Abstract

We analyzed the effect of fiber bending on spectral position and strength of the surface plasmon resonance arising due to the interaction of the fundamental mode guided in the core of the microstructured fiber with a metal layer. Fully vectorial simulations were performed using the finite element method with perfectly matched layers boundary conditions. To conduct the simulations, we adopted the concept of an equivalent bent fiber developed recently on the ground of transformation optics formalism. In this approach, the bent fiber with a metal layer is replaced by an equivalent fiber with appropriate spatial distributions of electric permittivity and magnetic permeability tensors. The obtained results explain the mechanisms responsible for the change in the SPR spectrum induced by bending and by the geometry of the microstructured fiber. By modifying the holes layout in the microstructured cladding, we designed the fiber, in which the depth of the surface plasmon resonance is in a high degree tunable by bending.

© 2013 OSA

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2011

2010

K. Takagi, H. Sasaki, A. Seki, and K. Watanabe, “Surface plasmon resonances of a curved hetero-core optical fiber sensor,” Sens. Actuat. A.161, 1–5 (2010).

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

2009

2008

M. Hautakorpi, M. Mattinen, and H. Ludvigsen, “Surface-plasmon-resonance sensor based on three-hole microstructured optical fiber,” Opt. Express16(12), 8427–8432 (2008).
[CrossRef] [PubMed]

A. Hassani and M. Skorobogatiy, “Surface Plasmon Resonance-like integrated sensor at terahertz frequencies for gaseous analytes,” Opt. Express16(25), 20206–20214 (2008).
[CrossRef] [PubMed]

D. M. Shyroki, “Exact equivalent straight waveguide model for bent and twisted waveguides,” IEEE Trans. Microw. Theory Tech.56(2), 414–419 (2008).
[CrossRef]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

R. K. Verma and B. D. Gupta, “Theoretical modelling of a bi-dimensional U-shaped surface plasmon resonance based fibre optic sensor for sensitivity enhancement,” J. Phys. D41(9), 095106 (2008).
[CrossRef]

2007

2006

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

M. Skorobogatiy and A. V. Kabashin, “Photon crystal waveguide-based surface plasmon resonance biosensor,” Appl. Phys. Lett.89(14), 143518 (2006).
[CrossRef]

2005

2004

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater.16(19), 1685–1706 (2004).
[CrossRef]

2003

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem.377(3), 528–539 (2003).
[CrossRef] [PubMed]

2002

K. Kurihara, K. Nakamura, E. Hirayama, and K. Suzuki, “An absorption-based surface plasmon resonance sensor applied to sodium ion sensing based on an ion-selective optode membrane,” Anal. Chem.74(24), 6323–6333 (2002).
[CrossRef] [PubMed]

2001

A. Diez, M. V. Andres, and J. L. Cruz, “In-line fiber-optic sensors based on the excitation of surface plasma modes in metal-coated tapered fibers,” Sens. Actuat. Biol. Chem.73, 95–99 (2001).

1999

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuat. Biol. Chem.54, 3–15 (1999).

1998

R. Slavik, J. Homola, and J. Ctyroky, “Miniaturization of fiber optic surface plasmon resonance sensor,” Sens. Actuat,” Biol. Chem.51, 311–315 (1998).

1991

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

1990

1975

M. Heiblum and J. Harris, “Analysis of Curved Optical-Waveguides by Conformal Transformation,” IEEE J. Quantum Electron.11(2), 75–83 (1975).
[CrossRef]

1971

E. Kretschmann, “Determination of optical Constants of metals by excitation of surface plasmons,” Z. Phys.241(4), 313–324 (1971).
[CrossRef]

Andres, M. V.

A. Diez, M. V. Andres, and J. L. Cruz, “In-line fiber-optic sensors based on the excitation of surface plasma modes in metal-coated tapered fibers,” Sens. Actuat. Biol. Chem.73, 95–99 (2001).

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Banerji, S.

Berghmans, F.

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

Booksh, K. S.

Cox, F. M.

Cruz, J. L.

A. Diez, M. V. Andres, and J. L. Cruz, “In-line fiber-optic sensors based on the excitation of surface plasma modes in metal-coated tapered fibers,” Sens. Actuat. Biol. Chem.73, 95–99 (2001).

Ctyroky, J.

R. Slavik, J. Homola, and J. Ctyroky, “Miniaturization of fiber optic surface plasmon resonance sensor,” Sens. Actuat,” Biol. Chem.51, 311–315 (1998).

Diez, A.

A. Diez, M. V. Andres, and J. L. Cruz, “In-line fiber-optic sensors based on the excitation of surface plasma modes in metal-coated tapered fibers,” Sens. Actuat. Biol. Chem.73, 95–99 (2001).

Docherty, A.

Erdmanis, M.

Fägerstam, L.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Fassi Fehri, M.

Fendler, J. H.

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater.16(19), 1685–1706 (2004).
[CrossRef]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuat. Biol. Chem.54, 3–15 (1999).

Gauvreau, B.

Gerritsma, G. J.

Golojuch, G.

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

Gupta, B. D.

R. K. Verma and B. D. Gupta, “Theoretical modelling of a bi-dimensional U-shaped surface plasmon resonance based fibre optic sensor for sensitivity enhancement,” J. Phys. D41(9), 095106 (2008).
[CrossRef]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Harris, J.

M. Heiblum and J. Harris, “Analysis of Curved Optical-Waveguides by Conformal Transformation,” IEEE J. Quantum Electron.11(2), 75–83 (1975).
[CrossRef]

Hassani, A.

Hautakorpi, M.

Heiblum, M.

M. Heiblum and J. Harris, “Analysis of Curved Optical-Waveguides by Conformal Transformation,” IEEE J. Quantum Electron.11(2), 75–83 (1975).
[CrossRef]

Hirayama, E.

K. Kurihara, K. Nakamura, E. Hirayama, and K. Suzuki, “An absorption-based surface plasmon resonance sensor applied to sodium ion sensing based on an ion-selective optode membrane,” Anal. Chem.74(24), 6323–6333 (2002).
[CrossRef] [PubMed]

Homola, J.

J. Homola, “Present and future of surface plasmon resonance biosensors,” Anal. Bioanal. Chem.377(3), 528–539 (2003).
[CrossRef] [PubMed]

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuat. Biol. Chem.54, 3–15 (1999).

R. Slavik, J. Homola, and J. Ctyroky, “Miniaturization of fiber optic surface plasmon resonance sensor,” Sens. Actuat,” Biol. Chem.51, 311–315 (1998).

Hutter, E.

E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater.16(19), 1685–1706 (2004).
[CrossRef]

Ivarsson, B.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Johnsson, B.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Jönsson, U.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Kabashin, A.

Kabashin, A. V.

M. Skorobogatiy and A. V. Kabashin, “Photon crystal waveguide-based surface plasmon resonance biosensor,” Appl. Phys. Lett.89(14), 143518 (2006).
[CrossRef]

Karlsson, R.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Kim, Y. C.

Kretschmann, E.

E. Kretschmann, “Determination of optical Constants of metals by excitation of surface plasmons,” Z. Phys.241(4), 313–324 (1971).
[CrossRef]

Kreuwel, H. J. M.

Kuhlmey, B. T.

Kurihara, K.

K. Kurihara, K. Nakamura, E. Hirayama, and K. Suzuki, “An absorption-based surface plasmon resonance sensor applied to sodium ion sensing based on an ion-selective optode membrane,” Anal. Chem.74(24), 6323–6333 (2002).
[CrossRef] [PubMed]

Lambeck, P. V.

Large, M. C. J.

Löfås, S.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Ludvigsen, H.

Lundh, K.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Makara, M.

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

Malmqvist, M.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Martynkien, T.

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

Mattinen, M.

Mergo, P.

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

Nakamura, K.

K. Kurihara, K. Nakamura, E. Hirayama, and K. Suzuki, “An absorption-based surface plasmon resonance sensor applied to sodium ion sensing based on an ion-selective optode membrane,” Anal. Chem.74(24), 6323–6333 (2002).
[CrossRef] [PubMed]

Napiorkowski, M.

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

Nasilowski, T.

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

Novotny, S.

Olszewski, J.

G. Statkiewicz-Barabach, J. Olszewski, M. Napiorkowski, G. Golojuch, T. Martynkien, K. Tarnowski, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, T. Nasilowski, F. Berghmans, and H. Thienpont, “Polarizing photonic crystal fiber with low index inclusion in the core,” J. Opt.12(7), 075402 (2010).
[CrossRef]

J. Olszewski, M. Szpulak, and W. Urbańczyk, “Effect of coupling between fundamental and cladding modes on bending losses in photonic crystal fibers,” Opt. Express13(16), 6015–6022 (2005).
[CrossRef] [PubMed]

Ostlin, H.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Pendry, J. B.

Peng, W.

Persson, B.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Popma, T. J. A.

Reinhoudt, D. N.

Rönnberg, I.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Roos, H.

U. Jönsson, L. Fägerstam, B. Ivarsson, B. Johnsson, R. Karlsson, K. Lundh, S. Löfås, B. Persson, H. Roos, I. Rönnberg, S. Sjolander, E. Stenberg, R. Stahlberg, C. Urbaniczky, H. Ostlin, and M. Malmqvist, “Real-time biospecific interaction analysis using surface plasmon resonance and a sensor chip technology,” Biotechniques11(5), 620–627 (1991).
[PubMed]

Santos, J. L.

Sasaki, H.

K. Takagi, H. Sasaki, A. Seki, and K. Watanabe, “Surface plasmon resonances of a curved hetero-core optical fiber sensor,” Sens. Actuat. A.161, 1–5 (2010).

Schurig, D.

Seki, A.

K. Takagi, H. Sasaki, A. Seki, and K. Watanabe, “Surface plasmon resonances of a curved hetero-core optical fiber sensor,” Sens. Actuat. A.161, 1–5 (2010).

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008).
[CrossRef] [PubMed]

Shyroki, D. M.

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Figures (8)

Fig. 1
Fig. 1

Transformation from Cartesian to cylindrical coordinates preserving the waveguide’s width and length.

Fig. 2
Fig. 2

Distribution of electric permittivity in straight fiber (a) and spatial dependence of the elements of ε and µ tensors in the equivalent fiber (b-c).

Fig. 3
Fig. 3

Microstructured fiber designs with high tunability of the surface plasmon resonance by bending.

Fig. 4
Fig. 4

Geometry of the microstructured fiber. Placing the analyte channel far from the core and reducing the diameter of selected holes increases bent-induced tunability of the surface plasmon resonance. Dotted line marks the bending plane.

Fig. 5
Fig. 5

SPR spectra calculated for na = 1.33 (red) and na = 1.34 (blue) in the wide wavelength range (a) and in the resonance neighborhood (b).

Fig. 6
Fig. 6

Amplification of the SPR spectrum induced by bending (a) and comparison of the normalized SPR spectra showing that the shape of the resonance curves is conserved for different bending radii (b).

Fig. 7
Fig. 7

Calculated field distribution of the fundamental mode for different bending radii. Smaller diameter of air holes enhances the fundamental mode leaking towards the analyte channel, which results in strong amplification of the SPR spectrum.

Fig. 8
Fig. 8

SPR spectra calculated for R = 5 mm have almost identical height, width at half-maximum and the resonance wavelength for three variants of the proposed fiber design. Spectra for the fiber no. 1 and no. 2 overlap.

Tables (2)

Tables Icon

Table 1 Transition loss in dB between segments of different curvature in the fiber no. 1

Tables Icon

Table 2 Confinement loss calculated for straight and bent fiber near the resonance wavelength λ = 590 nm

Equations (15)

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

ε i'j' = | det( Λ i' i ) | 1 Λ i' i Λ j' j ε ij ,
μ i'j' = | det( Λ i' i ) | 1 Λ i' i Λ j' j μ ij ,
Λ i' i = x i' x i .
u= x 2 + z 2 R v=R tan 1 ( z x ) y=y ,
Λ i' i =( x r z r 0 Rz r 2 Rx r 2 0 0 0 1 ),
r= x 2 + z 2 =u+R.
ε i'j' =( R+u R ε XX R+u R ε XY ε XZ R+u R ε YX R+u R ε YY ε YZ ε ZX ε ZY R R+u ε ZZ ),
μ i'j' =( R+u R μ XX R+u R μ XY μ XZ R+u R μ YX R+u R μ YY μ YZ μ ZX μ ZY R R+u μ ZZ ),
ε eq ε = μ eq μ =1+ u R .
n eq ( u )= ( 1+ u R ) 2 εμ =n( 1+ u R ),
ε( λ )=1+ i=1 3 A i λ 2 ( λ 2 Z i 2 ) ,
ε( ω )= ε ω p 2 ω( ω+i ω τ ) ,
S λ =| δ λ peak δ n a |=1400[ nm RIU ],
Δλ= S λ δ n a eff = S λ n a u R =5.9nm.
Γ( R 1 , R 2 )=10 log 10 [ | E R 1 ( x,y ) E R 2 ( x,y )dxdy | 2 | E R 1 ( x,y ) | 2 dxdy | E R 2 ( x,y ) | 2 dxdy ].

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