Abstract

We present a compact in-line fiber interferometric sensor fabricated in a boron doped two-mode highly birefringent microstructured fiber using a CO2 laser. The intermodal interference arises at the fiber output due to coupling between the fundamental and the first order modes occurring at two fiber tapers distant by a few millimeters. The visibility of intermodal interference fringes is modulated by a polarimetric differential signal and varies in response to measurand changes. The proposed interferometer was tested for measurements of the strain and temperature, respectively, in the range of 20700°C and 017mstrain. The sensitivity coefficients corresponding to fringe displacement and contrast variations are equal respectively for strain 2.51nm/mstrain and 0.02561/mstrain and for temperature 16.7pm/°C and 5.74×1051/°C. This allows for simultaneous measurements of the two parameters by interrogation of the visibility and the displacement of interference fringes.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (2)

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, 075402 (2010).
[CrossRef]

H. Y. Fu, Chuang Wu, M. L. V. Tse, L. Zhang, K.-C. Davis Cheng, H. Y. Tam, B.-O. Guan, and C. Lu, “High pressure sensor based on photonic crystal fiber for downhole application,” Appl. Opt. 49, 2639–2643 (2010).
[CrossRef]

2009 (2)

W. J. Bock, T. Eftimov, P. Mikulic, and J. Chen, “Novel fiber sensor based on in-line core-cladding intermodal interferometer and photonic crystal fiber,” in Proceedings of XIX IMEKO World Congress Fundamental and Applied Metrology (IMEKO, 2009), pp. 65–68.

J. Villatoro, V. Finazzi, G. Badenes, and V. Pruneri, “Highly sensitive sensors based on photonic crystal fiber modal interferometers,” J. Sensors 2009, 747803 (2009).

2008 (3)

2007 (5)

X. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90, 151113 (2007).
[CrossRef]

O. Frazăo, J. M. Baptista, and J. L. Santos, “Temperature-independent strain sensor based on a Hi-Bi photonic crystal fiber loop mirror,” IEEE Sens. J. 7, 1453–1455 (2007).
[CrossRef]

J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91, 091109 (2007).
[CrossRef]

J. Villatoro, V. P. Minkovich, V. Pruneri, and G. Badenes, “Simple all-microstructured-optical-fiber interferometer built via fusion splicing,” Opt. Express 15, 1491–1496 (2007).
[CrossRef] [PubMed]

H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15, 5711–5720 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (1)

2004 (3)

T. Ritari, J. Tuominen, H. Ludvigsen, J. Petersen, T. Sørensen, T. Hansen, and H. Simonsen, “Gas sensing using air-guiding photonic bandgap fibers,” Opt. Express 12, 4080–4087 (2004).
[CrossRef] [PubMed]

J. M. Fini, “Microstructure fibres for optical sensing in gases and liquids,” Meas. Sci. Technol. 15, 1120–1128 (2004).
[CrossRef]

G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Measurements of modal birefringence and polarimetric sensitivity of the birefringent holey fiber to hydrostatic pressure and strain,” Opt. Commun. 241, 339–348 (2004).
[CrossRef]

2003 (1)

P. Hlubina, “White-light spectral interferometry to measure intermodal dispersion in two-mode elliptical-core optical fibres,” Opt. Commun. 218, 283–289 (2003).
[CrossRef]

2001 (1)

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

1983 (1)

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Araújo, F. M.

O. Frazão, J. L. Santos, F. M. Araújo, and L. A. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photon. Rev. 2, 449–459 (2008).
[CrossRef]

Badenes, G.

J. Villatoro, V. Finazzi, G. Badenes, and V. Pruneri, “Highly sensitive sensors based on photonic crystal fiber modal interferometers,” J. Sensors 2009, 747803 (2009).

J. Villatoro, V. P. Minkovich, V. Pruneri, and G. Badenes, “Simple all-microstructured-optical-fiber interferometer built via fusion splicing,” Opt. Express 15, 1491–1496 (2007).
[CrossRef] [PubMed]

J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91, 091109 (2007).
[CrossRef]

Baggett, J. C.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Baptista, J. M.

O. Frazăo, J. M. Baptista, and J. L. Santos, “Temperature-independent strain sensor based on a Hi-Bi photonic crystal fiber loop mirror,” IEEE Sens. J. 7, 1453–1455 (2007).
[CrossRef]

Belardi, W.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

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, 075402 (2010).
[CrossRef]

Bock, W. J.

W. J. Bock, T. Eftimov, P. Mikulic, and J. Chen, “Novel fiber sensor based on in-line core-cladding intermodal interferometer and photonic crystal fiber,” in Proceedings of XIX IMEKO World Congress Fundamental and Applied Metrology (IMEKO, 2009), pp. 65–68.

Broderick, N. G. R.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Calixto, S.

Chen, J.

W. J. Bock, T. Eftimov, P. Mikulic, and J. Chen, “Novel fiber sensor based on in-line core-cladding intermodal interferometer and photonic crystal fiber,” in Proceedings of XIX IMEKO World Congress Fundamental and Applied Metrology (IMEKO, 2009), pp. 65–68.

Cheng, K.-C. Davis

Choi, H. Y.

Dong, X.

X. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90, 151113 (2007).
[CrossRef]

Eftimov, T.

W. J. Bock, T. Eftimov, P. Mikulic, and J. Chen, “Novel fiber sensor based on in-line core-cladding intermodal interferometer and photonic crystal fiber,” in Proceedings of XIX IMEKO World Congress Fundamental and Applied Metrology (IMEKO, 2009), pp. 65–68.

Ferreira, L. A.

O. Frazão, J. L. Santos, F. M. Araújo, and L. A. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photon. Rev. 2, 449–459 (2008).
[CrossRef]

Finazzi, V.

J. Villatoro, V. Finazzi, G. Badenes, and V. Pruneri, “Highly sensitive sensors based on photonic crystal fiber modal interferometers,” J. Sensors 2009, 747803 (2009).

J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91, 091109 (2007).
[CrossRef]

Fini, J. M.

J. M. Fini, “Microstructure fibres for optical sensing in gases and liquids,” Meas. Sci. Technol. 15, 1120–1128 (2004).
[CrossRef]

Frazao, O.

O. Frazăo, J. M. Baptista, and J. L. Santos, “Temperature-independent strain sensor based on a Hi-Bi photonic crystal fiber loop mirror,” IEEE Sens. J. 7, 1453–1455 (2007).
[CrossRef]

Frazão, O.

O. Frazão, J. L. Santos, F. M. Araújo, and L. A. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photon. Rev. 2, 449–459 (2008).
[CrossRef]

Fu, H. Y.

Furusawa, K.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

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, 075402 (2010).
[CrossRef]

Guan, B.-O.

Hansen, T.

Hautakorpi, M.

Hlubina, P.

P. Hlubina, “White-light spectral interferometry to measure intermodal dispersion in two-mode elliptical-core optical fibres,” Opt. Commun. 218, 283–289 (2003).
[CrossRef]

Hochman, A.

Jung, Y.

Kim, M. J.

Kotynski, R.

Lee, B. H.

Lee, S.

Leviatan, Y.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Lu, C.

Ludvigsen, H.

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, 075402 (2010).
[CrossRef]

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, 075402 (2010).
[CrossRef]

G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Measurements of modal birefringence and polarimetric sensitivity of the birefringent holey fiber to hydrostatic pressure and strain,” Opt. Commun. 241, 339–348 (2004).
[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, 075402 (2010).
[CrossRef]

Mikulic, P.

W. J. Bock, T. Eftimov, P. Mikulic, and J. Chen, “Novel fiber sensor based on in-line core-cladding intermodal interferometer and photonic crystal fiber,” in Proceedings of XIX IMEKO World Congress Fundamental and Applied Metrology (IMEKO, 2009), pp. 65–68.

Minkovich, V.

Minkovich, V. P.

Monro, T. M.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Monzon-Hernandez, D.

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, 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, 075402 (2010).
[CrossRef]

Oh, K.

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, 075402 (2010).
[CrossRef]

Panajotov, K.

Petersen, J.

Pruneri, V.

J. Villatoro, V. Finazzi, G. Badenes, and V. Pruneri, “Highly sensitive sensors based on photonic crystal fiber modal interferometers,” J. Sensors 2009, 747803 (2009).

J. Villatoro, V. P. Minkovich, V. Pruneri, and G. Badenes, “Simple all-microstructured-optical-fiber interferometer built via fusion splicing,” Opt. Express 15, 1491–1496 (2007).
[CrossRef] [PubMed]

J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91, 091109 (2007).
[CrossRef]

Richardson, D. J.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Ritari, T.

Santos, J. L.

O. Frazão, J. L. Santos, F. M. Araújo, and L. A. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photon. Rev. 2, 449–459 (2008).
[CrossRef]

O. Frazăo, J. M. Baptista, and J. L. Santos, “Temperature-independent strain sensor based on a Hi-Bi photonic crystal fiber loop mirror,” IEEE Sens. J. 7, 1453–1455 (2007).
[CrossRef]

Serebryannikov, E.

Shum, P.

X. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90, 151113 (2007).
[CrossRef]

Simonsen, H.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Sørensen, T.

Sotskaya, L.

Sotsky, A.

Statkiewicz, G.

G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Measurements of modal birefringence and polarimetric sensitivity of the birefringent holey fiber to hydrostatic pressure and strain,” Opt. Commun. 241, 339–348 (2004).
[CrossRef]

Statkiewicz-Barabach, 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, 075402 (2010).
[CrossRef]

Szpulak, M.

Tam, H. Y.

H. Y. Fu, Chuang Wu, M. L. V. Tse, L. Zhang, K.-C. Davis Cheng, H. Y. Tam, B.-O. Guan, and C. Lu, “High pressure sensor based on photonic crystal fiber for downhole application,” Appl. Opt. 49, 2639–2643 (2010).
[CrossRef]

X. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90, 151113 (2007).
[CrossRef]

Tarnowski, K.

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, 075402 (2010).
[CrossRef]

Thienpont, H.

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, 075402 (2010).
[CrossRef]

Tse, M. L. V.

Tuominen, J.

Urbanczyk, W.

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, 075402 (2010).
[CrossRef]

M. Szpulak, W. Urbanczyk, E. Serebryannikov, A. Zheltikov, A. Hochman, Y. Leviatan, R. Kotynski, and K. Panajotov, “Comparison of different methods for rigorous modeling of photonic crystal fibers,” Opt. Express 14, 5699–5714 (2006).
[CrossRef] [PubMed]

G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Measurements of modal birefringence and polarimetric sensitivity of the birefringent holey fiber to hydrostatic pressure and strain,” Opt. Commun. 241, 339–348 (2004).
[CrossRef]

Villatoro, J.

Wojcik, 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, 075402 (2010).
[CrossRef]

Wu, Chuang

Zhang, L.

Zheltikov, A.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

X. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90, 151113 (2007).
[CrossRef]

J. Villatoro, V. Finazzi, V. P. Minkovich, V. Pruneri, and G. Badenes, “Temperature-insensitive photonic crystal fiber interferometer for absolute strain sensing,” Appl. Phys. Lett. 91, 091109 (2007).
[CrossRef]

IEEE Sens. J. (1)

O. Frazăo, J. M. Baptista, and J. L. Santos, “Temperature-independent strain sensor based on a Hi-Bi photonic crystal fiber loop mirror,” IEEE Sens. J. 7, 1453–1455 (2007).
[CrossRef]

J. Opt. (1)

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, 075402 (2010).
[CrossRef]

J. Sensors (1)

J. Villatoro, V. Finazzi, G. Badenes, and V. Pruneri, “Highly sensitive sensors based on photonic crystal fiber modal interferometers,” J. Sensors 2009, 747803 (2009).

Laser Photon. Rev. (1)

O. Frazão, J. L. Santos, F. M. Araújo, and L. A. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photon. Rev. 2, 449–459 (2008).
[CrossRef]

Meas. Sci. Technol. (2)

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

J. M. Fini, “Microstructure fibres for optical sensing in gases and liquids,” Meas. Sci. Technol. 15, 1120–1128 (2004).
[CrossRef]

Opt. Commun. (2)

G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Measurements of modal birefringence and polarimetric sensitivity of the birefringent holey fiber to hydrostatic pressure and strain,” Opt. Commun. 241, 339–348 (2004).
[CrossRef]

P. Hlubina, “White-light spectral interferometry to measure intermodal dispersion in two-mode elliptical-core optical fibres,” Opt. Commun. 218, 283–289 (2003).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Other (2)

W. J. Bock, T. Eftimov, P. Mikulic, and J. Chen, “Novel fiber sensor based on in-line core-cladding intermodal interferometer and photonic crystal fiber,” in Proceedings of XIX IMEKO World Congress Fundamental and Applied Metrology (IMEKO, 2009), pp. 65–68.

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Figures (10)

Fig. 1
Fig. 1

SEM image of the birefringent MOF with boron doped inclusion in the center of the core (darker spot) used for fabrication of the intermodal interferometer.

Fig. 2
Fig. 2

Field distribution calculated for the fundamental (a) and the first order mode (b) at λ = 1.55 μm . Spectral dependence of the effective indices in the fiber with boron doped inclusion for the fundamental and the first order modes and the effective index change introduced by the inclusion (c).

Fig. 3
Fig. 3

Schematic configuration of the proposed intermodal interferometric sensor (a) and the microscope image of the microstructured fiber with the interferometer formed by two tapered regions (b).

Fig. 4
Fig. 4

The interference spectrum at the output of an in-fiber Mach–Zehnder intermodal interferometer fabricated in the microstructured fiber.

Fig. 5
Fig. 5

Calculated (solid line) and measured (dots) difference in group effective indices of the LP 01 and LP 11 modes averaged with respect to polarization.

Fig. 6
Fig. 6

Calculated group modal birefringence of the LP 01 (solid line) and LP 11 (dashed line) modes in the investigated fiber with boron doped inclusion (a) and comparison of the calculated (solid line) and measured (dots) birefringence difference (b).

Fig. 7
Fig. 7

Experimental setup for strain and temperature measurements.

Fig. 8
Fig. 8

Transmission characteristic registered in the full spectral range for selected values of applied strain (a) and variation of the modulation depth and displacement of the third fringe in response to applied strain (b).

Fig. 9
Fig. 9

Displacement of the third interference fringe against applied strain (a) and change in its visibility (b).

Fig. 10
Fig. 10

Displacement of the third interference fringe against temperature (a) and change of its visibility (b).

Equations (14)

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δ n eff 2 = δ n 2 | Ψ | 2 d A ,
I x ( λ ) = I 0 ( 1 + γ cos 2 π ( n 01 x n 11 x ) L λ )
I y ( λ ) = I 0 ( 1 + γ cos 2 π ( n 01 y n 11 y ) L λ ) ,
I ( λ ) = 2 I 0 [ 1 + γ cos ( π ( n 01 x + n 01 y n 11 x n 11 y ) L λ ) cos ( π ( n 01 x n 01 y n 11 x + n 11 y ) L λ ) ] .
I ( λ ) = 2 I 0 [ 1 + γ cos ( 2 π ( n 01 a n 11 a ) L λ ) cos ( π ( Δ n 01 Δ n 11 ) L λ ) ]
n 01 a = n 01 x + n 01 y 2 , n 11 a = n 11 x + n 11 y 2
Δ n 01 = n 01 x n 01 y , Δ n 11 = n 11 x n 11 y .
N 01 a N 11 a = λ 2 Δ λ L ,
Δ N 01 Δ N 11 = λ 2 2 Δ λ L ,
λ ( ( n 01 a n 11 a ) L λ ) Δ λ + X ( ( n 01 a n 11 a ) L λ ) Δ X = 0.
1 λ Δ λ Δ X = n 01 a n 11 a N 01 a N 11 a ( 1 L L X + 1 n 01 a n 11 a ( n 01 a n 11 a ) X )
Δ λ Δ X = λ 2 K X 2 π ( N 01 a N 11 a ) ,
K X = 1 L d ( φ 01 a φ 11 a ) d X
L max Δ X max < 2 π K X .

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