Abstract

We propose a novel device defined as Random Optical Grating by Ultraviolet or ultrafast laser Exposure (ROGUE), a new type of fiber Bragg grating (FBG), exhibiting a weak reflection over a large bandwidth, which is independent of the length of the grating. This FBG is fabricated simply by dithering the phase randomly during the writing process. This grating has an enhanced backscatter, several orders of magnitude above typical Rayleigh backscatter of standard SMF-28 optical fiber. The grating is used in distributed sensing using optical frequency domain reflectometry (OFDR), allowing a significant increase in signal to noise ratio for strain and temperature measurement. This enhancement results in significantly lower strain or temperature noise level and accuracy error, without sacrificing the spatial resolution. Using this method, we show a sensor with a backscatter level 50 dB higher than standard unexposed SMF-28, which can thus compensate for increased loss in the system.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  4. M. A. Soto, T. Nannipieri, A. Signorini, A. Lazzeri, F. Baronti, R. Roncella, G. Bolognini, and F. Di Pasquale, “Raman-based distributed temperature sensor with 1 m spatial resolution over 26 km SMF using low-repetition-rate cyclic pulse coding,” Opt. Lett. 36(13), 2557–2559 (2011).
    [Crossref] [PubMed]
  5. Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. 36(2), 277–279 (2011).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  22. L. Thévenaz, S. Chin, J. Sancho, and S. Sales, “Novel technique for distributed fibre sensing based on faint long gratings (FLOGs),” in 23rd International Conference on Optical Fibre Sensors, (International Society for Optics and Photonics, 2014), 91576W.
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    [Crossref]
  24. A. Mafi, “Anderson localization in a partially random Bragg grating and a conserved area theorem,” Opt. Lett. 40(15), 3603–3606 (2015).
    [Crossref] [PubMed]
  25. M. Gagné and R. Kashyap, “Demonstration of a 3 mW threshold Er-doped random fiber laser based on a unique fiber Bragg grating,” Opt. Express 17(21), 19067–19074 (2009).
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  26. N. Lizárraga, N. P. Puente, E. I. Chaikina, T. A. Leskova, and E. R. Méndez, “Single-mode Er-doped fiber random laser with distributed Bragg grating feedback,” Opt. Express 17(2), 395–404 (2009).
    [Crossref] [PubMed]
  27. M. Gagné, S. Loranger, J. Lapointe, and R. Kashyap, “Fabrication of high quality, ultra-long fiber Bragg gratings: up to 2 million periods in phase,” Opt. Express 22(1), 387–398 (2014).
    [Crossref] [PubMed]
  28. S. Loranger, V. Lambin-Iezzi, and R. Kashyap, “Reproducible ultra-long FBGs in phase corrected non-uniform fibers,” Optica 4(9), 1143 (2017).
    [Crossref]
  29. J. F. C. Kingman, Poisson Processes (Clarendon Press, 1992).
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  33. J. Liu, P. Lu, S. J. Mihailov, M. Wang, and J. Yao, “Real-time random grating sensor array for quasi-distributed sensing based on wavelength-to-time mapping and time-division multiplexing,” Opt. Lett. 44(2), 379–382 (2019).
    [Crossref] [PubMed]
  34. D. K. Gifford, M. E. Froggatt, and S. T. Kreger, “High precision, high sensitivity distributed displacement and temperature measurements using OFDR-based phase tracking,” in 21st International Conference on Optical Fiber Sensors, (International Society for Optics and Photonics, 2011), 77533I.
    [Crossref]
  35. Y. Xu, P. Lu, S. Gao, D. Xiang, P. Lu, S. Mihailov, and X. Bao, “Optical fiber random grating-based multiparameter sensor,” Opt. Lett. 40(23), 5514–5517 (2015).
    [Crossref] [PubMed]
  36. A. Beisenova, A. Issatayeva, S. Sovetov, S. Korganbayev, M. Jelbuldina, Z. Ashikbayeva, W. Blanc, E. Schena, S. Sales, C. Molardi, and D. Tosi, “Multi-fiber distributed thermal profiling of minimally invasive thermal ablation with scattering-level multiplexing in MgO-doped fibers,” Biomed. Opt. Express 10(3), 1282–1296 (2019).
    [Crossref] [PubMed]
  37. P. S. Westbrook, K. S. Feder, R. M. Ortiz, T. Kremp, E. M. Monberg, H. Wu, D. A. Simoff, and S. Shenk, “Kilometer length, low loss enhanced back scattering fiber for distributed sensing,” in 2017 25th Optical Fiber Sensors Conference (OFS), (IEEE, 2017), 1–5.
  38. S. L. Scholl, A. Jantzen, R. H. S. Bannerman, P. C. Gow, D. H. Smith, J. C. Gates, L. J. Boyd, P. G. R. Smith, and C. Holmes, “Thermal approach to classifying sequentially written fiber Bragg gratings,” Opt. Lett. 44(3), 703–706 (2019).
    [Crossref] [PubMed]

2019 (3)

2018 (2)

2017 (5)

2015 (3)

2014 (3)

2012 (1)

2011 (3)

2009 (2)

2005 (1)

1998 (1)

1986 (1)

A. Rogers, “Distributed optical-fibre sensors,” J. Phys. D Appl. Phys. 19(12), 2237–2255 (1986).
[Crossref]

1981 (1)

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single‐mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Antman, Y.

Ashikbayeva, Z.

Baiad, M. D.

Bannerman, R. H. S.

Bao, X.

Baronti, F.

Beisenova, A.

Blanc, W.

Boisvert, J. S.

Bolognini, G.

Boyd, L. J.

Buric, M.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

Chaikina, E. I.

Chen, K. P.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

T. Chen, Q. Wang, B. Zhang, R. Chen, and K. P. Chen, “Distributed flow sensing using optical hot -wire grid,” Opt. Express 20(8), 8240–8249 (2012).
[Crossref] [PubMed]

Chen, L.

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 1–8 (2014).
[Crossref]

Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. 36(2), 277–279 (2011).
[Crossref] [PubMed]

Chen, R.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

T. Chen, Q. Wang, B. Zhang, R. Chen, and K. P. Chen, “Distributed flow sensing using optical hot -wire grid,” Opt. Express 20(8), 8240–8249 (2012).
[Crossref] [PubMed]

Chen, T.

Cobo, A.

Cobo, L. R.

Cohen, R.

Cui, J.

Di Pasquale, F.

Ding, Z.

Dong, Y.

Eickhoff, W.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single‐mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Farries, M.

M. Farries and A. Rogers, “Distributed sensing using stimulated Raman interaction in a monomode optical fibre,” in 2nd Intl Conf on Optical Fiber Sensors: OFS’84, (International Society for Optics and Photonics, 1984), 121–133.
[Crossref]

Feder, K. S.

Fischer, B.

Froggatt, M.

Gagné, M.

Gao, S.

Gates, J. C.

Gow, P. C.

Holmes, C.

Huang, S.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

Iezzi, V. L.

Incera, A. Q.

Issatayeva, A.

Jantzen, A.

Jelbuldina, M.

Kadoury, S.

Kashyap, R.

Kimelfeld, N.

Ko, W.

Korganbayev, S.

Kremp, T.

Lambin-Iezzi, V.

S. Loranger, V. Lambin-Iezzi, and R. Kashyap, “Reproducible ultra-long FBGs in phase corrected non-uniform fibers,” Optica 4(9), 1143 (2017).
[Crossref]

S. Loranger, M. Gagné, V. Lambin-Iezzi, and R. Kashyap, “Rayleigh scatter based order of magnitude increase in distributed temperature and strain sensing by simple UV exposure of optical fibre,” Sci. Rep. 5(1), 11177 (2015).
[Crossref] [PubMed]

Lapointe, J.

Lazzeri, A.

Lee, S.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

Leskova, T. A.

Levanon, N.

Li, M. J.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

Li, S.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

Li, W.

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 1–8 (2014).
[Crossref]

Liu, J.

Lizárraga, N.

London, Y.

López-Higuera, J. M.

Loranger, S.

Lu, P.

Mafi, A.

Mandal, K. K.

Masoudi, A.

Méndez, E. R.

Mihailov, S.

Mihailov, S. J.

Molardi, C.

Monberg, E. M.

Moore, J.

Nannipieri, T.

Newson, T. P.

Ohodnicki, P.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

Ortiz, R. M.

Parent, F.

Puente, N. P.

Ramírez, J. A.

Rogers, A.

A. Rogers, “Distributed optical-fibre sensors,” J. Phys. D Appl. Phys. 19(12), 2237–2255 (1986).
[Crossref]

M. Farries and A. Rogers, “Distributed sensing using stimulated Raman interaction in a monomode optical fibre,” in 2nd Intl Conf on Optical Fiber Sensors: OFS’84, (International Society for Optics and Photonics, 1984), 121–133.
[Crossref]

Roncella, R.

Sales, S.

Schena, E.

Scholl, S. L.

Shapira, O.

Signorini, A.

Simoff, D. A.

Smith, D. H.

Smith, P. G. R.

Song, J.

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 1–8 (2014).
[Crossref]

Soto, M. A.

Sovetov, S.

Taunay, T. F.

Thévenaz, L.

Tosi, D.

Ulrich, R.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single‐mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Wang, M.

Wang, Q.

Westbrook, P. S.

Wu, H.

Xiang, D.

Xu, Y.

Y. Xu, P. Lu, S. Gao, D. Xiang, P. Lu, S. Mihailov, and X. Bao, “Optical fiber random grating-based multiparameter sensor,” Opt. Lett. 40(23), 5514–5517 (2015).
[Crossref] [PubMed]

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 1–8 (2014).
[Crossref]

Yan, A.

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

Yang, D.

Yao, J.

Zadok, A.

Zhang, B.

Zhao, S.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single‐mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Biomed. Opt. Express (2)

IEEE Photonics J. (1)

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 1–8 (2014).
[Crossref]

J. Lightwave Technol. (3)

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

J. Phys. D Appl. Phys. (1)

A. Rogers, “Distributed optical-fibre sensors,” J. Phys. D Appl. Phys. 19(12), 2237–2255 (1986).
[Crossref]

Opt. Express (5)

Opt. Lett. (7)

A. Mafi, “Anderson localization in a partially random Bragg grating and a conserved area theorem,” Opt. Lett. 40(15), 3603–3606 (2015).
[Crossref] [PubMed]

Y. Xu, P. Lu, S. Gao, D. Xiang, P. Lu, S. Mihailov, and X. Bao, “Optical fiber random grating-based multiparameter sensor,” Opt. Lett. 40(23), 5514–5517 (2015).
[Crossref] [PubMed]

J. Liu, P. Lu, S. J. Mihailov, M. Wang, and J. Yao, “Real-time random grating sensor array for quasi-distributed sensing based on wavelength-to-time mapping and time-division multiplexing,” Opt. Lett. 44(2), 379–382 (2019).
[Crossref] [PubMed]

A. Masoudi and T. P. Newson, “High spatial resolution distributed optical fiber dynamic strain sensor with enhanced frequency and strain resolution,” Opt. Lett. 42(2), 290–293 (2017).
[Crossref] [PubMed]

M. A. Soto, T. Nannipieri, A. Signorini, A. Lazzeri, F. Baronti, R. Roncella, G. Bolognini, and F. Di Pasquale, “Raman-based distributed temperature sensor with 1 m spatial resolution over 26 km SMF using low-repetition-rate cyclic pulse coding,” Opt. Lett. 36(13), 2557–2559 (2011).
[Crossref] [PubMed]

Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. 36(2), 277–279 (2011).
[Crossref] [PubMed]

S. L. Scholl, A. Jantzen, R. H. S. Bannerman, P. C. Gow, D. H. Smith, J. C. Gates, L. J. Boyd, P. G. R. Smith, and C. Holmes, “Thermal approach to classifying sequentially written fiber Bragg gratings,” Opt. Lett. 44(3), 703–706 (2019).
[Crossref] [PubMed]

Optica (1)

Sci. Rep. (2)

A. Yan, S. Huang, S. Li, R. Chen, P. Ohodnicki, M. Buric, S. Lee, M. J. Li, and K. P. Chen, “Distributed Optical Fiber Sensors with Ultrafast Laser Enhanced Rayleigh Backscattering Profiles for Real-Time Monitoring of Solid Oxide Fuel Cell Operations,” Sci. Rep. 7(1), 9360 (2017).
[Crossref] [PubMed]

S. Loranger, M. Gagné, V. Lambin-Iezzi, and R. Kashyap, “Rayleigh scatter based order of magnitude increase in distributed temperature and strain sensing by simple UV exposure of optical fibre,” Sci. Rep. 5(1), 11177 (2015).
[Crossref] [PubMed]

Other (12)

L. Thévenaz, S. Chin, J. Sancho, and S. Sales, “Novel technique for distributed fibre sensing based on faint long gratings (FLOGs),” in 23rd International Conference on Optical Fibre Sensors, (International Society for Optics and Photonics, 2014), 91576W.

S. T. Kreger, A. K. Sang, D. K. Gifford, and M. E. Froggatt, “Distributed strain and temperature sensing in plastic optical fiber using Rayleigh scatter,” in Fiber Optic Sensors and Applications VI, (International Society for Optics and Photonics, 2009), 73160A.

S. Rizzolo, A. Boukenter, J. Perisse, G. Bouwmans, H. El Hamzaoui, L. Bigot, Y. Ouerdane, M. Cannas, M. Bouazaoui, and J.-R. Macé, “Radiation response of OFDR distributed sensors based on microstructured pure silica optical fibers,” in Radiation and Its Effects on Components and Systems (RADECS),201515th European Conference on, (IEEE, 2015), 1–3.
[Crossref]

M. Farries and A. Rogers, “Distributed sensing using stimulated Raman interaction in a monomode optical fibre,” in 2nd Intl Conf on Optical Fiber Sensors: OFS’84, (International Society for Optics and Photonics, 1984), 121–133.
[Crossref]

Luna, “Optical Backscatter Reflectometer 4600 - User Guide”, retrieved http://lunainc.com/wp-content/uploads/2014/05/OBR-4600-UG6_SW3.10.1.pdf .

J. F. C. Kingman, Poisson Processes (Clarendon Press, 1992).

S. M. Ross, STOCHASTIC PROCESSES, 2ND ED (Wiley India Pvt. Limited, 2008).

R. Kashyap, Fiber Bragg Gratings (Academic press, 2009).

W. Bai, H. Yu, D. Jiang, and M. Yang, “All fiber grating (AFG): a new platform for fiber optic sensing technologies,” in 24th International Conference on Optical Fibre Sensors, (International Society for Optics and Photonics, 2015), 96342A.

D. K. Gifford, M. E. Froggatt, and S. T. Kreger, “High precision, high sensitivity distributed displacement and temperature measurements using OFDR-based phase tracking,” in 21st International Conference on Optical Fiber Sensors, (International Society for Optics and Photonics, 2011), 77533I.
[Crossref]

K. J. Peters, R. G. Duncan, M. E. Froggatt, S. T. Kreger, R. J. Seeley, D. K. Gifford, A. K. Sang, and M. S. Wolfe, “High-accuracy fiber-optic shape sensing,” in Sensor Systems and Networks: Phenomena, Technology, and Applications for NDE and Health Monitoring 2007, (2007).

P. S. Westbrook, K. S. Feder, R. M. Ortiz, T. Kremp, E. M. Monberg, H. Wu, D. A. Simoff, and S. Shenk, “Kilometer length, low loss enhanced back scattering fiber for distributed sensing,” in 2017 25th Optical Fiber Sensors Conference (OFS), (IEEE, 2017), 1–5.

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Figures (11)

Fig. 1
Fig. 1 Talbot interferometer used for the fabrication of the ROGUE. The phase mask above generates different diffraction orders. The first two orders ( + 1 and −1) are reflected by mirrors onto the fiber, where an interference fringe pattern is created. The UV exposure increases the refractive index periodically, creating an FBG. By changing the angle of the mirrors, the interference fringe pattern (and thus the FBG wavelength) can be modified. The random electrical wave applied to the piezoelectric element induces imperfect overlap of the interference pattern, creating a ROGUE.

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Fig. 2
Fig. 2 Cross-correlation result (a) before and (b) after the sinc interpolation. The fiber used is a standard SMF-28 fiber inscribed with a ROGUE, interrogated over a 42.90 nm bandwidth with a 10 mm gauge length. The original data set of (a) has 521 points, while the interpolation of (b) is performed by adding 2,000 padding zeroes to the data.

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Fig. 3
Fig. 3 (a) Schematic illustration showing the difference between a regular in-phase FBG, exhibiting a very narrow bandwidth (typical full-width at half-maximum (FWHM) taken from [28]), and a ROGUE, composed of multiple out-of-phase µFBGs of different lengths, resulting in a much wider bandwidth. Experimental measurements for a 1-meter-long ROGUE written in SMF-28 fiber are presented (b) in the temporal domain, showing over 30 dB in backscattered amplitude enhancement, and (c) in the spectral domain, where an 8 nm FWHM (41 nm full width) can be observed. Rayleigh scattering baseline can be observed out-of-band of the grating, at around −60 dB. The ROGUE was written using 37 mW of 213 nm UV laser power, at a writing speed of 0.2 mm/s. Measurements were made with the largest bandwidth of 88.24 nm available on the OBR4600.

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Fig. 4
Fig. 4 Gain of the backscattering signal of the ROGUE as a function of writing speed vs untreated fiber. The ROGUE was written using a noise amplitude of 5 V (~10 periods) and a frequency bandwidth of 20 Hz. A SMF-28 fiber from Corning (orange) and a SM1500 fiber from Fibercore (green) were tested, using 22 mW (solid line) and 37 mW (dashed line) of laser power. 0 dB corresponds to the signal level of untreated fiber both for SMF-28 and SM1500). Measurements made on the OBR4600 using a 21.16 nm scanning bandwidth, the bandwidth most suitable for sensing, as will be shown in the next sections. The gain was measured in the temporal domain (see Fig. 3b).

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Fig. 5
Fig. 5 FWHM bandwidth of the ROGUE, as a function of length. The experimental data is limited to 400 mm, with models using the parameters k1 = 500 m−1 and k2 = 1.4e4 m−1. The µFBG were considered as uniform gratings, with a central wavelength of 1555 nm. The phase and amplitude of each µFBG is random. The bandwidth asymptotically approaches 7 nm for a ROGUE length > 100 mm for an average µFBG length of 72.5 µm.

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Fig. 6
Fig. 6 Calculated spectral shift as a function of the elongation, where the method is compared between the OBR’s internal algorithm and the one described earlier, using a number N of padding zeroes. Solid black curve is the applied strain value. (a) is taken right after the cross-correlation, and (b) is taken after applying an additional quadratic fit. Measurements were made using the OBR4600 from Luna with a 42.90 nm bandwidth, the largest available bandwidth on the OBR for sensing.

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Fig. 7
Fig. 7 RMS noise level in a uniform and stable environment of 300 mm of both unexposed SMF-28 fiber and ROGUE written in SMF-28. The fibers are placed in an insulated box, averaged over 15 measurements. A 30 dB enhanced ROGUE was used for these measurements.

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Fig. 8
Fig. 8 RMS strain error while stretching the fiber as a function of scanning bandwidth, for both unexposed fiber and ROGUE. The spectral shift is calculated for the 20 µm stretching, across 80 mm of sensing fiber along the 1.15 m fiber length. It can be observed that, using a ROGUE, a scanning bandwidth of only 5.24 nm is sufficient to achieve better accuracy to the one obtained with unexposed SMF-28. A 30 dB enhanced ROGUE was used for these measurements.

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Fig. 9
Fig. 9 RMS noise level as a function of gauge length, for both unexposed fiber and ROGUE, when placed in an insulated box, averaged over 15 measurements, for bandwidths of 5.24 and 42.90 nm. The gauge length is varied from 0.5 mm to 200 mm. As can be seen, a ROGUE scanned with a 5.24 nm bandwidth requires a gauge length of only 2 mm to beat the noise level of SMF-28 with a 42.90 nm bandwidth and a 10 mm gauge length. A 30 dB enhanced ROGUE was used for these measurements.

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Fig. 10
Fig. 10 Strain RMS error calculated over a 20 µm stretching and 80 mm of sensing fiber along the 1.15 m fiber length. (a) Spectral shift accuracy as a function of ROGUE gain (linear scale in y). The ROGUEs were written using 21 mW of UV power, by varying the writing speed from 0.05 mm/s to 10 mm/s. The 0 dB gain value represents an unexposed SMF-28 fiber.

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Fig. 11
Fig. 11 Spectral shift accuracy for three ROGUEs of different gains, as a function of optical loss induced before the ROGUE by an optical attenuator (logarithmic scale in y).

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Equations (7)

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X 1 =X
Y 1 | x 1 =Y+ x 1
X n | y n−1 =X+ y n−1
Y n | x n =Y+ x n
ρ= − κ ac sinh(αL) δsinh(αL)−iαcosh(αL) ,
δ= κ dc + 1 2 ( Δβ− dϕ(z) dz ),
α= | κ ac | 2 − δ 2 ,

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