Abstract

In this paper a flexible hollow core waveguide for the terahertz spectral range is demonstrated. Its cladding is composed of a circular arrangement of dielectric tubes surrounded by a heat-shrink jacket that allows the fiber to be flexible. Characterization of straight samples shows that the hollow core allows the absorption caused by the polymethylmethacrylate tubes of the cladding to be reduced by 31 times at 0.375 THz and 272 times at 0.828 THz with respect to the bulk material, achieving losses of 0.3 and 0.16 dB/cm respectively. Bending loss is also experimentally measured and compared to numerical results. For large bending radii bending loss scales as Rb2, whereas for small bending radii additional resonances between core and cladding appear. The transmission window bandwidth is also shown to shrink as the bending radius is reduced. An analytical model is proposed to predict and quantify both of these bending effects.

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References

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  1. J. Anthony, R. Leonhardt, S. G. Leon-Saval, and A. Argyros, “Thz propagation in kagome hollow-core microstructured fibers,” Opt. Express19, 18470–18478 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. L. Vincetti, V. Setti, and M. Zoboli, “Terahertz tube lattice fibers with octagonal symmetry,” IEEE Photon. Technol. Lett.22, 972–974 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. 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. Express18, 309–322 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. B. You, J. Y. Lu, C. P. Yu, T. A. Liu, and J. L. Peng, “Terahertz refractive index sensors using dielectric pipe waveguides,” Opt. Express20, 5858–5866 (2012).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  18. Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core kagome hollow-core photonic crystal fiber,” Opt. Lett.36, 669–671 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  29. J. Olszewski, M. Szpulak, and W. Urbańczyk, “Effect of coupling between fundamental and cladding modes on bending losses in photonic crystal fibers,” Opt. Express13, 6015–6022 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2012 (5)

2011 (8)

J. Anthony, R. Leonhardt, S. G. Leon-Saval, and A. Argyros, “Thz propagation in kagome hollow-core microstructured fibers,” Opt. Express19, 18470–18478 (2011).
[CrossRef] [PubMed]

A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express19, 25723–25728 (2011).
[CrossRef]

J. Anthony, R. Leonhardt, A. Argyros, and M. C. J. Large, “Characterization of a microstructured zeonex terahertz fiber,” J. Opt. Soc. Am. B28, 1013–1018 (2011).
[CrossRef]

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core kagome hollow-core photonic crystal fiber,” Opt. Lett.36, 669–671 (2011).
[CrossRef] [PubMed]

A. Dupuis, K. Stoeffler, B. Ung, C. Dubois, and M. Skorobogatiy, “Transmission measurements of hollow-core thz bragg fibers,” J. Opt. Soc. Am. B28, 896–907 (2011).
[CrossRef]

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

J. T. Lu, C. H. Lai, T. F. Tseng, H. Chen, Y. F. Tsai, I. J. Chen, Y. J. Hwang, H. C. Chang, and C. K. Sun, “Terahertz polarization-sensitive rectangular pipe waveguides,” Opt. Express19, 21532–21539 (2011).
[CrossRef] [PubMed]

D. S. Wu, A. Argyros, and S. G. Leon-Saval, “Reducing the size of hollow terahertz waveguides,” J. Lightwave Technol.29, 97–103 (2011).
[CrossRef]

2010 (6)

2009 (2)

2008 (2)

2007 (3)

2006 (1)

Y. S. Jun, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Kor. Phys. Soc.49, 513–517 (2006).

2005 (1)

2001 (1)

1981 (1)

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J.43, 1783–1809 (1964).

Adam, A. J. L.

Anthony, J.

Argyros, A.

Astapovich, M. S.

Auguste, J. L.

Bang, O.

Benabid, F.

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core kagome hollow-core photonic crystal fiber,” Opt. Lett.36, 669–671 (2011).
[CrossRef] [PubMed]

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science318, 1118–1121 (2007).
[CrossRef] [PubMed]

Biriukov, A. S.

Blondy, J. M.

Burger, S.

Chang, H. C.

Chen, H.

Chen, H. Z.

Chen, I. J.

Churbanov, M. F.

Coen, S.

Couny, F.

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core kagome hollow-core photonic crystal fiber,” Opt. Lett.36, 669–671 (2011).
[CrossRef] [PubMed]

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science318, 1118–1121 (2007).
[CrossRef] [PubMed]

de Sterke, C. M.

Dianov, E. M.

Docherty, A.

Doradla, P.

Dubois, C.

Dupuis, A.

Engeness, T.

Estacio, E.

Fèrachou, D.

Fink, Y.

Gérôme, F.

Giles, R. H.

Grujic, T.

Hsueh, Y. C.

Huang, Y. R.

Humbert, G.

Hwang, Y. J.

Ibanescu, M.

Jacobs, S.

Jamier, R.

Jeon, S. G.

Y. S. Jun, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Kor. Phys. Soc.49, 513–517 (2006).

Jepsen, P. U.

Joannopoulos, J.

Johnson, S.

Joseph, C. S.

Jun, Y. S.

Y. S. Jun, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Kor. Phys. Soc.49, 513–517 (2006).

Kawakami, S.

Kim, G. J.

Y. S. Jun, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Kor. Phys. Soc.49, 513–517 (2006).

Knight, J. C.

Kosolapov, A. F.

Kuhlmey, B. T.

Kumar, J.

Lai, C. H.

Large, M. C. J.

Leonhardt, R.

Leon-Saval, S. G.

Light, P. S.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science318, 1118–1121 (2007).
[CrossRef] [PubMed]

Liou, J. H.

Liu, T. A.

Lu, J. T.

Lu, J. Y.

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J.43, 1783–1809 (1964).

Miyagi, M.

Nguema, E.

Nielsen, K.

Olszewski, J.

Pearce, G. J.

Peng, J. L.

Pla, J.

Planken, P. C. M.

Plotnichenko, V. G.

Pobre, R.

Ponseca, C. S.

Poulton, C. G.

Pryamikov, A. D.

Rasmussen, H. K.

Raymer, M. G.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science318, 1118–1121 (2007).
[CrossRef] [PubMed]

Roberts, P. J.

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core kagome hollow-core photonic crystal fiber,” Opt. Lett.36, 669–671 (2011).
[CrossRef] [PubMed]

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science318, 1118–1121 (2007).
[CrossRef] [PubMed]

Russell, P. S. J.

Sarukura, N.

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J.43, 1783–1809 (1964).

Setti, V.

Shiryaev, V. S.

Skorobogatiy, M.

Snopatin, G. E.

Soljacic, M.

Stoeffler, K.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw Hill, 1941). Section 9.15.

Sun, C. K.

Szpulak, M.

Tsai, Y. F.

Tseng, T. F.

Ung, B.

Urbanczyk, W.

van Eijkelenborg, M. A.

Vincetti, L.

Wadsworth, W. J.

Wang, Y. Y.

Weisberg, O.

Wheeler, N. V.

Wiederhecker, G. S.

Wu, D. S.

You, B.

Yu, C. P.

Yu, F.

Zoboli, M.

L. Vincetti, V. Setti, and M. Zoboli, “Terahertz tube lattice fibers with octagonal symmetry,” IEEE Photon. Technol. Lett.22, 972–974 (2010).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J.43, 1783–1809 (1964).

IEEE Photon. Technol. Lett. (1)

L. Vincetti, V. Setti, and M. Zoboli, “Terahertz tube lattice fibers with octagonal symmetry,” IEEE Photon. Technol. Lett.22, 972–974 (2010).
[CrossRef]

J. Kor. Phys. Soc. (1)

Y. S. Jun, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Kor. Phys. Soc.49, 513–517 (2006).

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Opt. Express (18)

B. You, J. Y. Lu, J. H. Liou, C. P. Yu, H. Z. Chen, T. A. Liu, and J. L. Peng, “Subwavelength film sensing based on terahertz anti-resonant reflecting hollow waveguides,” Opt. Express18, 19353–19360 (2010).
[CrossRef] [PubMed]

L. Vincetti and V. Setti, “Waveguiding mechanism in tube lattice fibers,” Opt. Express18, 23133–23146 (2010).
[CrossRef] [PubMed]

T. Grujic, B. T. Kuhlmey, A. Argyros, S. Coen, and C. M. de Sterke, “Solid-core fiber with ultra-wide bandwidth transmission window due to inhibited coupling,” Opt. Express18, 25556–25566 (2010).
[CrossRef] [PubMed]

J. T. Lu, Y. C. Hsueh, Y. R. Huang, Y. J. Hwang, and C. K. Sun, “Bending loss of terahertz pipe waveguides,” Opt. Express18, 26332–26338 (2010).
[CrossRef] [PubMed]

S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core omniguide fibers,” Opt. Express9, 748–779 (2001).
[CrossRef] [PubMed]

J. Olszewski, M. Szpulak, and W. Urbańczyk, “Effect of coupling between fundamental and cladding modes on bending losses in photonic crystal fibers,” Opt. Express13, 6015–6022 (2005).
[CrossRef] [PubMed]

A. Argyros and J. Pla, “Hollow-core polymer fibres with a kagome lattice: potential for transmission in the infrared,” Opt. Express15, 7713–7719 (2007).
[CrossRef] [PubMed]

G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. S. J. Russell, “Models for guidance in kagome-structured hollow-core photonic crystal fibers,” Opt. Express15, 12680–12685 (2007).
[CrossRef] [PubMed]

A. Argyros, S. G. Leon-Saval, J. Pla, and A. Docherty, “Antiresonance and inhibited coupling in hollow core square lattice optical fibres,” Opt. Express16, 5642–5648 (2008).
[CrossRef] [PubMed]

P. Doradla, C. S. Joseph, J. Kumar, and R. H. Giles, “Characterization of bending loss in hollow flexible terahertz weaveguides,” Opt. Express20, 19176–19184 (2012).
[CrossRef] [PubMed]

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. Express17, 8592–8601 (2009).
[CrossRef] [PubMed]

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. Express18, 309–322 (2009).
[CrossRef]

J. Anthony, R. Leonhardt, S. G. Leon-Saval, and A. Argyros, “Thz propagation in kagome hollow-core microstructured fibers,” Opt. Express19, 18470–18478 (2011).
[CrossRef] [PubMed]

J. T. Lu, C. H. Lai, T. F. Tseng, H. Chen, Y. F. Tsai, I. J. Chen, Y. J. Hwang, H. C. Chang, and C. K. Sun, “Terahertz polarization-sensitive rectangular pipe waveguides,” Opt. Express19, 21532–21539 (2011).
[CrossRef] [PubMed]

A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express19, 25723–25728 (2011).
[CrossRef]

B. You, J. Y. Lu, C. P. Yu, T. A. Liu, and J. L. Peng, “Terahertz refractive index sensors using dielectric pipe waveguides,” Opt. Express20, 5858–5866 (2012).
[CrossRef] [PubMed]

F. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3 – 4 μm spectral region,” Opt. Express20, 11153–11158 (2012).
[CrossRef] [PubMed]

L. Vincetti and V. Setti, “Extra loss due to fano resonances in inhibited coupling fibers based on a lattice of tubes,” Opt. Express20, 14350–14361 (2012).
[CrossRef] [PubMed]

Opt. Lett. (4)

Science (1)

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science318, 1118–1121 (2007).
[CrossRef] [PubMed]

Other (2)

A. D. Pryamikov, A. F. Kosolapov, V. G. Plotnichenko, and E. M. Dianov, Transmission of CO2 Laser Radiation through Class Hollow Core Microstructured Fibers (InTech, 2012), chap. 8, pp. 227–247.

J. A. Stratton, Electromagnetic Theory (McGraw Hill, 1941). Section 9.15.

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Figures (5)

Fig. 1
Fig. 1

(a) Microscope image of the transverse cross section of the manufactured fiber along with its physical dimensions and dielectric properties. (b) Side picture of the fiber. (c) THz-TDS setup that have been used to characterize the straight fiber. (e) Frequency dependence of ℜ(nH) and ℑ(nH) measured experimentally for a PMMA disk.

Fig. 2
Fig. 2

(a) Top and middle panels show the numerical dispersion curves for two dielectric modes with different periodicity along the transverse direction, the core mode and hole modes. For the hole modes the color intensity is proportional to the power inside the hole regions normalized with respect to the total power of the mode. Experimental data is also shown. Bottom panel shows numerical propagation loss for the core mode with different values of ℑ(nH) and also experimentally measured loss. (c) Example images for the three different classes of modes supported by the waveguide.

Fig. 3
Fig. 3

(a) THz-TDS setup that have been used to characterize the 20 cm fiber sample for the bending. (b) A picture of the setup. (c) Experimental and numerical normalized transmission of the 20 cm TLF sample for different bending radii. (d) Comparison of propagation loss in case of bending for CTLFs with transparent and PMMA tubes.

Fig. 4
Fig. 4

(a) Effect of the conformal mapping on the refractive index of the fiber in the transverse direction. (b) Propagation loss of the core mode in the first transmission window for Rb = {4, 6, 8, 10} cm (from light to dark blue). (c) Propagation loss of the core mode in the second transmission window for Rb = {18, 22, 26, 30} cm (from light to dark violet). The resonance between core and hole mode is highlighted in the inset. (d) Evaluation of Eq. (4) for the first resonance edge (red) and of Eq. (5) for the resonances between core and hole modes (green) in the two transmission windows.

Fig. 5
Fig. 5

(a) Numerical (dots) and analytical (dashed lines) effective indices for the hole modes and the core mode of the CTLF. (b) Bending loss for CTLFs with 8 (red dots) and 9 (green dots) transparent cladding tubes and for a 8 PMMA tubes CTLF (blue) at 0.86 THz. Dashed lines represent the asymptotic R b 2 trend. (c) Poynting vector intensities for the core mode at the high loss peaks reported in (b).

Equations (12)

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

f R m = m c 2 t n ¯ H 2 n L 2 , m ,
n eff = n L 1 2 ( u ν μ c 2 π f R n L ) 2
n ˜ ( x , y ) = n ( x , y ) e ξ / R b .
f R m = m c 2 t ( n ¯ H e x ^ / R b ) 2 n L 2
R b = x c ln [ M ( R c o ) 2 + ( M ( R c o ) 2 ) 2 M ( r int ) + 1 ] , M ( R ) = 1 1 2 ( u n m c 2 π f R ) 2 .
[ J ν ( K L R ) J ν ( K L R ) K L K H H ν ( 1 ) ( K H R ) H ν ( 1 ) ( K H R ) ] [ J ν ( K L R ) J ν ( K L R ) K L K H n H 2 n L 2 H ν ( 1 ) ( K H R ) H ν ( 1 ) ( K H R ) ] = [ ν β K L 2 R 2 ( K L 2 K H 2 1 ) ] 2
H ν ( 1 ) ( K H R ) H ν ( 1 ) ( K H R ) i ,
J ν 1 ( K L R ) = i η ( n H n L ) 2 1 K L K 0 n L J ν ( K L R ) ,
η = { 1 2 [ 1 + ( n H n L ) 2 ] for H E ν μ and E H ν μ modes 1 for T E 0 μ modes ( n H n L ) 2 for T M 0 μ modes
K L u ν μ R [ 1 i ν 1 K 0 n L R η ( n H n L ) 2 1 ] ,
β = Re { K 0 2 n L 2 K L 2 } 2 π f c n L [ 1 1 2 ( u ν μ c 2 π f R n L ) 2 ] ,
n eff = β K 0 = n L 1 2 ( u ν μ c 2 π f R n L ) 2 .

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