Abstract

For the first time, the quasiperiodic Bragg fibers with geometrically distributed multilayered cladding are proposed and analyzed. We demonstrate that hollow-core Bragg fibers with quasiperiodic dielectric multilayer cladding can achieve low loss transmission over a broadband wavelength range of more than an octave (from 0.81 μm to 1.7 μm). The periods of the Bragg blocks follows a geometrical progression with a common ratio r<rc, where rc is defined as the critical ratio of the periods of two adjacent Bragg blocks. The arrangement of the quasiperiodic cladding can significantly modify the characteristics of the fiber, leading to a broadening of the guiding range compared to a hollow Bragg fiber with uniform periodic multilayer cladding structure. In general, a larger r value results in a broader guiding range. More Bragg blocks in the cladding and more unit cells in each Bragg block lead to a lower fiber modal loss.

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References

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  1. P. Yeh, A. Yariv, and E. Maron, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68(9), 1196–1201 (1978).
    [CrossRef]
  2. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
    [CrossRef] [PubMed]
  3. D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
    [CrossRef]
  4. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
    [CrossRef] [PubMed]
  5. G. Vienne, Y. Xu, C. Jakobsen, H.-J. Deyerl, J. Jensen, T. Sorensen, T. Hansen, Y. Huang, M. Terrel, R. Lee, N. Mortensen, J. Broeng, H. Simonsen, A. Bjarklev, and A. Yariv, “Ultra-large bandwidth hollow-core guiding in all-silica Bragg fibers with nano-supports,” Opt. Express 12(15), 3500–3508 (2004).
    [CrossRef] [PubMed]
  6. A. Husakov and J. Herrmann, “Chirped multilayer hollow waveguides with broadband transmission,” Opt. Express 17(5), 3025–3024 (2009).
    [CrossRef]
  7. M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17(17), 14851–14864 (2009).
    [CrossRef] [PubMed]
  8. G. Alagappan and P. Wu, “Geometrically distributed one-dimensional photonic crystals for light-reflection in all angles,” Opt. Express 17(14), 11550–11557 (2009).
    [CrossRef] [PubMed]
  9. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
    [CrossRef] [PubMed]
  10. J. D. Joannapolous, R. D. Meade, and J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton University Press, 1995).
  11. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley-Interscience 2003)
  12. S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008)
  13. Published Database of optical constants by Photonic Bandgap Fibers & Devices Group [Online]. Available: http://mit-pbg.mit.edu/pages/database.html
  14. G. Xu, W. Zhang, Y. Huang, and J. Peng, “Loss characteristics of single-HE11-mode Bragg fiber,” J. Lightwave Technol. 25(1), 359–366 (2007).
    [CrossRef]
  15. K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Opt. Express 12(8), 1510–1517 (2004).
    [CrossRef] [PubMed]

2009 (3)

2008 (1)

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

2007 (1)

2004 (2)

2002 (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[CrossRef] [PubMed]

2001 (1)

1998 (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

1978 (1)

Alagappan, G.

Bayindir, M.

Benoit, G.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Opt. Express 12(8), 1510–1517 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[CrossRef] [PubMed]

Bjarklev, A.

Bjarklev, A. O.

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

Broeng, J.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

Cucinotta, A.

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

Deyerl, H.-J.

Engeness, T. D.

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

Fink, Y.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Opt. Express 12(8), 1510–1517 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[CrossRef] [PubMed]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

Foroni, M.

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

Hansen, T.

Hart, S. D.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Opt. Express 12(8), 1510–1517 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[CrossRef] [PubMed]

Herrmann, J.

Huang, Y.

Husakov, A.

Ibanescu, M.

Jacobs, S. A.

Jakobsen, C.

Jensen, J.

Joannopoulos, J. D.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Opt. Express 12(8), 1510–1517 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[CrossRef] [PubMed]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

Johnson, S. G.

Kuriki, K.

Kuriki, Y.

Laegsgaard, J.

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

Lee, R.

Maron, E.

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

Mortensen, N.

Mortensen, N. A.

Passaro, D.

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

Peng, J.

Poli, F.

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

Selleri, S.

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

Shapira, O.

Simonsen, H.

Skorobogatiy, M.

Soljacic, M.

Sorensen, T.

Temelkuran, B.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[CrossRef] [PubMed]

Terrel, M.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

Vienne, G.

Viens, J. F.

Weisberg, O.

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

Wu, P.

Xu, G.

Xu, Y.

Yan, M.

Yariv, A.

Yeh, P.

Zhang, W.

IEEE Sens. J. (1)

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-Silica Hollow-Core Microstructured Bragg Fibers for Biosensor Application,” IEEE Sens. J. 8(7), 1280–1286 (2008).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Nature (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[CrossRef] [PubMed]

Opt. Express (6)

Science (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef] [PubMed]

Other (4)

J. D. Joannapolous, R. D. Meade, and J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton University Press, 1995).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley-Interscience 2003)

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008)

Published Database of optical constants by Photonic Bandgap Fibers & Devices Group [Online]. Available: http://mit-pbg.mit.edu/pages/database.html

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Figures (10)

Fig. 1
Fig. 1

(a) Schematic diagram of the hollow-core Bragg fiber cross-section. (b) The quasiperiodic cladding is formed by m numbers of Bragg blocks; there are N unit cells in each block, i.e. N pairs of two dielectric materials alternating in the block. The period for k-th Bragg block is pk . The ratio of the periods in two adjacent Bragg block is r = pk/ pk-1 . (c) An example of a quasiperiodic Bragg fiber with m = 2, N = 4, r = 1.5, and (d) its refractive index profile in radial direction.

Fig. 2
Fig. 2

rc as a function of incidence angel θ i n c and polarization. The refractive index nL = 1.625, nH = 2.896, 3.6, 4.6 respectively.

Fig. 3
Fig. 3

Projected band structure of the planar periodic multilayer structure. The refractive index of the two materials in the Bragg cladding nL = 1.625, nH = 2.896. The solid line is the light line. The gray and black regions correspond to TE allowed band, and TM allowed band respectively. The white regions correspond to the total bandgaps.

Fig. 4
Fig. 4

The reflection R versus wavelength λ and incidence angle θ for both TE and TM polarization. The Bragg cladding has the following parameters: nL = 1.625, nH = 2.896, m = 5, N = 6, (a) periodic 1D PC, p 1 = p 2 = = p m = 287 nm. (b) quasiperiodic Bragg cladding, p 1 = 287 nm, p m / p 1 = 1.2.

Fig. 5
Fig. 5

(a) The bandedge wavelengths of the fundamental bandgap for the periodic 1D PC (upper), and the quasiperiodic 1D PC (lower). There is obvious broadening in omni-reflection range marked by the solid-dash lines. (b) The transmission at incidence angle θ = 90 ° for TE (dashed) and TM (solid) polarizations.

Fig. 6
Fig. 6

Material refractive index of PES and As2Se3 [13]

Fig. 7
Fig. 7

Loss of TE01 mode of the periodic Bragg fiber, and quasiperiodic Bragg fiber with hetero-structured cladding. The fiber parameters are: nL , nH are assuming zero absorption loss. Other fiber parameters are: (a) Periodic Bragg fiber, N = 3, m = 5 (circle). Quasiperiodic Bragg fiber, p m / p 1 = 1.2 , N = 3, m = 5 (star); N = 6, m = 5 (triangle); and N = 3, m = 10 (square); (b) Quasiperiodic Bragg fiber, p m / p 1 = 1.2 , N = 6, m = 5 (star); p m / p 1 = 1.4 , N = 6, m = 5 (circle); p m / p 1 = 1.6 , N = 6, m = 5 (triangle); and N = 6, m = 10 (square).

Fig. 8
Fig. 8

The azimuthal electric field profile E θ of TE01 mode of the hollow Bragg fiber at λ = 1.0, 1.4, and 1.6 μ m . (a) The cladding is periodic PC. (b) The cladding is quasiperiodic PC.

Fig. 9
Fig. 9

Loss of TE01 mode of the periodic (solid curve) and quasiperiodic Bragg fiber (solid curve with circles). (a) The Bragg cladding has the following parameters: nL , nH are from [13], m = 5, N = 6, the periodic Bragg fiber has 1D PC, p 1 = p 2 = = p m = 287 nm. The quasiperiodic Bragg fiber has hetero-structured cladding, p 1 = 287 nm, p m / p 1 = 1.2. (b) The cladding materials are SiO2/As2Se3, the fiber structural parameters are the same as those used in Fig. 9(a) with cladding materials of PES/As2Se3. The Loss of TE01 mode of the quasiperiodic Bragg fiber shows an evident broadening with p m / p 1 varying from 1.0 (solid star line) to 1.2 (solid square line).

Fig. 10
Fig. 10

Loss of TE01 mode of the quasiperiodic Bragg fiber with hetero-structured cladding. The fiber parameters are: p 1 = 287 nm, p m / p 1 = 1.2, nL , nH are from [13]. Other fiber parameters are: (a) m = 5. The loss curve of the fiber with N = 6 is plotted in solid curve with circles, N = 12 is plotted in solid curve with stars. (b) N = 6. The loss curve of the fiber with m = 5 is plotted in solid curve with circles, and m = 10 is plotted in solid curve with stars.

Equations (17)

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k t , i 2 = k i 2 k z 2
l i = λ t , i 4 + s λ t , i 2 s = 0 , 1 , 2...
l H / L = λ 4 n H / L 2 n 0 2 = λ 4 n H / L 2 1
M T = 1 1 ρ T 2 [ e j ( δ H + δ L ) ρ T 2 e j ( δ H δ L ) 2 j ρ T e j δ H sin δ L 2 j ρ T e j δ H sin δ L e j ( δ H + δ L ) ρ T 2 e j ( δ H δ L ) ]
n H T = { n H cos θ H n H cos θ H n L T = { n L cos θ L n L cos θ L   TM polarization TE polarization
sin θ H / L = n 0 n H / L sin θ i n c = sin θ i n c n H / L
a = cos ( δ H + δ L ) ρ T 2 cos ( δ H δ L ) 1 ρ T 2
cos 2 ( δ H + δ L 2 ) = ρ T 2 cos 2 ( δ H δ L 2 )
δ H ± δ L 2 = ( k H l H cos θ H ± k L l L cos θ L ) 2 = k L ± 2
cos ( π λ 1 L + ) = | ρ T | cos ( π λ 1 L ) cos ( π λ 2 L + ) = | ρ T | cos ( π λ 2 L )
λ k , = λ 1 = π L + cos 1 ( | ρ T | ) = π L + π / 2 + sin 1 ( | ρ T | ) λ k , + = λ 2 = π L + cos 1 ( | ρ T | ) = π L + π / 2 sin 1 ( | ρ T | )
l H = p k n L n H + n L l L = p k n H n H + n L
r c = π / 2 + sin 1 ( ρ T ) π / 2 sin 1 ( ρ T )
[ t 2 + k t , i 2 ] { E z ( r , θ ) H z ( r , θ ) } = 0
E z = [ A m J m ( k t , i r ) + B m H m ( k t , i r ) ] exp ( i m θ ) H z = [ C m J m ( k t , i r ) + D m H m ( k t , i r ) ] exp ( i m θ )
[ A m 1 B m 1 C m 1 D m 1 ] = M r 1 M r 2 M r ( N 1 ) [ A m N B m N C m N D m N ]
C L = k 20 ln ( 10 ) 10 9 Im ( n eff )

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