Abstract

A rigorous theoretical analysis of a fiber optic surface plasmon resonance sensor is presented. The sensor is based on the spectroscopy of mixed surface plasmon – fiber cladding modes excited by the fundamental mode of an optical fiber via a Bragg grating formed in the fiber core. The transmission spectrum is calculated by means of the Coupled Mode Theory. The modal structure is theoretically analyzed using a 3-D method based on a field expansion approach for matching the field continuity at the boundary of the layers. The theoretical analysis revealed a series of narrow transmission dips associated with the coupling of the fundamental mode to the mixed surface plasmon – fiber cladding modes. The sensitivity of these dips to changes in the refractive index of the analyte is calculated. Moreover, the refractive index resolution of the sensor was estimated to be better than 2 × 10−6 RIU.

© 2009 OSA

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References

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  1. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
    [CrossRef] [PubMed]
  2. R. C. Jorgenson and S. S. Yee, “A fiber optic chemical sensor-based on surface plasmon resonance,” Sens. Actuators B Chem. 12(3), 213–220 (1993).
    [CrossRef]
  3. J. Homola, “Optical-fiber sensor-based on surface-plasmon excitation,” Sens. Actuators B Chem. 29(1-3), 401–405 (1995).
    [CrossRef]
  4. M. Piliarik, J. Homola, Z. Maníková, and J. Čtyroký, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003).
    [CrossRef]
  5. R. Slavík, J. Homola, J. Čtyroký, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sensors and Actuators B 74(1-3), 106–111 (2001).
    [CrossRef]
  6. W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, “The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor,” Sens. Actuators A Phys. 84(3), 198–204 (2000).
    [CrossRef]
  7. J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
    [CrossRef]
  8. Y. J. He, Y. L. Lo, and J. F. Huang, “Optical-fiber surface-plasmon-resonance sensor employing long-period fiber gratings in multiplexing,” J. Opt. Soc. Am. B 23(5), 801–811 (2006).
    [CrossRef]
  9. M. L. Nesterov, A. V. Kats, and S. K. Turitsyn, “Extremely short-length surface plasmon resonance devices,” Opt. Express 16(25), 20227–20240 (2008).
    [CrossRef] [PubMed]
  10. G. Nemova and R. Kashyap, “Fiber-Bragg-grating-assisted surface plasmon-polariton sensor,” Opt. Lett. 31(14), 2118–2120 (2006).
    [CrossRef] [PubMed]
  11. J. Čtyroký, F. Abdelmalek, W. Ecke, and K. Usbeck, “Modelling of the surface plasmon resonance waveguide sensor with Bragg grating,” Opt. Quantum Electron. 31(9/10), 927–941 (1999).
    [CrossRef]
  12. Y. Y. Shevchenko and J. Albert, “Plasmon resonances in gold-coated tilted fiber Bragg gratings,” Opt. Lett. 32(3), 211–213 (2007).
    [CrossRef] [PubMed]
  13. B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
    [CrossRef]
  14. A. Yariv, “Coupled-mode theory for Guided-Wave Optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
    [CrossRef]
  15. K. Iizuka, Elements of Photonics, Volume II: For Fiber and Integrated Optics (John Wiley & Sons, Inc., 2002).
  16. Wolfram Research, Inc., http://functions.wolfram.com .
  17. Wolfram Research, Inc., http://mathworld.wolfram.com .
  18. A. Othonos, and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).
  19. P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High-pressure H-2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29(13), 1191–1193 (1993).
    [CrossRef]
  20. M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
    [CrossRef] [PubMed]

2009

B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
[CrossRef]

M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
[CrossRef] [PubMed]

2008

M. L. Nesterov, A. V. Kats, and S. K. Turitsyn, “Extremely short-length surface plasmon resonance devices,” Opt. Express 16(25), 20227–20240 (2008).
[CrossRef] [PubMed]

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[CrossRef] [PubMed]

2007

2006

2003

M. Piliarik, J. Homola, Z. Maníková, and J. Čtyroký, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003).
[CrossRef]

2001

R. Slavík, J. Homola, J. Čtyroký, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sensors and Actuators B 74(1-3), 106–111 (2001).
[CrossRef]

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

2000

W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, “The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor,” Sens. Actuators A Phys. 84(3), 198–204 (2000).
[CrossRef]

1999

J. Čtyroký, F. Abdelmalek, W. Ecke, and K. Usbeck, “Modelling of the surface plasmon resonance waveguide sensor with Bragg grating,” Opt. Quantum Electron. 31(9/10), 927–941 (1999).
[CrossRef]

1995

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

1993

R. C. Jorgenson and S. S. Yee, “A fiber optic chemical sensor-based on surface plasmon resonance,” Sens. Actuators B Chem. 12(3), 213–220 (1993).
[CrossRef]

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High-pressure H-2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29(13), 1191–1193 (1993).
[CrossRef]

1973

A. Yariv, “Coupled-mode theory for Guided-Wave Optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[CrossRef]

Abdelmalek, F.

J. Čtyroký, F. Abdelmalek, W. Ecke, and K. Usbeck, “Modelling of the surface plasmon resonance waveguide sensor with Bragg grating,” Opt. Quantum Electron. 31(9/10), 927–941 (1999).
[CrossRef]

Albert, J.

Atkins, R. M.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High-pressure H-2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29(13), 1191–1193 (1993).
[CrossRef]

Brynda, E.

R. Slavík, J. Homola, J. Čtyroký, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sensors and Actuators B 74(1-3), 106–111 (2001).
[CrossRef]

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

Ctyroký, J.

M. Piliarik, J. Homola, Z. Maníková, and J. Čtyroký, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003).
[CrossRef]

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

R. Slavík, J. Homola, J. Čtyroký, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sensors and Actuators B 74(1-3), 106–111 (2001).
[CrossRef]

J. Čtyroký, F. Abdelmalek, W. Ecke, and K. Usbeck, “Modelling of the surface plasmon resonance waveguide sensor with Bragg grating,” Opt. Quantum Electron. 31(9/10), 927–941 (1999).
[CrossRef]

Dostálek, J.

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

Ecke, W.

J. Čtyroký, F. Abdelmalek, W. Ecke, and K. Usbeck, “Modelling of the surface plasmon resonance waveguide sensor with Bragg grating,” Opt. Quantum Electron. 31(9/10), 927–941 (1999).
[CrossRef]

Gagnaire, A.

W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, “The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor,” Sens. Actuators A Phys. 84(3), 198–204 (2000).
[CrossRef]

Gagnaire, H.

W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, “The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor,” Sens. Actuators A Phys. 84(3), 198–204 (2000).
[CrossRef]

He, Y. J.

Homola, J.

B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
[CrossRef]

M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
[CrossRef] [PubMed]

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[CrossRef] [PubMed]

M. Piliarik, J. Homola, Z. Maníková, and J. Čtyroký, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003).
[CrossRef]

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

R. Slavík, J. Homola, J. Čtyroký, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sensors and Actuators B 74(1-3), 106–111 (2001).
[CrossRef]

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

Huang, J. F.

Jaffrezic-Renault, N.

W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, “The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor,” Sens. Actuators A Phys. 84(3), 198–204 (2000).
[CrossRef]

Jorgenson, R. C.

R. C. Jorgenson and S. S. Yee, “A fiber optic chemical sensor-based on surface plasmon resonance,” Sens. Actuators B Chem. 12(3), 213–220 (1993).
[CrossRef]

Kashyap, R.

Kats, A. V.

Kvasnicka, P.

B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
[CrossRef]

Lemaire, P. J.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High-pressure H-2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29(13), 1191–1193 (1993).
[CrossRef]

Lin, W. B.

W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, “The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor,” Sens. Actuators A Phys. 84(3), 198–204 (2000).
[CrossRef]

Lo, Y. L.

Maníková, Z.

M. Piliarik, J. Homola, Z. Maníková, and J. Čtyroký, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003).
[CrossRef]

Mizrahi, V.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High-pressure H-2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29(13), 1191–1193 (1993).
[CrossRef]

Nekvindová, P.

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

Nemova, G.

Nesterov, M. L.

Piliarik, M.

B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
[CrossRef]

M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
[CrossRef] [PubMed]

M. Piliarik, J. Homola, Z. Maníková, and J. Čtyroký, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003).
[CrossRef]

Rajarajan, M.

B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
[CrossRef]

Reed, W. A.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High-pressure H-2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29(13), 1191–1193 (1993).
[CrossRef]

Schrofel, J.

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

Shevchenko, Y. Y.

Skalský, M.

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

Škvor, J.

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

Slavík, R.

R. Slavík, J. Homola, J. Čtyroký, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sensors and Actuators B 74(1-3), 106–111 (2001).
[CrossRef]

Špacková, B.

B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
[CrossRef]

Špirková, J.

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

Themistos, C.

B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
[CrossRef]

Turitsyn, S. K.

Usbeck, K.

J. Čtyroký, F. Abdelmalek, W. Ecke, and K. Usbeck, “Modelling of the surface plasmon resonance waveguide sensor with Bragg grating,” Opt. Quantum Electron. 31(9/10), 927–941 (1999).
[CrossRef]

Yariv, A.

A. Yariv, “Coupled-mode theory for Guided-Wave Optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[CrossRef]

Yee, S. S.

R. C. Jorgenson and S. S. Yee, “A fiber optic chemical sensor-based on surface plasmon resonance,” Sens. Actuators B Chem. 12(3), 213–220 (1993).
[CrossRef]

Chem. Rev.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[CrossRef] [PubMed]

Electron. Lett.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, and W. A. Reed, “High-pressure H-2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibers,” Electron. Lett. 29(13), 1191–1193 (1993).
[CrossRef]

IEEE J. Quantum Electron.

A. Yariv, “Coupled-mode theory for Guided-Wave Optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

J. Čtyroký, F. Abdelmalek, W. Ecke, and K. Usbeck, “Modelling of the surface plasmon resonance waveguide sensor with Bragg grating,” Opt. Quantum Electron. 31(9/10), 927–941 (1999).
[CrossRef]

Sens. Actuators A Phys.

W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, “The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor,” Sens. Actuators A Phys. 84(3), 198–204 (2000).
[CrossRef]

Sens. Actuators B Chem.

J. Dostálek, J. Čtyroký, J. Homola, E. Brynda, M. Skalský, P. Nekvindová, J. Špirková, J. Škvor, and J. Schrofel, “Surface plasmon resonance biosensor based on integrated optical waveguide,” Sens. Actuators B Chem. 76(1-3), 8–12 (2001).
[CrossRef]

B. Špačková, M. Piliarik, P. Kvasnička, C. Themistos, M. Rajarajan, and J. Homola, “Novel concept of multi-channel fiber optic surface plasmon resonance sensor,” Sens. Actuators B Chem. 139(1), 199–203 (2009).
[CrossRef]

R. C. Jorgenson and S. S. Yee, “A fiber optic chemical sensor-based on surface plasmon resonance,” Sens. Actuators B Chem. 12(3), 213–220 (1993).
[CrossRef]

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

M. Piliarik, J. Homola, Z. Maníková, and J. Čtyroký, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003).
[CrossRef]

Sensors and Actuators B

R. Slavík, J. Homola, J. Čtyroký, and E. Brynda, “Novel spectral fiber optic sensor based on surface plasmon resonance,” Sensors and Actuators B 74(1-3), 106–111 (2001).
[CrossRef]

Other

K. Iizuka, Elements of Photonics, Volume II: For Fiber and Integrated Optics (John Wiley & Sons, Inc., 2002).

Wolfram Research, Inc., http://functions.wolfram.com .

Wolfram Research, Inc., http://mathworld.wolfram.com .

A. Othonos, and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the sensing fiber optic structure

Fig. 2
Fig. 2

Azimuthal distribution of the magnetic field of the 138th – 140th mode (top). Distribution of the real part of the refractive index (bottom).

Fig. 3
Fig. 3

Attenuation of the even and odd (inset) modes for different rg .

Fig. 4
Fig. 4

Coupling constant of the 134th – 146th mode for rg = 20 - 40 nm. Coupling constant for all the cladding modes for rg = 40 nm (inset).

Fig. 5
Fig. 5

Part of the transmission spectrum which corresponds to 134th - 146th mode for rg = 20 - 40 nm. Transmission spectrum which corresponds to the core and all the cladding modes for rg = 40 nm (inset). L = 2 mm, Δε = 10−2, nsur = 1.325.

Fig. 6
Fig. 6

Transmission spectrum which corresponds to 134th - 146th cladding modes. rg = 30nm, nsur = 1.325, L = 2mm, Δε = 10−2.

Fig. 7
Fig. 7

Normalized transmission spectrum as a function of refractive index of surrounding medium. rg = 30nm, L = 2mm, Δε = 10−2.

Fig. 8
Fig. 8

Sensitivity of 134th - 140th cladding mode as a function of rg. nsur = 1.325. Resonant wavelength of 136th and 137th cladding modes as a function of rg (inset).

Fig. 9
Fig. 9

FWHM wμ of the transmission dip corresponding to 134th - 140th cladding mode as a function of rg. (solid line, left axes). The transmittance at a resonance T μ r e s corresponding to the mode 134th - 140th cladding mode as a function of rg. . (dashed line, right axes). nsur = 1.325.

Equations (17)

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

λ r e s μ = ( n e f f 1 + n e f f μ ) Λ ,
E z = [ A I 1 ( γ r ) + B K 1 ( γ r ) ] cos ( φ ) exp ( i β z ) H z = [ C I 1 ( γ r ) + D K 1 ( γ r ) ] sin ( φ ) exp ( i β z ) E φ = [ a r A I 1 ( γ r ) + a r B K 1 ( γ r ) + b C I 1 ' ( γ r ) + b D K 1 ' ( γ r ) ] sin ( φ ) exp ( i β z ) H φ = [ c A I 1 ' ( γ r ) + c B K 1 ' ( γ r ) + a r C I 1 ( γ r ) + a r D K 1 ( γ r ) ] cos ( φ ) exp ( i β z ) I 1 ' ( γ r ) = γ I 0 I 1 r , K 1 ' ( γ r ) = γ K 0 K 1 r γ = k 0 n e f f 2 ε , a = β γ 2 , b = i ω μ γ 2 , c = i ω ε γ 2 ,
det ( A 1 1 - B 1 2 0 0 0 B 2 2 - B 2 3 0 0 0 B 3 3 - C 3 4 ) = 0
A 1 1 = ( I 1 ( γ 1 r 1 ) 0 0 I 1 ( γ 1 r 1 ) a 1 r 1 I 1 ( γ 1 r 1 ) b 1 I 1 ' ( γ 1 r 1 ) c 1 I 1 ' ( γ 1 r 1 ) a 1 r 1 I 1 ( γ 1 r 1 ) )
B k l = ( 1 1 0 0 0 0 1 1 a l r k a l r k b l I 1 ' ( γ l r k ) I 1 ( γ l r k ) b l I 1 ' ( γ l r k ) I 1 ( γ l r k ) c l I 1 ' ( γ l r k ) I 1 ( γ l r k ) c l K 1 ' ( γ l r k ) K 1 ( γ l r k ) a l r k a l r k ) , k l
B k k = ( 1 1 0 0 0 0 1 1 a k r k I 1 ( γ k r k ) I 1 ( γ l r k ) a k r k K 1 ( γ k r k ) K 1 ( γ l r k ) b k I 1 ' ( γ k r k ) I 1 ( γ l r k ) b k I 1 ' ( γ k r k ) I 1 ( γ l r k ) c k I 1 ' ( γ k r k ) I 1 ( γ l r k ) c k K 1 ' ( γ k r k ) K 1 ( γ l r k ) a k r k I 1 ( γ k r k ) I 1 ( γ l r k ) a k r k K 1 ( γ k r k ) K 1 ( γ l r k ) ) , k l
C 34 = ( K 1 ( γ 4 r 3 ) 0 0 K 1 ( γ 4 r 3 ) a 4 r 3 K 1 ( γ 4 r 3 ) b 4 K 1 ' ( γ 4 r 3 ) c 4 K 1 ' ( γ 4 r 3 ) a 4 r 3 K 1 ( γ 4 r 3 ) )
K ν ( α ) K η ( β ) = β α S ν ( α ) S η ( β ) exp ( β α ) I ν ( α ) I η ( β ) = β α S ν + ( α ) exp ( α ) + i | α | α S ν ( α ) exp ( α ) S η + ( β ) exp ( β ) + i | β | β S η ( β ) exp ( β )       | α | , | β | β α S ν + ( α ) S η + ( β ) exp ( α β ) S ν ± ( α ) = k = 0 n ( ν + 1 2 ) k ( 1 2 ν ) k k ! ( ± 1 2 α ) k + O ( 1 α n + 1 ) .
T μ = | δ exp ( 1 2 i L Δ β 1 μ ) 1 2 i Δ β 1 μ sin ( δ L ) δ cos ( δ L ) | 2
δ = ( Δ β 1 μ 2 ) 2 | κ 1 μ | 2 ,
Δ β 1 μ = β 1 + β μ 2 π Λ .
κ 1 μ = i ω ε 0 4 | β μ | β μ A Δ ε e 1 e μ ,
T μ r e s = | 1 cos ( i | κ 1 μ | L ) | ,
S μ = d λ r e s μ d n s u r
S μ = Λ d { n e f f μ ( λ r e s μ ) } d n s u r .
A = K r s σ I ( t h ) I 0 N ,
B = w μ 1 T μ r e s 1 S μ .

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