Abstract

By coating a single-mode–multimode–single-mode (SMS) structure with a high refractive index thin-film it is possible to obtain a transition of modes for specific combinations of thin-film thickness, thin-film refractive index and surrounding medium refractive index, which permits to develop devices with a high sensitivity to specific parameters. In order to gain a better knowledge of the phenomenon the experimental results are corroborated numerically with the Transfer-Matrix-Method. The influence of losses in the thin-film has also been studied. The results obtained prove that a thin-film coated SMS structure is a simple and cost-effective platform for development of sensors and optical filters.

© 2013 OSA

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    [CrossRef]

2012

2011

Q. Wu, Y. Semenova, P. Wang, and G. Farrell, “High sensitivity SMS fiber structure based refractometer--analysis and experiment,” Opt. Express19(9), 7937–7944 (2011).
[CrossRef] [PubMed]

C. R. Zamarreño, M. Hernáez, I. Del Villar, I. R. Matías, and F. J. Arregui, “Optical fiber pH sensor based on lossy-mode resonances by means of thin polymeric coatings,” Sens. Actuators B Chem.155(1), 290–297 (2011).
[CrossRef]

Q. Wu, Y. Semenova, P. Wang, A. M. Hatta, and G. Farrell, “Experimental demonstration of a simple displacement sensor based on a bent single-mode–multimode–single-mode fiber structure,” Meas. Sci. Technol.22(2), 025203 (2011).
[CrossRef]

Q. Wu, Y. Semenova, A. M. Hatta, P. Wang, and G. Farrell, “Single-mode–multimode–singlemode fiber structures for simultaneous measurement of strain and temperature,” Microw. Opt. Technol. Lett.53(9), 2181–2185 (2011).
[CrossRef]

V. I. Ruiz-Pérez, M. A. Basurto-Pensado, P. LiKamWa, J. J. Sánchez-Mondragón, and D. A. May-Arrioja, “Fiber optic pressure sensor using multimode interference,” J. Phys. Conf. Ser.274, 012025 (2011).
[CrossRef]

2010

2007

2006

2005

I. Del Villar, I. R. Matias, F. J. Arregui, and M. Achaerandio, “Nanodeposition of materials with complex refractive index in long-period fiber gratings,” J. Lightwave Technol.23(12), 4192–4199 (2005).
[CrossRef]

I. Del Villar, I. R. Matias, F. J. Arregui, and R. O. Claus, “Fiber-optic hydrogen peroxide nanosensor,” IEEE Sens. J.5(3), 365–371 (2005).
[CrossRef]

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
[CrossRef]

I. Del Villar, I. R. Matías, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Express13(1), 56–69 (2005).
[CrossRef] [PubMed]

2003

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett.15(8), 1129–1131 (2003).
[CrossRef]

2002

1999

1997

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

G. Decher, “Fuzzy nanoassemblies: toward layered polymeric multicomposites,” Science277(5330), 1232–1237 (1997).
[CrossRef]

1995

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.13(4), 615–627 (1995).
[CrossRef]

1978

Achaerandio, M.

Antonio-Lopez, J. E.

Arregui, F. J.

A. B. Socorro, I. Del Villar, J. M. Corres, F. J. Arregui, and I. R. Matias, “Lossy mode resonances dependence on the geometry of a tapered monomode optical fiber,” Sens. Actuators A Phys.180, 25–31 (2012).
[CrossRef]

C. R. Zamarreño, M. Hernáez, I. Del Villar, I. R. Matías, and F. J. Arregui, “Optical fiber pH sensor based on lossy-mode resonances by means of thin polymeric coatings,” Sens. Actuators B Chem.155(1), 290–297 (2011).
[CrossRef]

J. M. Corres, I. del Villar, I. R. Matias, and F. J. Arregui, “Fiber-optic pH-sensors in long-period fiber gratings using electrostatic self-assembly,” Opt. Lett.32(1), 29–31 (2007).
[CrossRef] [PubMed]

I. Del Villar, I. R. Matias, F. J. Arregui, and M. Achaerandio, “Nanodeposition of materials with complex refractive index in long-period fiber gratings,” J. Lightwave Technol.23(12), 4192–4199 (2005).
[CrossRef]

I. Del Villar, I. R. Matías, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Express13(1), 56–69 (2005).
[CrossRef] [PubMed]

I. Del Villar, I. R. Matias, F. J. Arregui, and R. O. Claus, “Fiber-optic hydrogen peroxide nanosensor,” IEEE Sens. J.5(3), 365–371 (2005).
[CrossRef]

Ashwell, G. J.

Basurto-Pensado, M. A.

V. I. Ruiz-Pérez, M. A. Basurto-Pensado, P. LiKamWa, J. J. Sánchez-Mondragón, and D. A. May-Arrioja, “Fiber optic pressure sensor using multimode interference,” J. Phys. Conf. Ser.274, 012025 (2011).
[CrossRef]

Biazoli, C. R.

Campopiano, S.

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Mode transition in high refractive index coated long period gratings,” Opt. Express14(1), 19–34 (2006).
[CrossRef] [PubMed]

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
[CrossRef]

Castillo-Guzman, A.

Chern, G. W.

Claus, R. O.

I. Del Villar, I. R. Matias, F. J. Arregui, and R. O. Claus, “Fiber-optic hydrogen peroxide nanosensor,” IEEE Sens. J.5(3), 365–371 (2005).
[CrossRef]

Contessa, L.

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Mode transition in high refractive index coated long period gratings,” Opt. Express14(1), 19–34 (2006).
[CrossRef] [PubMed]

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
[CrossRef]

Cooper, K. L.

D. W. Kim, Y. Zhang, K. L. Cooper, and A. Wang, “Fibre-optic interferometric immuno-sensor using long period grating,” Electron. Lett.42(6), 324–325 (2006).
[CrossRef]

Cordeiro, C. M. B.

Corres, J. M.

A. B. Socorro, I. Del Villar, J. M. Corres, F. J. Arregui, and I. R. Matias, “Lossy mode resonances dependence on the geometry of a tapered monomode optical fiber,” Sens. Actuators A Phys.180, 25–31 (2012).
[CrossRef]

J. M. Corres, I. del Villar, I. R. Matias, and F. J. Arregui, “Fiber-optic pH-sensors in long-period fiber gratings using electrostatic self-assembly,” Opt. Lett.32(1), 29–31 (2007).
[CrossRef] [PubMed]

Cusano, A.

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Mode transition in high refractive index coated long period gratings,” Opt. Express14(1), 19–34 (2006).
[CrossRef] [PubMed]

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
[CrossRef]

Cutolo, A.

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Mode transition in high refractive index coated long period gratings,” Opt. Express14(1), 19–34 (2006).
[CrossRef] [PubMed]

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
[CrossRef]

Decher, G.

G. Decher, “Fuzzy nanoassemblies: toward layered polymeric multicomposites,” Science277(5330), 1232–1237 (1997).
[CrossRef]

Del Villar, I.

A. B. Socorro, I. Del Villar, J. M. Corres, F. J. Arregui, and I. R. Matias, “Lossy mode resonances dependence on the geometry of a tapered monomode optical fiber,” Sens. Actuators A Phys.180, 25–31 (2012).
[CrossRef]

C. R. Zamarreño, M. Hernáez, I. Del Villar, I. R. Matías, and F. J. Arregui, “Optical fiber pH sensor based on lossy-mode resonances by means of thin polymeric coatings,” Sens. Actuators B Chem.155(1), 290–297 (2011).
[CrossRef]

J. M. Corres, I. del Villar, I. R. Matias, and F. J. Arregui, “Fiber-optic pH-sensors in long-period fiber gratings using electrostatic self-assembly,” Opt. Lett.32(1), 29–31 (2007).
[CrossRef] [PubMed]

I. Del Villar, I. R. Matias, F. J. Arregui, and R. O. Claus, “Fiber-optic hydrogen peroxide nanosensor,” IEEE Sens. J.5(3), 365–371 (2005).
[CrossRef]

I. Del Villar, I. R. Matias, F. J. Arregui, and M. Achaerandio, “Nanodeposition of materials with complex refractive index in long-period fiber gratings,” J. Lightwave Technol.23(12), 4192–4199 (2005).
[CrossRef]

I. Del Villar, I. R. Matías, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Express13(1), 56–69 (2005).
[CrossRef] [PubMed]

Erdogan, T.

Farrell, G.

Q. Wu, Y. Semenova, A. M. Hatta, P. Wang, and G. Farrell, “Single-mode–multimode–singlemode fiber structures for simultaneous measurement of strain and temperature,” Microw. Opt. Technol. Lett.53(9), 2181–2185 (2011).
[CrossRef]

Q. Wu, Y. Semenova, P. Wang, A. M. Hatta, and G. Farrell, “Experimental demonstration of a simple displacement sensor based on a bent single-mode–multimode–single-mode fiber structure,” Meas. Sci. Technol.22(2), 025203 (2011).
[CrossRef]

Q. Wu, Y. Semenova, P. Wang, and G. Farrell, “High sensitivity SMS fiber structure based refractometer--analysis and experiment,” Opt. Express19(9), 7937–7944 (2011).
[CrossRef] [PubMed]

Franco, M. A. R.

Frazão, O.

Gao, K.

Giordano, M.

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Mode transition in high refractive index coated long period gratings,” Opt. Express14(1), 19–34 (2006).
[CrossRef] [PubMed]

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
[CrossRef]

Gu, X.

Gu, Z.

Hatta, A. M.

Q. Wu, Y. Semenova, P. Wang, A. M. Hatta, and G. Farrell, “Experimental demonstration of a simple displacement sensor based on a bent single-mode–multimode–single-mode fiber structure,” Meas. Sci. Technol.22(2), 025203 (2011).
[CrossRef]

Q. Wu, Y. Semenova, A. M. Hatta, P. Wang, and G. Farrell, “Single-mode–multimode–singlemode fiber structures for simultaneous measurement of strain and temperature,” Microw. Opt. Technol. Lett.53(9), 2181–2185 (2011).
[CrossRef]

Hayashi, J. G.

Hernáez, M.

C. R. Zamarreño, M. Hernáez, I. Del Villar, I. R. Matías, and F. J. Arregui, “Optical fiber pH sensor based on lossy-mode resonances by means of thin polymeric coatings,” Sens. Actuators B Chem.155(1), 290–297 (2011).
[CrossRef]

Iadicicco, A.

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Mode transition in high refractive index coated long period gratings,” Opt. Express14(1), 19–34 (2006).
[CrossRef] [PubMed]

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
[CrossRef]

James, S. W.

Johnson, E. G.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett.15(8), 1129–1131 (2003).
[CrossRef]

Jorge, P.

Kim, D. W.

D. W. Kim, Y. Zhang, K. L. Cooper, and A. Wang, “Fibre-optic interferometric immuno-sensor using long period grating,” Electron. Lett.42(6), 324–325 (2006).
[CrossRef]

Lalanne, P.

LiKamWa, P.

V. I. Ruiz-Pérez, M. A. Basurto-Pensado, P. LiKamWa, J. J. Sánchez-Mondragón, and D. A. May-Arrioja, “Fiber optic pressure sensor using multimode interference,” J. Phys. Conf. Ser.274, 012025 (2011).
[CrossRef]

J. E. Antonio-Lopez, A. Castillo-Guzman, D. A. May-Arrioja, R. Selvas-Aguilar, and P. Likamwa, “Tunable multimode-interference bandpass fiber filter,” Opt. Lett.35(3), 324–326 (2010).
[CrossRef] [PubMed]

Malcata, F. X.

Marom, E.

Matias, I. R.

A. B. Socorro, I. Del Villar, J. M. Corres, F. J. Arregui, and I. R. Matias, “Lossy mode resonances dependence on the geometry of a tapered monomode optical fiber,” Sens. Actuators A Phys.180, 25–31 (2012).
[CrossRef]

J. M. Corres, I. del Villar, I. R. Matias, and F. J. Arregui, “Fiber-optic pH-sensors in long-period fiber gratings using electrostatic self-assembly,” Opt. Lett.32(1), 29–31 (2007).
[CrossRef] [PubMed]

I. Del Villar, I. R. Matias, F. J. Arregui, and R. O. Claus, “Fiber-optic hydrogen peroxide nanosensor,” IEEE Sens. J.5(3), 365–371 (2005).
[CrossRef]

I. Del Villar, I. R. Matias, F. J. Arregui, and M. Achaerandio, “Nanodeposition of materials with complex refractive index in long-period fiber gratings,” J. Lightwave Technol.23(12), 4192–4199 (2005).
[CrossRef]

Matías, I. R.

C. R. Zamarreño, M. Hernáez, I. Del Villar, I. R. Matías, and F. J. Arregui, “Optical fiber pH sensor based on lossy-mode resonances by means of thin polymeric coatings,” Sens. Actuators B Chem.155(1), 290–297 (2011).
[CrossRef]

I. Del Villar, I. R. Matías, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in long period fiber gratings with overlay deposition,” Opt. Express13(1), 56–69 (2005).
[CrossRef] [PubMed]

May-Arrioja, D. A.

V. I. Ruiz-Pérez, M. A. Basurto-Pensado, P. LiKamWa, J. J. Sánchez-Mondragón, and D. A. May-Arrioja, “Fiber optic pressure sensor using multimode interference,” J. Phys. Conf. Ser.274, 012025 (2011).
[CrossRef]

J. E. Antonio-Lopez, A. Castillo-Guzman, D. A. May-Arrioja, R. Selvas-Aguilar, and P. Likamwa, “Tunable multimode-interference bandpass fiber filter,” Opt. Lett.35(3), 324–326 (2010).
[CrossRef] [PubMed]

Mehta, A.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett.15(8), 1129–1131 (2003).
[CrossRef]

Mohammed, W.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett.15(8), 1129–1131 (2003).
[CrossRef]

Mohammed, W. S.

Pachon, E. G. P.

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.13(4), 615–627 (1995).
[CrossRef]

Pilla, P.

A. Cusano, A. Iadicicco, P. Pilla, L. Contessa, S. Campopiano, A. Cutolo, and M. Giordano, “Mode transition in high refractive index coated long period gratings,” Opt. Express14(1), 19–34 (2006).
[CrossRef] [PubMed]

P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
[CrossRef]

Rees, N. D.

Ruiz-Pérez, V. I.

V. I. Ruiz-Pérez, M. A. Basurto-Pensado, P. LiKamWa, J. J. Sánchez-Mondragón, and D. A. May-Arrioja, “Fiber optic pressure sensor using multimode interference,” J. Phys. Conf. Ser.274, 012025 (2011).
[CrossRef]

Sánchez-Mondragón, J. J.

V. I. Ruiz-Pérez, M. A. Basurto-Pensado, P. LiKamWa, J. J. Sánchez-Mondragón, and D. A. May-Arrioja, “Fiber optic pressure sensor using multimode interference,” J. Phys. Conf. Ser.274, 012025 (2011).
[CrossRef]

Selvas-Aguilar, R.

Semenova, Y.

Q. Wu, Y. Semenova, P. Wang, and G. Farrell, “High sensitivity SMS fiber structure based refractometer--analysis and experiment,” Opt. Express19(9), 7937–7944 (2011).
[CrossRef] [PubMed]

Q. Wu, Y. Semenova, A. M. Hatta, P. Wang, and G. Farrell, “Single-mode–multimode–singlemode fiber structures for simultaneous measurement of strain and temperature,” Microw. Opt. Technol. Lett.53(9), 2181–2185 (2011).
[CrossRef]

Q. Wu, Y. Semenova, P. Wang, A. M. Hatta, and G. Farrell, “Experimental demonstration of a simple displacement sensor based on a bent single-mode–multimode–single-mode fiber structure,” Meas. Sci. Technol.22(2), 025203 (2011).
[CrossRef]

Silva, S.

Smith, P. W. E.

Socorro, A. B.

A. B. Socorro, I. Del Villar, J. M. Corres, F. J. Arregui, and I. R. Matias, “Lossy mode resonances dependence on the geometry of a tapered monomode optical fiber,” Sens. Actuators A Phys.180, 25–31 (2012).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.13(4), 615–627 (1995).
[CrossRef]

Tatam, R. P.

Wang, A.

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[CrossRef]

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Q. Wu, Y. Semenova, P. Wang, A. M. Hatta, and G. Farrell, “Experimental demonstration of a simple displacement sensor based on a bent single-mode–multimode–single-mode fiber structure,” Meas. Sci. Technol.22(2), 025203 (2011).
[CrossRef]

Q. Wu, Y. Semenova, A. M. Hatta, P. Wang, and G. Farrell, “Single-mode–multimode–singlemode fiber structures for simultaneous measurement of strain and temperature,” Microw. Opt. Technol. Lett.53(9), 2181–2185 (2011).
[CrossRef]

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[CrossRef] [PubMed]

Wu, Q.

Q. Wu, Y. Semenova, P. Wang, and G. Farrell, “High sensitivity SMS fiber structure based refractometer--analysis and experiment,” Opt. Express19(9), 7937–7944 (2011).
[CrossRef] [PubMed]

Q. Wu, Y. Semenova, A. M. Hatta, P. Wang, and G. Farrell, “Single-mode–multimode–singlemode fiber structures for simultaneous measurement of strain and temperature,” Microw. Opt. Technol. Lett.53(9), 2181–2185 (2011).
[CrossRef]

Q. Wu, Y. Semenova, P. Wang, A. M. Hatta, and G. Farrell, “Experimental demonstration of a simple displacement sensor based on a bent single-mode–multimode–single-mode fiber structure,” Meas. Sci. Technol.22(2), 025203 (2011).
[CrossRef]

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Xue, L. L.

Yang, L.

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Zamarreño, C. R.

C. R. Zamarreño, M. Hernáez, I. Del Villar, I. R. Matías, and F. J. Arregui, “Optical fiber pH sensor based on lossy-mode resonances by means of thin polymeric coatings,” Sens. Actuators B Chem.155(1), 290–297 (2011).
[CrossRef]

Zhang, Y.

D. W. Kim, Y. Zhang, K. L. Cooper, and A. Wang, “Fibre-optic interferometric immuno-sensor using long period grating,” Electron. Lett.42(6), 324–325 (2006).
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D. W. Kim, Y. Zhang, K. L. Cooper, and A. Wang, “Fibre-optic interferometric immuno-sensor using long period grating,” Electron. Lett.42(6), 324–325 (2006).
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P. Pilla, A. Iadicicco, L. Contessa, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, “Optical chemo-sensor based on long period fiber gratings coated with d form syndiotactic polystyrene,” IEEE Photon. Technol. Lett.17(8), 1713–1715 (2005).
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I. Del Villar, I. R. Matias, F. J. Arregui, and R. O. Claus, “Fiber-optic hydrogen peroxide nanosensor,” IEEE Sens. J.5(3), 365–371 (2005).
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Meas. Sci. Technol.

Q. Wu, Y. Semenova, P. Wang, A. M. Hatta, and G. Farrell, “Experimental demonstration of a simple displacement sensor based on a bent single-mode–multimode–single-mode fiber structure,” Meas. Sci. Technol.22(2), 025203 (2011).
[CrossRef]

Microw. Opt. Technol. Lett.

Q. Wu, Y. Semenova, A. M. Hatta, P. Wang, and G. Farrell, “Single-mode–multimode–singlemode fiber structures for simultaneous measurement of strain and temperature,” Microw. Opt. Technol. Lett.53(9), 2181–2185 (2011).
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[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Experimental and theoretical spectra of uncoated SMS structure for different MMF section lengths: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 and 58 mm.

Fig. 3
Fig. 3

Evolution of the spectrum as a function of thickness for an SMS structure of 58 mm (experimental results).

Fig. 4
Fig. 4

Evolution of the spectrum as a function of thickness for an SMS structure of 58 mm (simulation with thin-film refractive index 1.5).

Fig. 5
Fig. 5

Evolution of the spectrum as a function of thickness for an SMS structure of 58 mm (simulation with thin-film refractive index 1.5 + 0.0025i).

Fig. 6
Fig. 6

Evolution as a function of thickness of a) the central wavelength of two transmission bands obtained with an SMS structure of 58 mm b) the maximum power of two transmission bands obtained with an SMS structure of 58 mm.

Fig. 7
Fig. 7

Evolution as a function of thickness of the effective index of modes in the MMF section of an SMS structure (incidence wavelength 1550 nm).

Fig. 8
Fig. 8

Evolution as a function of thickness of the constructive interference wavelengths of mode HE1,1 and HE1,3 in the MMF section of and SMS structure.

Fig. 9
Fig. 9

Evolution as a function of thickness of the coupling between the fundamental mode of the SMF section and the modes in the MMF section in an SMS structure (incidence wavelength 1550 nm).

Fig. 10
Fig. 10

Evolution of the spectrum as a function of thickness for an SMS structure of 20 mm (experimental results).

Fig. 11
Fig. 11

Evolution of the spectrum as a function of thickness for an SMS structure of 20 mm (simulation with thin-film refractive index 1.5).

Fig. 12
Fig. 12

Evolution of the spectrum as a function of thickness for an SMS structure of 20 mm (simulation with thin-film refractive index 1.5 + 0.0025i).

Equations (7)

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( A 11 (c) B 11 (c) A 12 (c) B 12 (c) A 1N (c) B 1N (c) )= H cb F H ba ( A 11 (a) B 11 (a) A 12 (a) B 12 (a) A 1N (a) B 1N (a) )
( A 11 (c) B 11 (c) A 12 (c) B 12 (c) A 0N (c) B 1N (c) )=( 1 2 ( I 11,11 + J 11,11 ) 1 2 ( I 11,11 J 11,11 ) 1 2 ( I 11,12 + J 11,12 ) 1 2 ( I 11,12 J 11,12 ) 1 2 ( I 11,1N + J 11,1N ) 1 2 ( I 11,1N J 11,1N ) 1 2 ( I 11,11 J 11,11 ) 1 2 ( I 11,11 + J 11,11 ) 1 2 ( I 11,12 J 11,12 ) 1 2 ( I 11,12 + J 11,12 ) 1 2 ( I 11,1N + J 11,1N ) 1 2 ( I 11,1N + J 11,1N ) 1 2 ( I 12,11 + J 12,11 ) 1 2 ( I 12,11 J 12,11 ) 1 2 ( I 12,12 + J 12,12 ) 1 2 ( I 12,12 J 12,12 ) 1 2 ( I 12,1N + J 12,1N ) 1 2 ( I 12,1N + J 12,1N ) 1 2 ( I 12,11 J 12,11 ) 1 2 ( I 12,11 + J 12,11 ) 1 2 ( I 12,12 J 12,12 ) 1 2 ( I 12,12 + J 12,12 ) 1 2 ( I 12,1N + J 12,1N ) 1 2 ( I 12,1N + J 12,1N ) 1 2 ( I 1N,11 + J 1N,11 ) 1 2 ( I 1N,11 J 1N,11 ) 1 2 ( I 1N,12 + J 1N,12 ) 1 2 ( I 1N,12 J 1N,12 ) 1 2 ( I 1N,1N + J 1N,1N ) 1 2 ( I 1N,1N + J 1N,1N ) 1 2 ( I 1N,11 J 1N,11 ) 1 2 ( I 1N,11 + J 1N,11 ) 1 2 ( I 1N,12 J 1N,12 ) 1 2 ( I 1N,12 + J 1N,12 ) 1 2 ( I 1N,1N + J 1N,1N ) 1 2 ( I 1N,1N + J 1N,1N ) )( A 11 (b) B 11 (b) A 12 (b) B 12 (b) A 1N (b) A 1N (b) )
I 1k,1j = P 1j 1 P 1k 1 1 2 Re ϕ=0 2π dϕ r=0 [ E 1,jr b ( r ) H 1,kϕ a ( r ) H 1,kr a ( r ) E 1,jϕ b ( r ) ] rdr
J 1k,1j = P 1j 1 P 1k 1 1 2 Re ϕ=0 2π dϕ r=0 [ E 1,jr a ( r ) H 1,kϕ b ( r ) H 1,kr b ( r ) E 1,jϕ a ( r ) ] rdr
F=( exp(j β 11 L) 0 0 0 0 0 0 exp(j β 11 L) 0 0 0 0 0 0 exp(j β 12 L) 0 0 0 0 0 0 exp(j β 12 L) 0 0 0 0 0 0 exp(j β 1N L) 0 0 0 0 0 0 exp(j β 1N L) )
T= | A 11 c | 2
Z i = 4 D 2 n λ

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