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

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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2013

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]

2012

2011

2010

2009

2008

2007

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]

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]

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

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

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

2006

2005

2004

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

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

2002

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]

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]

2000

1997

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

1996

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

1986

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]

1978

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

1976

1975

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

Abbott, D.

Afshar V, S.

Atakaramians, S.

Auguste, J. L.

Bang, O.

Blondy, J. M.

Bowden, B.

Chan, W. L.

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

Chang, H.-C.

Chen, H.-W.

Chen, L.-J.

Chew, W. C.

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

Cho, M.

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]

Cole, J. H.

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]

Deibel, J.

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

Duguay, M. A.

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]

Dupuis, A.

Federici, J.

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

Feng, N. N.

Férachou, D.

Fischer, B. M.

Gallot, G.

Gambling, W. A.

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

Gopinath, A.

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

Gorgutsa, S.

Grischkowsky, D.

Han, H.

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]

Harrington, J. A.

Harris, J. H.

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

Hassani, A.

Heiblum, M.

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

Hidaka, T.

Hsueh, Y.-C.

Huang, W. P.

Huang, Y. D.

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]

Huang, Y.-J.

Huang, Y.-R.

Humbert, G.

Hwang, Y.-J.

Ichikawa, S.

Ito, H.

Jamison, S. P.

Jepsen, P. U.

Kakihara, K.

Kao, T.-F.

Kim, J.

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]

Kim, S.

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

Koch, T. L.

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]

Kokubun, Y.

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]

Kono, N.

Koshiba, M.

Kurz, H.

Lai, C.-H.

Liu, J.

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]

Liu, T.-A.

Lu, J.-T.

Lu, J.-Y.

Marchewka, A.

Marcuse, D.

Markov, A.

Matsumura, H.

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

Mazhorova, A.

McGowan, R. W.

Minamide, H.

Mitrofanov, O.

Mittleman, D. M.

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

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

Moeller, L.

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

Monro, T. M.

Nagel, M.

Nguema, E.

Ni, H.

Nielsen, K.

Nishizawa, J.-I.

Park, H.

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]

Peng, J.-L.

Pfeiffer, L.

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]

Ragdale, C. M.

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

Rasmussen, H. K.

Rozé, M.

Saitoh, K.

Schermer, R. T.

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]

Shen, J. L.

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]

Siegel, P. H.

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

Skorobogatiy, M.

Sun, C.-K.

Sun, X.

Tamura, K.

Teixeira, F. L.

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

Tonouchi, M.

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

Ung, B.

Walther, M.

Wang, K.

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

Xiao, J.

Xiao, M. F.

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]

Xu, C.

You, B.

Yu, C.-P.

Zhang, W.

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]

Zhang, X.-C.

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

Zhou, G. R.

Appl. Phys. Lett.

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]

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]

Electron. Lett.

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

IEEE J. Quantum Electron.

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

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]

IEEE Microwave Guided Wave Lett.

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

IEEE Trans. Microw. Theory Tech.

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

J. Appl. Phys.

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

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Nat. Photonics

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

Nature

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

Opt. Commun.

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]

Opt. Express

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]

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]

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]

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]

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]

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]

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

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

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]

Opt. Lett.

Proc. IEEE

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

Rep. Prog. Phys.

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

Other

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

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Figures (11)

Fig. 1
Fig. 1

(a) Structure and (b) cross-section of the bent THz pipe waveguide.

Fig. 2
Fig. 2

Attenuation spectra of the bent and straight THz pipe waveguides. For the bent case, the bending radius R = 200 cm.

Fig. 3
Fig. 3

(a) Intensity distributions of the y-polarized mode. (b) Intensity distributions and electric field vector distributions of the x- and y-polarized modes for the bent case, which are obtained at 800 GHz and R = 75 cm.

Fig. 4
Fig. 4

Attenuation constants as a function of bending radius. The frequency is 800 GHz.

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.

Fig. 6
Fig. 6

Attenuation constants as a function of core diameter for the straight and bent THz pipe waveguides. In the top axis, the core diameter is normalized with respect to the wavelength. (a) 200 GHz. (b) 500 GHz. (c) 800 GHz. The colored arrows indicate the critical diameters at which transition between the perturbed mode and the whispering gallery mode occurs. Each arrow corresponds to a curve of the same color.

Fig. 7
Fig. 7

(a) Ray propagation of the perturbed mode. (b) Ray propagation of the whispering gallery mode. (c) A diagram used to find the condition where transition between the two propagation modes occurs.

Fig. 8
Fig. 8

Critical incident angles θWGM and estimated incident angles θi for the bent pipe waveguides. The frequency is 500 GHz. (a) R = 75 cm. (b) R = 200 cm. (c) R = 500 cm. (d) R = 1000 cm.

Fig. 9
Fig. 9

Intensity distributions and electric field vector distributions of the straight and bent THz pipe waveguides. The frequency is 500 GHz and the bending radius is 500 cm.

Fig. 10
Fig. 10

Total power losses of the bent pipe waveguide as a function of waveguide length. The frequency is 500 GHz. (a) R = 500 cm. (b) R = 200 cm. (c) R = 75 cm.

Fig. 11
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.

Equations (9)

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f m = mc 2 n 1 t ( n 2 / n 1 ) 2 1 , m=1,2,3,
[ P xx P xy P yx P yy ][ E x E y ]= β 2 [ E x E y ],
θ WGM = sin 1 ( OB ¯ OA ¯ )= sin 1 ( R(D/2) R+(D/2) ),
P i = | E in · E i * dxdy | 2 | E in | 2 dxdy | Ε i | 2 dxdy ,
P out = i=1 N P i exp( α i L) ,
θ i = sin 1 ( Re(β) n 1 k 0 ),
n (x,y)=n(x,y)exp( x R )n(x,y)( 1+ x R ),
n eq = n 1 ( 1+ x max R ).
θ i = sin 1 ( Re(β) n eq k 0 ).

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