Abstract

We have investigated the basic properties of subwavelength-diameter hollow optical fiber with exact solutions of Maxwell’s equations. The characteristics of modal field and waveguide dispersion have been studied. It shows that the subwavelength-diameter hollow optical fibers have interesting properties, such as enhanced evanescent field, local enhanced intensity in the hollow core and large waveguide dispersion that are very promising for many miniaturized high performance and novel photonic devices.

© 2007 Optical Society of America

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  1. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
    [CrossRef] [PubMed]
  2. L. M. Tong, J. Y. Lou, and E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Express 12, 1025-1035 (2004).
    [CrossRef] [PubMed]
  3. J. Y. Lou, L. M. Tong, and Z. Z. Ye, "Dispersion shifts in optical nanowires with thin dielectric coatings," Opt. Express 14, 6993-6998 (2006).
    [CrossRef] [PubMed]
  4. L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
    [CrossRef]
  5. D. Penman, "Spider silk delivers finest optical fibres," New Scientist 12, (2003).
  6. E. Karadeniz and P. Kornreich, "Intercore-cladding uniaxial dielectric thin film optical fibers," Opt. Eng. 45, 085001-1-10 (2006).
    [CrossRef]
  7. U. Schröter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001).
    [CrossRef]
  8. A. W. Snyder, and J. D. Love, Optical waveguide theory (Chapman and Hall, New York, 1983).
  9. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and confining light in void nanostructure," Opt. Lett. 29, 1209-1211 (2004).
    [CrossRef] [PubMed]
  10. G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
    [CrossRef]

2007

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

2006

2004

2003

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
[CrossRef]

2001

U. Schröter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Almeida, V. R.

Ashcom, J. B.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Barrios, C. A.

Benabid, F.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Cordeiro, C. M. B.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Couny, F.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Cruz, C. H. B.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Dereux, A.

U. Schröter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Fragnito, H. L.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Gattass, R. R.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Hayashi, C. Y.

L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
[CrossRef]

He, S. L.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Huang, L. M.

L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
[CrossRef]

Knight, J. C.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Lipson, M.

Lou, J. Y.

Maier, S. A.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Maxwell, I.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. M. Tong, J. Y. Lou, and E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Express 12, 1025-1035 (2004).
[CrossRef] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Schröter, U.

U. Schröter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Shen, M. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Tian, B. Z.

L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
[CrossRef]

Tong, L. M.

Wang, H. T.

L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
[CrossRef]

Wiederhecker, G. S.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Xu, Q.

Yan, Y. S.

L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
[CrossRef]

Ye, Z. Z.

Zhao, D. Y.

L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
[CrossRef]

J. Mater. Chem.

L. M. Huang, H. T. Wang, C. Y. Hayashi, B. Z. Tian, D. Y. Zhao and Y. S. Yan, "Single-strand spider silk templating for the formation of hierarchically ordered hollow mesoporous silica fibers," J. Mater. Chem. 13, 666-668 (2003).
[CrossRef]

Nature

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Nature Photonics

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

U. Schröter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Other

A. W. Snyder, and J. D. Love, Optical waveguide theory (Chapman and Hall, New York, 1983).

D. Penman, "Spider silk delivers finest optical fibres," New Scientist 12, (2003).

E. Karadeniz and P. Kornreich, "Intercore-cladding uniaxial dielectric thin film optical fibers," Opt. Eng. 45, 085001-1-10 (2006).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

The cross-section and parameters of the SHOF.

Fig. 2.
Fig. 2.

Variation of B with wavelength for SHOF with (a) different b; (b) different a.

Fig. 3.
Fig. 3.

Electric components of HE11 modes of silica SHOF at 633 nm wavelength with different dielectric region radius.

Fig. 4.
Fig. 4.

Z-direction power density of silica SHOF with (a) a=10 nm, b=100 nm and (b) a=100 nm, b=400 nm. Mesh, field inside the dielectric region. Gradient, field outside the dielectric region.

Fig. 5.
Fig. 5.

Fraction power of the fundamental modes inside (a) the central hollow region, and (b) the central and the dielectric region of SHOFs at 633 nm wavelength.

Fig. 6.
Fig. 6.

Wavelength-dependent waveguide dispersion of fundamental modes of SHOF with (a) different b; (b) different a.

Equations (14)

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[ 1 r r ( r r ) + 1 r 2 2 ∂ϕ 2 + ( k 0 2 n 2 β 2 ) ] ( E z H z ) = 0 ,
E z = { A I m ( u 1 r ) f c , 0 < r < a [ B J m ( u 2 r ) + C Y m ( u 2 r ) ] f c , D K m ( u 3 r ) f c , r > b a < r < b ,
H z = { A ´ I m ( u 1 r ) f s , 0 < r < a [ B ´ J m ( u 2 r ) + C ´ Y m ( u 2 r ) ] f s , D ´ K m ( u 3 r ) f s , r > b a < r < b ,
E r = j k 0 2 n 2 β 2 ( β E z r + w μ 0 r H z ∂ϕ ) ,
E ϕ = j k 0 2 n 2 β 2 ( β r E z ∂ϕ w μ 0 H z r ) ,
H r = j k 0 2 n 2 β 2 ( β H z r w ε 0 n 2 r E z ∂ϕ ) ,
H ϕ = j k 0 2 n 2 β 2 ( β r H z ∂ϕ + w ε 0 n 2 E z r ) .
det [ M ( β ) ] = 0 ,
v g = dw = 2 πc λ 2 ,
D w = d ( v g 1 ) .
S z = 1 2 [ E r H ϕ * E ϕ H r * ] .
n 2 1 = 0.6961663 λ 2 λ 2 ( 0.0684043 ) 2 + 0.4079426 λ 2 λ 2 ( 0.1162414 ) 2 + 0.8974794 λ 2 λ 2 ( 9089616 ) 2 ,
η 1 = 0 a S z 1 dA 0 a S z 1 dA + a b S z 2 dA + b S z 3 dA ,
η 2 = 0 a S z 1 dA + a b S z 2 dA 0 a S z 1 dA + a b S z 2 dA + b S z 3 dA ,

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