Abstract

As compared to the well-known traditional couple-mode theory, in this study, we proposed a visual, graphical, and simple numerical simulation method for long-period fiber-grating surface-plasmon-resonance (LPG-SPR) sensors. This method combines the finite element method and the eigenmode expansion method. The finite element method was used to solve for the guided modes in fiber structures, including the surface plasmon wave. The eigenmode expansion method was used to calculate the power transfer phenomenon of the guided modes in the fiber structure. This study provides a detailed explanation of the key reasons why the periodic structure of long-period fiber-grating (LPG) can achieve significantly superior results for our method compared to those obtained using other numerical methods, such as the finite-difference time-domain and beam propagation methods. All existing numerical simulation methods focus on large-sized periodic components; only the method established in this study has 3D design and analysis capabilities. In addition, unlike the offset phenomenon of the design wavelength λD and the maximum transmission wavelength λmax of the traditional coupled-mode theory, the method established in this study has rapid scanning LPG period capabilities. Therefore, during the initial component design process, only the operating wavelength must be set to ensure that the maximum transmission wavelength of the final product is accurate to the original setup, for example, λ = 1550 nm. We verified that the LPG-SPR sensor designed in this study provides a resolution of ~-45 dB and a sensitivity of ~27000 nm/RIU (refractive index unit). The objective of this study was to use the combination of these two numerical simulation methods in conjunction with a rigorous, simple, and complete design process to provide a graphical and simplistic simulation technique that reduces the learning time and professional threshold required for research and applications of LPG-SPR sensors.

© 2013 OSA

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  1. J. Homola, “Optical fiber sensor based on surface plasmon excitation,” Sens. Actuators B Chem.29(1-3), 401–405 (1995).
    [CrossRef]
  2. R. Slavík, J. Homola, and J. Čtyroký, “Single-mode optical fiber surface plasmon resonance sensor,” Sens. Actuators B Chem.54(1-2), 74–79 (1999).
    [CrossRef]
  3. S.-M. Tseng, K.-Y. Hsu, H.-S. Wei, and K.-F. Chen, “Analysis and experiment of thin metal-clad fiber polarizer with index overlay,” IEEE Photon. Technol. Lett.9(5), 628–630 (1997).
    [CrossRef]
  4. Ó. Esteban, R. Alonso, M. C. Navarrete, and A. González-Cano, “Surface plasmon excitation in fiber-optical sensors: a novel theoretical approach,” J. Lightwave Technol.20(3), 448–453 (2002).
    [CrossRef]
  5. S. Patskovsky, A. V. Kabashin, M. Meunier, and J. H. Luong, “Silicon-based surface plasmon resonance sensing with two surface plasmon polariton modes,” Appl. Opt.42(34), 6905–6909 (2003).
    [CrossRef] [PubMed]
  6. S. Patskovsky, A. V. Kabashin, M. Meunier, and J. H. Luong, “Properties and sensing characteristics of surface-plasmon resonance in infrared light,” J. Opt. Soc. Am. A20(8), 1644–1650 (2003).
    [CrossRef] [PubMed]
  7. A. J. C. Tubb, F. P. Payne, R. B. Millington, and C. R. Lowe, “Single-mode optical fibre surface plasma wave chemical sensor,” Sens. Actuators B Chem.41(1-3), 71–79 (1997).
    [CrossRef]
  8. S. Maruo, O. Nakamura, and S. Kawata, “Evanescent-wave holography by use of surface-plasmon resonance,” Appl. Opt.36(11), 2343–2346 (1997).
    [CrossRef] [PubMed]
  9. Y. J. He, Y. L. Lo, and J. F. Huang, “Optical-fiber surface-plasmon-resonance sensor employing long-period fiber grating in multiplexing,” J. Opt. Soc. Am. B23(5), 801–811 (2006).
    [CrossRef]
  10. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).
  11. D. Sun, J. Manges, Xingchao Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag.37(5), 12–24 (1995).
    [CrossRef]
  12. C. H. Herry and Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron.27(3), 523–530 (1991).
    [CrossRef]
  13. G. Sztefka and H. P. Nolting, “Bidirectional eigenmode Propagation for Large refractive index steps,” IEEE Photon. Technol. Lett.5(5), 554–557 (1993).
    [CrossRef]
  14. D. F. G. Gallagher and T. P. Felici, “Eigenmode expansion methods for simulation of optical propagation in photonics-Pros and cons,” Proc. SPIE4987, 69–82 (2003).
    [CrossRef]
  15. T. Erdogan, “Cladding-mode resonances in short and long period fiber grating filters,” J. Opt. Soc. Am. A14(8), 1760–1773 (1997).
    [CrossRef]
  16. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997).
    [CrossRef]

2006 (1)

2003 (3)

2002 (1)

1999 (1)

R. Slavík, J. Homola, and J. Čtyroký, “Single-mode optical fiber surface plasmon resonance sensor,” Sens. Actuators B Chem.54(1-2), 74–79 (1999).
[CrossRef]

1997 (5)

S.-M. Tseng, K.-Y. Hsu, H.-S. Wei, and K.-F. Chen, “Analysis and experiment of thin metal-clad fiber polarizer with index overlay,” IEEE Photon. Technol. Lett.9(5), 628–630 (1997).
[CrossRef]

A. J. C. Tubb, F. P. Payne, R. B. Millington, and C. R. Lowe, “Single-mode optical fibre surface plasma wave chemical sensor,” Sens. Actuators B Chem.41(1-3), 71–79 (1997).
[CrossRef]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997).
[CrossRef]

T. Erdogan, “Cladding-mode resonances in short and long period fiber grating filters,” J. Opt. Soc. Am. A14(8), 1760–1773 (1997).
[CrossRef]

S. Maruo, O. Nakamura, and S. Kawata, “Evanescent-wave holography by use of surface-plasmon resonance,” Appl. Opt.36(11), 2343–2346 (1997).
[CrossRef] [PubMed]

1995 (2)

D. Sun, J. Manges, Xingchao Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag.37(5), 12–24 (1995).
[CrossRef]

J. Homola, “Optical fiber sensor based on surface plasmon excitation,” Sens. Actuators B Chem.29(1-3), 401–405 (1995).
[CrossRef]

1993 (1)

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode Propagation for Large refractive index steps,” IEEE Photon. Technol. Lett.5(5), 554–557 (1993).
[CrossRef]

1991 (1)

C. H. Herry and Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron.27(3), 523–530 (1991).
[CrossRef]

Alonso, R.

Cendes, Z.

D. Sun, J. Manges, Xingchao Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag.37(5), 12–24 (1995).
[CrossRef]

Chen, K.-F.

S.-M. Tseng, K.-Y. Hsu, H.-S. Wei, and K.-F. Chen, “Analysis and experiment of thin metal-clad fiber polarizer with index overlay,” IEEE Photon. Technol. Lett.9(5), 628–630 (1997).
[CrossRef]

Ctyroký, J.

R. Slavík, J. Homola, and J. Čtyroký, “Single-mode optical fiber surface plasmon resonance sensor,” Sens. Actuators B Chem.54(1-2), 74–79 (1999).
[CrossRef]

Erdogan, T.

Esteban, Ó.

Felici, T. P.

D. F. G. Gallagher and T. P. Felici, “Eigenmode expansion methods for simulation of optical propagation in photonics-Pros and cons,” Proc. SPIE4987, 69–82 (2003).
[CrossRef]

Gallagher, D. F. G.

D. F. G. Gallagher and T. P. Felici, “Eigenmode expansion methods for simulation of optical propagation in photonics-Pros and cons,” Proc. SPIE4987, 69–82 (2003).
[CrossRef]

González-Cano, A.

He, Y. J.

Herry, C. H.

C. H. Herry and Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron.27(3), 523–530 (1991).
[CrossRef]

Homola, J.

R. Slavík, J. Homola, and J. Čtyroký, “Single-mode optical fiber surface plasmon resonance sensor,” Sens. Actuators B Chem.54(1-2), 74–79 (1999).
[CrossRef]

J. Homola, “Optical fiber sensor based on surface plasmon excitation,” Sens. Actuators B Chem.29(1-3), 401–405 (1995).
[CrossRef]

Hsu, K.-Y.

S.-M. Tseng, K.-Y. Hsu, H.-S. Wei, and K.-F. Chen, “Analysis and experiment of thin metal-clad fiber polarizer with index overlay,” IEEE Photon. Technol. Lett.9(5), 628–630 (1997).
[CrossRef]

Huang, J. F.

Kabashin, A. V.

Kawata, S.

Lo, Y. L.

Lowe, C. R.

A. J. C. Tubb, F. P. Payne, R. B. Millington, and C. R. Lowe, “Single-mode optical fibre surface plasma wave chemical sensor,” Sens. Actuators B Chem.41(1-3), 71–79 (1997).
[CrossRef]

Luong, J. H.

Manges, J.

D. Sun, J. Manges, Xingchao Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag.37(5), 12–24 (1995).
[CrossRef]

Maruo, S.

Meunier, M.

Millington, R. B.

A. J. C. Tubb, F. P. Payne, R. B. Millington, and C. R. Lowe, “Single-mode optical fibre surface plasma wave chemical sensor,” Sens. Actuators B Chem.41(1-3), 71–79 (1997).
[CrossRef]

Nakamura, O.

Navarrete, M. C.

Nolting, H. P.

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode Propagation for Large refractive index steps,” IEEE Photon. Technol. Lett.5(5), 554–557 (1993).
[CrossRef]

Patskovsky, S.

Payne, F. P.

A. J. C. Tubb, F. P. Payne, R. B. Millington, and C. R. Lowe, “Single-mode optical fibre surface plasma wave chemical sensor,” Sens. Actuators B Chem.41(1-3), 71–79 (1997).
[CrossRef]

Shani, Y.

C. H. Herry and Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron.27(3), 523–530 (1991).
[CrossRef]

Slavík, R.

R. Slavík, J. Homola, and J. Čtyroký, “Single-mode optical fiber surface plasmon resonance sensor,” Sens. Actuators B Chem.54(1-2), 74–79 (1999).
[CrossRef]

Sun, D.

D. Sun, J. Manges, Xingchao Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag.37(5), 12–24 (1995).
[CrossRef]

Sztefka, G.

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode Propagation for Large refractive index steps,” IEEE Photon. Technol. Lett.5(5), 554–557 (1993).
[CrossRef]

Tseng, S.-M.

S.-M. Tseng, K.-Y. Hsu, H.-S. Wei, and K.-F. Chen, “Analysis and experiment of thin metal-clad fiber polarizer with index overlay,” IEEE Photon. Technol. Lett.9(5), 628–630 (1997).
[CrossRef]

Tubb, A. J. C.

A. J. C. Tubb, F. P. Payne, R. B. Millington, and C. R. Lowe, “Single-mode optical fibre surface plasma wave chemical sensor,” Sens. Actuators B Chem.41(1-3), 71–79 (1997).
[CrossRef]

Wei, H.-S.

S.-M. Tseng, K.-Y. Hsu, H.-S. Wei, and K.-F. Chen, “Analysis and experiment of thin metal-clad fiber polarizer with index overlay,” IEEE Photon. Technol. Lett.9(5), 628–630 (1997).
[CrossRef]

Xingchao Yuan,

D. Sun, J. Manges, Xingchao Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag.37(5), 12–24 (1995).
[CrossRef]

Appl. Opt. (2)

IEEE Antennas Propag. Mag. (1)

D. Sun, J. Manges, Xingchao Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag.37(5), 12–24 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. H. Herry and Y. Shani, “Analysis of mode propagation in optical waveguide devices by Fourier expansion,” IEEE J. Quantum Electron.27(3), 523–530 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

G. Sztefka and H. P. Nolting, “Bidirectional eigenmode Propagation for Large refractive index steps,” IEEE Photon. Technol. Lett.5(5), 554–557 (1993).
[CrossRef]

S.-M. Tseng, K.-Y. Hsu, H.-S. Wei, and K.-F. Chen, “Analysis and experiment of thin metal-clad fiber polarizer with index overlay,” IEEE Photon. Technol. Lett.9(5), 628–630 (1997).
[CrossRef]

J. Lightwave Technol. (2)

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

J. Opt. Soc. Am. B (1)

Proc. SPIE (1)

D. F. G. Gallagher and T. P. Felici, “Eigenmode expansion methods for simulation of optical propagation in photonics-Pros and cons,” Proc. SPIE4987, 69–82 (2003).
[CrossRef]

Sens. Actuators B Chem. (3)

A. J. C. Tubb, F. P. Payne, R. B. Millington, and C. R. Lowe, “Single-mode optical fibre surface plasma wave chemical sensor,” Sens. Actuators B Chem.41(1-3), 71–79 (1997).
[CrossRef]

J. Homola, “Optical fiber sensor based on surface plasmon excitation,” Sens. Actuators B Chem.29(1-3), 401–405 (1995).
[CrossRef]

R. Slavík, J. Homola, and J. Čtyroký, “Single-mode optical fiber surface plasmon resonance sensor,” Sens. Actuators B Chem.54(1-2), 74–79 (1999).
[CrossRef]

Other (1)

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

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Figures (29)

Fig. 1
Fig. 1

The relationship between the refractive index and the wavelength of gold.

Fig. 2
Fig. 2

The geometric structure and parameter schematic of typical fibers and LPG-SPR sensors.

Fig. 3
Fig. 3

The triangular cut of the fiber cross-section (X-Y plane) structure performed using the finite element method.

Fig. 4
Fig. 4

The 2D power distribution of the core mode (HE11) with an effective refractive index of n eff core =1.43944.

Fig. 5
Fig. 5

The 3D power distribution of the core mode (HE11) with an effective refractive index of n eff core =1.43944.

Fig. 6
Fig. 6

The 2D power distribution of the SPW (ν = 9) with an effective refractive index of n eff SPW =1.412378+j0.0001421444.

Fig. 7
Fig. 7

The 3D power distribution of the SPW (ν = 9) with an effective refractive index of n eff SPW =1.412378+j0.0001421444.

Fig. 8
Fig. 8

The relationships between the orthogonal values of the 20 modes.

Fig. 9
Fig. 9

Each cut block object in a segment object is considered a uniform waveguide with a fixed refractive index.

Fig. 10
Fig. 10

Cutting schematic for the LPG propagation direction in LPG-SPR periodic object.

Fig. 11
Fig. 11

Fourier series expansion for the forward and backward propagation modes.

Fig. 12
Fig. 12

The relationship between the field strength of the two adjacent uniform block objects Bkk-1 and Bkk.

Fig. 13
Fig. 13

The relationships between Fourier series expansion position and power loss for the eigenmode expansion method that employed 20 guided modes.

Fig. 14
Fig. 14

Flowchart of the LPG-SPR sensor design and analysis.

Fig. 15
Fig. 15

The X-Z plane geometric structure of LPG-SPR sensor.

Fig. 16
Fig. 16

The transmission power and LPG period relationship of the core mode fully coupled to SPW, ν = 9, of the same propagation direction.

Fig. 17
Fig. 17

The transmission power and LPG period number relationship of the core mode fully coupled to the SPW, ν = 9, of the same propagation direction.

Fig. 18
Fig. 18

The X-Z plane power transmission of the core mode fully coupled to the SPW, ν = 9, of the same propagation direction.

Fig. 19
Fig. 19

The 2D power distribution of the SPW at z = 990 μm.

Fig. 20
Fig. 20

The 3D power distribution of the SPW at z = 990 μm.

Fig. 21
Fig. 21

The 2D power distribution of the SPW at z = 1100 μm.

Fig. 22
Fig. 22

The 3D power distribution of the SPW at z = 1100 μm.

Fig. 23
Fig. 23

The 2D power distribution of the SPW at z = 1379.64571 μm.

Fig. 24
Fig. 24

The 3D power distribution of the SPW at z = 1379.64571 μm.

Fig. 25
Fig. 25

The relationships between the orthogonal values of the 20 modes.

Fig. 26
Fig. 26

The relationships between the Fourier series expansion positions and power losses of the core mode fully coupled to the SPW, ν = 9, of the same propagation direction.

Fig. 27
Fig. 27

Spectrum graph of the core mode fully coupled to the SPW, ν = 9, of the same propagation direction.

Fig. 28
Fig. 28

Spectrum changes for the SPW, ν = 9, of the same propagation direction when the analyte refractive index n4 changed.

Fig. 29
Fig. 29

The relationships between the analyte refractive index n4 and the SPW’s resonance wavelength.

Equations (13)

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n 1 (z)= n 1 +δn[ 1+cos( 2π Λ z) ].
d A μ dz =i A ν K νμ exp[ i( β ν β μ )z ]
K νμ = w 2 Δε A ( E r ν E r μ + E φ ν E φ μ )dA Δε Δε+ε A ( E z ν E z μ )dA 0 2π 0 ( E r μ H φ μ E φ μ H r μ )dA .
t = = | R(z) | 2 | R(0) | 2 ,
t × = | S(z) | 2 | R(0) | 2 .
A E tν × H tμ z ^ dA= A E tμ × H tν z ^ dA=0forνμ
E(x,y,z)= Φ n (x,y) e i β n z
B k k (+) = n=1 m C n f Φ n ( x,y ) e i β n z
B k k () = n=1 m C n b Φ n ( x,y ) e i β n z
E(x,y,z)= n=1 m ( C n f e i β n z + C n b e i β n z ) E n (x,y)
H(x,y,z)= n=1 m ( C n f e i β n z C n b e i β n z ) H n (x,y)
[ B k k1 () B k k (+) ]= J k1 [ B k k1 (+) B k k () ]
λ D = λ max [ n eff core Re( n eff SPW ) ]Λ

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