Abstract

We present a modeling study carried out to support the design of a novel, to our knowledge, kind of photonic-crystal fiber (PCF)-based sensor. This device, based on a PCF Bragg grating, detects the presence of selected single-stranded DNA molecules, hybridized to a biofilm in the air holes of the PCF, by measuring their interaction with the fiber modes. To model the system a method derived from the perturbation theory for Maxwell’s equations has been used. This method has been fully characterized, and some of its properties are here pointed out.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  12. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
    [CrossRef]

2004 (2)

2003 (2)

2002 (2)

G. Kakarantzas, T. A. Birks, and P. St. J. Russel, “Structural long-period gratings in photonic crystal fibers”, Opt. Lett.  27, 1013–1015 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
[CrossRef]

2001 (1)

1999 (1)

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibers for evanescent field devices,” Electron. Lett.  35, 1188–1189 (1999).
[CrossRef]

1997 (1)

1993 (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.  62, 1035–1037 (1993).
[CrossRef]

Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.  62, 1035–1037 (1993).
[CrossRef]

Bennett, P. J.

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibers for evanescent field devices,” Electron. Lett.  35, 1188–1189 (1999).
[CrossRef]

Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.  62, 1035–1037 (1993).
[CrossRef]

Birks, T. A.

Bjarklev, A.

J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. FolkenbergJ. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett.  29, 1974–1976 (2004).
[CrossRef] [PubMed]

A. Bjarklev, J. Broeng, and A. Sanchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

P. E. Hoiby, L. B. Nielsen, L. H. Pedersen, J. B. Jensen, A. Bjarklev, and T. P. Hansen, “Molecular immobilization and detection in a photonic crystal fiber,” in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317220–223 (2004).
[CrossRef]

Bjarklev, A. Sanchez

A. Bjarklev, J. Broeng, and A. Sanchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

Broeng, J.

A. Bjarklev, J. Broeng, and A. Sanchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

Carlsen, A.

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
[CrossRef]

Folkenberg, J. R.

Hansen, K. P.

Hansen, T. P.

Hill, K. O.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.  62, 1035–1037 (1993).
[CrossRef]

Ho, H. L.

Hoiby, P. E.

J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. FolkenbergJ. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett.  29, 1974–1976 (2004).
[CrossRef] [PubMed]

P. E. Hoiby, L. B. Nielsen, L. H. Pedersen, J. B. Jensen, A. Bjarklev, and T. P. Hansen, “Molecular immobilization and detection in a photonic crystal fiber,” in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317220–223 (2004).
[CrossRef]

Hoo, Y. L.

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
[CrossRef]

Jensen, J. B.

J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. FolkenbergJ. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett.  29, 1974–1976 (2004).
[CrossRef] [PubMed]

P. E. Hoiby, L. B. Nielsen, L. H. Pedersen, J. B. Jensen, A. Bjarklev, and T. P. Hansen, “Molecular immobilization and detection in a photonic crystal fiber,” in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317220–223 (2004).
[CrossRef]

Jin, W.

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express  8, 173–190 (2001).
[CrossRef] [PubMed]

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.  62, 1035–1037 (1993).
[CrossRef]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express  8, 173–190 (2001).
[CrossRef] [PubMed]

Kakarantzas, G.

Knight, J. C.

Ludvigsen, H.

Malo, B.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.  62, 1035–1037 (1993).
[CrossRef]

Monro, T. M.

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibers for evanescent field devices,” Electron. Lett.  35, 1188–1189 (1999).
[CrossRef]

Nielsen, K.

Nielsen, L. B.

J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. FolkenbergJ. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett.  29, 1974–1976 (2004).
[CrossRef] [PubMed]

P. E. Hoiby, L. B. Nielsen, L. H. Pedersen, J. B. Jensen, A. Bjarklev, and T. P. Hansen, “Molecular immobilization and detection in a photonic crystal fiber,” in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317220–223 (2004).
[CrossRef]

Noordegraaf, D.

Pedersen, L. H.

J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. FolkenbergJ. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett.  29, 1974–1976 (2004).
[CrossRef] [PubMed]

P. E. Hoiby, L. B. Nielsen, L. H. Pedersen, J. B. Jensen, A. Bjarklev, and T. P. Hansen, “Molecular immobilization and detection in a photonic crystal fiber,” in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317220–223 (2004).
[CrossRef]

Petersen, J. C.

Richardson, D. J.

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibers for evanescent field devices,” Electron. Lett.  35, 1188–1189 (1999).
[CrossRef]

Riishede, J.

Ritari, T.

Ruan, S. C.

Russel, P. St.

Shi, C.

Simonsen, H. R.

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
[CrossRef]

Sørensen, T.

Tuominen, J.

Wang, D. N.

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.  62, 1035–1037 (1993).
[CrossRef]

Electron. Lett. (1)

T. M. Monro, D. J. Richardson, and P. J. Bennett, “Developing holey fibers for evanescent field devices,” Electron. Lett.  35, 1188–1189 (1999).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. E (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E  65, 066611 (2002).
[CrossRef]

Other (2)

P. E. Hoiby, L. B. Nielsen, L. H. Pedersen, J. B. Jensen, A. Bjarklev, and T. P. Hansen, “Molecular immobilization and detection in a photonic crystal fiber,” in Optical Fibers and Sensors for Medical Applications IV, I.Gannot, ed., Proc. SPIE 5317220–223 (2004).
[CrossRef]

A. Bjarklev, J. Broeng, and A. Sanchez Bjarklev, Photonic Crystal Fibres (Kluwer Academic, 2003).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

(a) Schematic representation of the doped silica–air cross section used in the numerical calculations to model the NL-1550 PCF. (b) Pattern of the fundamental mode guided by the NL-1550. (c) Fundamental-mode effective index versus normalized frequency for different values of d Λ . The data have been derived by using the MIT Photonic Bands package[8] ( Supercell size = 10 Λ × 10 Λ ; Resolution = 32   grid points Λ ).

Fig. 2
Fig. 2

(a) Schematic representation of the silica–air cross section used in the numerical calculations to model the LMA-15 PCF. (b) Pattern of the fundamental mode guided by the LMA-15. (c) Estimation of Δ n eff for different values of d Λ . Also here MIT Photonic Bands package has been used to estimate either n eff - co ( Supercell size = 10 Λ × 10 Λ ; Resolution = 32   grid-points Λ ) and n eff - cl ( Resolution = 256   grid points Λ ) .

Fig. 3
Fig. 3

Schematic representation of a standard hybridization-detection experiment. (a) Section of a generic cladding hole. (b) Inner structure of the 20 nm layer coating the inner surface of the fiber after the first step. (c) Inner structure of the same layer after hybridization. In the lower part, transmitted power (T) spectra for a broadband signal launched into the fiber is shown.

Fig. 4
Fig. 4

Schematic representation of a two-dimensional system made up by two media, of relative dielectric constant ϵ 1 and ϵ 2 , separated by a boundary line S. The added layer, of constant thickness h and relative dielectric constant ϵ 3 , is considered as a structural perturbation.

Fig. 5
Fig. 5

Schematic representation of the cross section used to model the LMA-15 PCF in the (a) unperturbed case and (b) perturbed case.

Fig. 6
Fig. 6

First-order correction n ( 1 ) eff for the fundamental mode guided in a PCF designed like the NL-1550 versus unperturbed normalized frequency.

Fig. 7
Fig. 7

First-order correction Δ n ( 1 ) eff for the modes coupling into a PCF designed like the LMA-15 versus unperturbed normalized frequency.

Fig. 8
Fig. 8

(a) Fundamental-mode effective index versus normalized frequency for a NL-1550-like PCF. (b) First-order correction n ( 1 ) eff for the fundamental mode guided in a NL-1550-like PCF versus unperturbed normalized frequency.

Fig. 9
Fig. 9

(a) Estimation of Δ n eff for different designs of a LMA-15-like PCF. (b) First-order correction Δ n ( 1 ) eff for the modes coupling into a LMA-15-like PCF versus unperturbed normalized frequency. For all the graphs water has been assumed as filling the holes.

Equations (13)

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Λ G = λ 2 n eff ,
Λ LPG = λ n eff co n eff cl = λ Δ n eff ,
Δ × 1 ϵ Δ × H = ( ω c ) 2 H ,
ω n , k p = m = 0 ω n , k ( m ) ( h Λ ) m .
ω n , k ( 1 ) = ω n , k 2 E n , k ϵ ( r ) h E n , k ,
F , G = F * ( r ) G ( r ) d r
E n , k ϵ E n , k = 1 .
ω n , k ( 1 ) = ω n , k 2 ( ϵ 3 ϵ 2 ) E p , n , k 2 ( ϵ 3 1 ϵ 2 1 ) D n , n , k 2 d S ,
ω n , k ( 1 ) = d ω n , k 4 I , J 0 2 π ( ϵ 3 ϵ 2 ) E p , n , k ( I , J ) 2 ( ϵ 3 1 ϵ 2 1 ) D n , n , k ( I , J ) 2 d θ .
n eff p ( h ) = β c ω 1 p β c ω 1 h Λ ω 1 ( 1 ) n eff [ 1 h Λ ω 1 ( 1 ) ω 1 ] .
λ ( h ) λ 1 = 2 Δ G n eff ( 1 ) h Λ ,
λ ( h ) λ 1 = Δ LPG Δ n eff ( 1 ) h Λ .
Δ n eff ( 1 ) = n eff - cl ω cl ( 1 ) ω cl n eff - co ω co ( 1 ) ω co .

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