to its equivalent straight waveguide with a modified refractive index distribution:
n(x,y)=n(x,y)exp(xR)n(x,y)(1+xR),
(7)
where n(x, y) is the original refractive index profile of the bent pipe waveguide, and n'(x, y) is the transformed index profile of its equivalent straight waveguide. In Eq. (7), the latter approximation holds when x R, i.e., the distance from the waveguide center is far smaller than the bending radius. The transformed index distribution n' is tilted with respect to the original one, as shown in Fig. 11(b), where the corresponding field distribution for the bent pipe waveguide is illustrated as well. The index distribution and the field profile are shown along the x-axis (y = 0). It is noted that refractive index of the core of the equivalent straight waveguide, after conformal transformation, is no longer homogeneous. This prevents the direct usage of Eq. (6) to determine the incident angle, because the core index becomes position dependent. However, since most of the energy is around the peak of the field, it seems reasonable to represent the core index with the equivalent one neq, which is the refractive index in the position xmax where the field peak takes place. The equivalent index neq is given by
neq=n1(1+xmaxR).
(8)
By replacing n1 in Eq. (6) with neq, the incident angle θi at the outer core-cladding interface of the bent pipe waveguide may be estimated as

θi=sin1(Re(β)neqk0).
(9)

Acknowledgment

This work was supported in part by the National Science Council of the Republic of China under grants NSC100-2218-E-224-015 and NSC102-2221-E-224-069-MY3.

References and links

1.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]

2.

D. Abbott and X.-C. Zhang, “Scanning the issue: T-ray imaging, sensing, and retection,” Proc. IEEE 95(8), 1509–1513 (2007). [CrossRef]

3.

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004). [CrossRef]

4.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007). [CrossRef]

5.

J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010). [CrossRef]

6.

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000). [CrossRef]

7.

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

8.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80(15), 2634–2636 (2002). [CrossRef]

9.

T. Hidaka, H. Minamide, H. Ito, J.-I. Nishizawa, K. Tamura, and S. Ichikawa, “Ferroelectric PVDF cladding terahertz waveguide,” J. Lightwave Technol. 23(8), 2469–2473 (2005). [CrossRef]

10.

L.-J. Chen, H.-W. Chen, T.-F. Kao, J.-Y. Lu, and C.-K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31(3), 308–310 (2006). [CrossRef] [PubMed]

11.

M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14(21), 9944–9954 (2006). [CrossRef] [PubMed]

12.

B. Bowden, J. A. Harrington, and O. Mitrofanov, “Silver/polystyrene-coated hollow glass waveguides for the transmission of terahertz radiation,” Opt. Lett. 32(20), 2945–2947 (2007). [CrossRef] [PubMed]

13.

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

14.

S. Atakaramians, S. Afshar V, B. M. Fischer, D. Abbott, and T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16(12), 8845–8854 (2008). [CrossRef] [PubMed]

15.

K. Nielsen, H. K. Rasmussen, P. U. Jepsen, and O. Bang, “Porous-core honeycomb bandgap THz fiber,” Opt. Lett. 36(5), 666–668 (2011). [CrossRef] [PubMed]

16.

M. Rozé, B. Ung, A. Mazhorova, M. Walther, and M. Skorobogatiy, “Suspended core subwavelength fibers: towards practical designs for low-loss terahertz guidance,” Opt. Express 19(10), 9127–9138 (2011). [CrossRef] [PubMed]

17.

C.-H. Lai, Y.-C. Hsueh, H.-W. Chen, Y.-J. Huang, H.-C. Chang, and C.-K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett. 34(21), 3457–3459 (2009). [CrossRef] [PubMed]

18.

C.-H. Lai, B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, C.-K. Sun, and H.-C. Chang, “Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding,” Opt. Express 18(1), 309–322 (2010). [CrossRef] [PubMed]

19.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986). [CrossRef]

20.

E. Nguema, D. Férachou, G. Humbert, J. L. Auguste, and J. M. Blondy, “Broadband terahertz transmission within the air channel of thin-wall pipe,” Opt. Lett. 36(10), 1782–1784 (2011). [CrossRef] [PubMed]

21.

B. You, J.-Y. Lu, C.-P. Yu, T.-A. Liu, and J.-L. Peng, “Terahertz refractive index sensors using dielectric pipe waveguides,” Opt. Express 20(6), 5858–5866 (2012). [CrossRef] [PubMed]

22.

A. Mazhorova, A. Markov, B. Ung, M. Rozé, S. Gorgutsa, and M. Skorobogatiy, “Thin chalcogenide capillaries as efficient waveguides from mid-infrared to terahertz,” J. Opt. Soc. Am. B 29(8), 2116–2123 (2012). [CrossRef]

23.

M. F. Xiao, J. Liu, W. Zhang, J. L. Shen, and Y. D. Huang, “THz wave transmission in thin-wall PMMA pipes fabricated by fiber drawing technique,” Opt. Commun. 298-299, 101–105 (2013). [CrossRef]

24.

J.-T. Lu, Y.-C. Hsueh, Y.-R. Huang, Y.-J. Hwang, and C.-K. Sun, “Bending loss of terahertz pipe waveguides,” Opt. Express 18(25), 26332–26338 (2010). [CrossRef] [PubMed]

25.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14(5), 130–132 (1978). [CrossRef]

26.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975). [CrossRef]

27.

S. Kim and A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14(9), 2085–2092 (1996). [CrossRef]

28.

N. N. Feng, G. R. Zhou, C. Xu, and W. P. Huang, “Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers,” J. Lightwave Technol. 20(11), 1976–1980 (2002). [CrossRef]

29.

K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14(23), 11128–11141 (2006). [CrossRef] [PubMed]

30.

J. Xiao, H. Ni, and X. Sun, “Full-vector mode solver for bending waveguides based on the finite-difference frequency-domain method in cylindrical coordinate systems,” Opt. Lett. 33(16), 1848–1850 (2008). [CrossRef] [PubMed]

31.

F. L. Teixeira and W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7(9), 285–287 (1997). [CrossRef]

32.

D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66(3), 216–220 (1976). [CrossRef]

33.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007). [CrossRef]

34.

M. Skorobogatiy, K. Saitoh, and M. Koshiba, “Full-vectorial coupled mode theory for the evaluation of macro-bending loss in multimode fibers. application to the hollow-core photonic bandgap fibers,” Opt. Express 16(19), 14945–14953 (2008). [CrossRef] [PubMed]

35.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.7370) Optical devices : Waveguides
(040.2235) Detectors : Far infrared or terahertz

ToC Category:
Terahertz optics

History
Original Manuscript: January 2, 2014
Revised Manuscript: February 14, 2014
Manuscript Accepted: March 13, 2014
Published: April 2, 2014

Citation
Chih-Hsien Lai, Teng Chang, and Yi-Siang Yeh, "Characteristics of bent terahertz antiresonant reflecting pipe waveguides," Opt. Express 22, 8460-8472 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8460


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References

  1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]
  2. D. Abbott, X.-C. Zhang, “Scanning the issue: T-ray imaging, sensing, and retection,” Proc. IEEE 95(8), 1509–1513 (2007). [CrossRef]
  3. P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004). [CrossRef]
  4. W. L. Chan, J. Deibel, D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007). [CrossRef]
  5. J. Federici, L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010). [CrossRef]
  6. G. Gallot, S. P. Jamison, R. W. McGowan, D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000). [CrossRef]
  7. K. Wang, D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef] [PubMed]
  8. H. Han, H. Park, M. Cho, J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80(15), 2634–2636 (2002). [CrossRef]
  9. T. Hidaka, H. Minamide, H. Ito, J.-I. Nishizawa, K. Tamura, S. Ichikawa, “Ferroelectric PVDF cladding terahertz waveguide,” J. Lightwave Technol. 23(8), 2469–2473 (2005). [CrossRef]
  10. L.-J. Chen, H.-W. Chen, T.-F. Kao, J.-Y. Lu, C.-K. Sun, “Low-loss subwavelength plastic fiber for terahertz waveguiding,” Opt. Lett. 31(3), 308–310 (2006). [CrossRef] [PubMed]
  11. M. Nagel, A. Marchewka, H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14(21), 9944–9954 (2006). [CrossRef] [PubMed]
  12. B. Bowden, J. A. Harrington, O. Mitrofanov, “Silver/polystyrene-coated hollow glass waveguides for the transmission of terahertz radiation,” Opt. Lett. 32(20), 2945–2947 (2007). [CrossRef] [PubMed]
  13. A. Hassani, A. Dupuis, M. Skorobogatiy, “Porous polymer fibers for low-loss Terahertz guiding,” Opt. Express 16(9), 6340–6351 (2008). [CrossRef] [PubMed]
  14. S. Atakaramians, S. Afshar V, B. M. Fischer, D. Abbott, T. M. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16(12), 8845–8854 (2008). [CrossRef] [PubMed]
  15. K. Nielsen, H. K. Rasmussen, P. U. Jepsen, O. Bang, “Porous-core honeycomb bandgap THz fiber,” Opt. Lett. 36(5), 666–668 (2011). [CrossRef] [PubMed]
  16. M. Rozé, B. Ung, A. Mazhorova, M. Walther, M. Skorobogatiy, “Suspended core subwavelength fibers: towards practical designs for low-loss terahertz guidance,” Opt. Express 19(10), 9127–9138 (2011). [CrossRef] [PubMed]
  17. C.-H. Lai, Y.-C. Hsueh, H.-W. Chen, Y.-J. Huang, H.-C. Chang, C.-K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett. 34(21), 3457–3459 (2009). [CrossRef] [PubMed]
  18. C.-H. Lai, B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, C.-K. Sun, H.-C. Chang, “Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding,” Opt. Express 18(1), 309–322 (2010). [CrossRef] [PubMed]
  19. M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2–Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986). [CrossRef]
  20. E. Nguema, D. Férachou, G. Humbert, J. L. Auguste, J. M. Blondy, “Broadband terahertz transmission within the air channel of thin-wall pipe,” Opt. Lett. 36(10), 1782–1784 (2011). [CrossRef] [PubMed]
  21. B. You, J.-Y. Lu, C.-P. Yu, T.-A. Liu, J.-L. Peng, “Terahertz refractive index sensors using dielectric pipe waveguides,” Opt. Express 20(6), 5858–5866 (2012). [CrossRef] [PubMed]
  22. A. Mazhorova, A. Markov, B. Ung, M. Rozé, S. Gorgutsa, M. Skorobogatiy, “Thin chalcogenide capillaries as efficient waveguides from mid-infrared to terahertz,” J. Opt. Soc. Am. B 29(8), 2116–2123 (2012). [CrossRef]
  23. M. F. Xiao, J. Liu, W. Zhang, J. L. Shen, Y. D. Huang, “THz wave transmission in thin-wall PMMA pipes fabricated by fiber drawing technique,” Opt. Commun. 298-299, 101–105 (2013). [CrossRef]
  24. J.-T. Lu, Y.-C. Hsueh, Y.-R. Huang, Y.-J. Hwang, C.-K. Sun, “Bending loss of terahertz pipe waveguides,” Opt. Express 18(25), 26332–26338 (2010). [CrossRef] [PubMed]
  25. W. A. Gambling, H. Matsumura, C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14(5), 130–132 (1978). [CrossRef]
  26. M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975). [CrossRef]
  27. S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14(9), 2085–2092 (1996). [CrossRef]
  28. N. N. Feng, G. R. Zhou, C. Xu, W. P. Huang, “Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers,” J. Lightwave Technol. 20(11), 1976–1980 (2002). [CrossRef]
  29. K. Kakihara, N. Kono, K. Saitoh, M. Koshiba, “Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14(23), 11128–11141 (2006). [CrossRef] [PubMed]
  30. J. Xiao, H. Ni, X. Sun, “Full-vector mode solver for bending waveguides based on the finite-difference frequency-domain method in cylindrical coordinate systems,” Opt. Lett. 33(16), 1848–1850 (2008). [CrossRef] [PubMed]
  31. F. L. Teixeira, W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7(9), 285–287 (1997). [CrossRef]
  32. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66(3), 216–220 (1976). [CrossRef]
  33. R. T. Schermer, J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007). [CrossRef]
  34. M. Skorobogatiy, K. Saitoh, M. Koshiba, “Full-vectorial coupled mode theory for the evaluation of macro-bending loss in multimode fibers. application to the hollow-core photonic bandgap fibers,” Opt. Express 16(19), 14945–14953 (2008). [CrossRef] [PubMed]
  35. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

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