Abstract

A method that enables polarization-resolved spatial characterization of fiber Bragg gratings is presented. The polarization-resolved reflection spectrum of the grating is measured using optical-frequency domain reflectometry. A polarization-resolved layer-peeling algorithm is used to compute the spatial profile, including the local birefringence and the local polarization-dependent index modulation. A strain-tuned distributed feedback fiber laser is used as source. With closed-loop control of the laser sweep, 0.14 % maximum deviation from constant sweep rate is achieved, which is much better than commercial available tunable lasers. The polarization of the source is modulated synchronous with the laser sweep by passing the light through a three-armed Mach-Zehnder-type interferometer having different retardation. The method is used to investigate the polarization-dependence of the index modulation amplitude of a fiber Bragg grating.

© 2006 Optical Society of America

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  1. D.-W. Huang and C.-C. Yang, "Reconstruction of fiber grating refractive-index profiles from complex Bragg reflection spectra," Appl. Opt. 38, 4494-4498 (1999).
    [CrossRef]
  2. S. Keren and M. Horowitz, "Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses," Opt. Lett. 26, 328-330 (2001).
    [CrossRef]
  3. P. Giaccari, H. Limberger, and R. Salathe, "Local coupling-coefficient characterization in fiber Bragg gratings," Opt. Lett. 28, 598-600 (2003).
    [CrossRef] [PubMed]
  4. D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitunal structure characterization of fiber Bragg gratings," IEEE J. Lightwave Technol. 16, 2435-2442 (1998).
    [CrossRef]
  5. O. Waagaard, E. Rønnekleiv, and J.T. Kringlebotn, "Spatial characterization of strong fiber Bragg gatings," in Proceedings of SPIE, Fiber-Based Components Fabrication, Testing, and Connectorization, V. Pruneri, R. Dahlgren, and G. Sanger, eds., vol. 4943, pp. 16-24 (2003).
  6. O. Waagaard, "Spatial characterization of strong fiber Bragg gratings using thermal chirp and optical-frequency-domain reflectometry," IEEE J. Lightwave Technol. 23, 909-914 (2005).
    [CrossRef]
  7. W. Eickhoff and R. Ulrich, "Optical frequency-domain reflectometry in single-mode fiber," Applied Physics Letters 39, 693-695 (1981).
    [CrossRef]
  8. U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," IEEE J. Lightwave Technol. 11, 1377-1384 (1993).
    [CrossRef]
  9. J. von der Weid, R. Passy, G. Mussi, and N. Gisin, "On the characterization of optical network componenents with optical frequency domain reflectometry," IEEE J. Lightwave Technol. 15, 1131-1141 (1997).
    [CrossRef]
  10. G. Meltz and W. W. Morey, "Bragg grating formation and germanosilicate fiber photosensitivity," in International workshop on photoinduced self-organization effects in optical fiber, Proc. Soc. Photo-Opt.Instrum. Eng. 1516, 185-199 (1991).
  11. K. O. Hill, F. Bilodeau, B. Malo, and D. C. Johnson, "Birefringent photosensitivity in monomode optical fibre: application to external writing of rocking filters," Electron. Lett. 27, 1548-1550 (1991).
    [CrossRef]
  12. T. Erdogan and V. Mizrahi, "Characterization of UV-induced birefringence in photosensitive Ge-doped silica optical fibers," J. Opt. Soc. Am. B 11, 2100-2105 (1994).
    [CrossRef]
  13. S. Pereira, J. E. Sipe, R. E. Slusher, and S. Spalter, "Enhanced and suppressed birefringence in fiber Bragg gratings," J. Opt. Soc. Am. B 19, 1509-1515 (2002).
    [CrossRef]
  14. B. Soller, D. Gifford, M. Wolfe, and M. Foggatt, "High resolution optical frequency domain reflectometry for characterization of components and assemblies," Opt. Express 13, 666-674 (2005).
    [CrossRef] [PubMed]
  15. O. Waagaard and J. Skaar, "Synthesis of birefringent reflective gratings," J. Opt. Soc. Am. A 21, 1207-1220 (2004).
    [CrossRef]
  16. Luna Technologies white paper, "Optical vector network analyzer for single scan measurements of loss, group delay and polarization mode dispersion," http://www.lunatechnologies.com/products/ova/files/OVAwhitePaper.pdf (Luna Technologies, 2005).
  17. Agilent Technologies white paper, "Agilent 81910A Photonic All-Parameter Analyzer User Guide," http://www.home.agilent.com/agilent/facet.jspx?kt=1&cc=US&lc=eng&k=81910 (Agilent, 2005).
  18. R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
    [CrossRef]
  19. J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
    [CrossRef]
  20. J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
    [CrossRef]
  21. R. Azzam and N. Bashara, Ellipsometry and polarized light (North-Holland, 1977).
  22. E. Rønnekleiv, "Frequency and Intensity Noise of Single Frequency Fiber Bragg Grating Lasers," Opt. Fiber Technol. 7, 206-235 (2001).
    [CrossRef]
  23. P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
    [CrossRef]
  24. S. Kakuma, K. Ohmura, and R. Ohba, "Improved uncertainty of optical frequency domain reflectometry based length measurement by linearizing the frequency chirping of a laser diode," Opt. Rev. 10, 182-183 (2003).
    [CrossRef]
  25. A. Asseh, H. Storøy, B. Sahlgren, S. Sandgren, and R. Stubbe, "A writing technique for long fiber bragg gratings with complex reflectivity profiles," IEEE J. Lightwave Technol. 15, 1419-1423 (1997).
    [CrossRef]
  26. F. Kherbouche and B. Poumellec, "UV-induced stress fields during Bragg grating inscription in optical fibers," J. Opt. A 3, 429-439 (2001).
    [CrossRef]

2005

O. Waagaard, "Spatial characterization of strong fiber Bragg gratings using thermal chirp and optical-frequency-domain reflectometry," IEEE J. Lightwave Technol. 23, 909-914 (2005).
[CrossRef]

B. Soller, D. Gifford, M. Wolfe, and M. Foggatt, "High resolution optical frequency domain reflectometry for characterization of components and assemblies," Opt. Express 13, 666-674 (2005).
[CrossRef] [PubMed]

2004

2003

P. Giaccari, H. Limberger, and R. Salathe, "Local coupling-coefficient characterization in fiber Bragg gratings," Opt. Lett. 28, 598-600 (2003).
[CrossRef] [PubMed]

J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
[CrossRef]

S. Kakuma, K. Ohmura, and R. Ohba, "Improved uncertainty of optical frequency domain reflectometry based length measurement by linearizing the frequency chirping of a laser diode," Opt. Rev. 10, 182-183 (2003).
[CrossRef]

2002

2001

E. Rønnekleiv, "Frequency and Intensity Noise of Single Frequency Fiber Bragg Grating Lasers," Opt. Fiber Technol. 7, 206-235 (2001).
[CrossRef]

F. Kherbouche and B. Poumellec, "UV-induced stress fields during Bragg grating inscription in optical fibers," J. Opt. A 3, 429-439 (2001).
[CrossRef]

S. Keren and M. Horowitz, "Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses," Opt. Lett. 26, 328-330 (2001).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

2000

P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
[CrossRef]

1999

D.-W. Huang and C.-C. Yang, "Reconstruction of fiber grating refractive-index profiles from complex Bragg reflection spectra," Appl. Opt. 38, 4494-4498 (1999).
[CrossRef]

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

1998

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitunal structure characterization of fiber Bragg gratings," IEEE J. Lightwave Technol. 16, 2435-2442 (1998).
[CrossRef]

1997

J. von der Weid, R. Passy, G. Mussi, and N. Gisin, "On the characterization of optical network componenents with optical frequency domain reflectometry," IEEE J. Lightwave Technol. 15, 1131-1141 (1997).
[CrossRef]

A. Asseh, H. Storøy, B. Sahlgren, S. Sandgren, and R. Stubbe, "A writing technique for long fiber bragg gratings with complex reflectivity profiles," IEEE J. Lightwave Technol. 15, 1419-1423 (1997).
[CrossRef]

1994

1993

U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," IEEE J. Lightwave Technol. 11, 1377-1384 (1993).
[CrossRef]

1991

G. Meltz and W. W. Morey, "Bragg grating formation and germanosilicate fiber photosensitivity," in International workshop on photoinduced self-organization effects in optical fiber, Proc. Soc. Photo-Opt.Instrum. Eng. 1516, 185-199 (1991).

K. O. Hill, F. Bilodeau, B. Malo, and D. C. Johnson, "Birefringent photosensitivity in monomode optical fibre: application to external writing of rocking filters," Electron. Lett. 27, 1548-1550 (1991).
[CrossRef]

1981

W. Eickhoff and R. Ulrich, "Optical frequency-domain reflectometry in single-mode fiber," Applied Physics Letters 39, 693-695 (1981).
[CrossRef]

Asseh, A.

A. Asseh, H. Storøy, B. Sahlgren, S. Sandgren, and R. Stubbe, "A writing technique for long fiber bragg gratings with complex reflectivity profiles," IEEE J. Lightwave Technol. 15, 1419-1423 (1997).
[CrossRef]

Bilodeau, F.

K. O. Hill, F. Bilodeau, B. Malo, and D. C. Johnson, "Birefringent photosensitivity in monomode optical fibre: application to external writing of rocking filters," Electron. Lett. 27, 1548-1550 (1991).
[CrossRef]

Borchert, B.

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitunal structure characterization of fiber Bragg gratings," IEEE J. Lightwave Technol. 16, 2435-2442 (1998).
[CrossRef]

Brinkmeyer, E.

U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," IEEE J. Lightwave Technol. 11, 1377-1384 (1993).
[CrossRef]

Eickhoff, W.

W. Eickhoff and R. Ulrich, "Optical frequency-domain reflectometry in single-mode fiber," Applied Physics Letters 39, 693-695 (1981).
[CrossRef]

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

T. Erdogan and V. Mizrahi, "Characterization of UV-induced birefringence in photosensitive Ge-doped silica optical fibers," J. Opt. Soc. Am. B 11, 2100-2105 (1994).
[CrossRef]

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

Foggatt, M.

Giaccari, P.

Gifford, D.

Gisin, N.

P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
[CrossRef]

J. von der Weid, R. Passy, G. Mussi, and N. Gisin, "On the characterization of optical network componenents with optical frequency domain reflectometry," IEEE J. Lightwave Technol. 15, 1131-1141 (1997).
[CrossRef]

Glombitza, U.

U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," IEEE J. Lightwave Technol. 11, 1377-1384 (1993).
[CrossRef]

Guinnard, L.

P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
[CrossRef]

Guinnard, O.

P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
[CrossRef]

Heise, G.

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitunal structure characterization of fiber Bragg gratings," IEEE J. Lightwave Technol. 16, 2435-2442 (1998).
[CrossRef]

Hill, K. O.

K. O. Hill, F. Bilodeau, B. Malo, and D. C. Johnson, "Birefringent photosensitivity in monomode optical fibre: application to external writing of rocking filters," Electron. Lett. 27, 1548-1550 (1991).
[CrossRef]

Horowitz, M.

Huang, D.-W.

Hutter, B.

P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
[CrossRef]

Johnson, D. C.

K. O. Hill, F. Bilodeau, B. Malo, and D. C. Johnson, "Birefringent photosensitivity in monomode optical fibre: application to external writing of rocking filters," Electron. Lett. 27, 1548-1550 (1991).
[CrossRef]

Kakuma, S.

S. Kakuma, K. Ohmura, and R. Ohba, "Improved uncertainty of optical frequency domain reflectometry based length measurement by linearizing the frequency chirping of a laser diode," Opt. Rev. 10, 182-183 (2003).
[CrossRef]

Keren, S.

Kherbouche, F.

F. Kherbouche and B. Poumellec, "UV-induced stress fields during Bragg grating inscription in optical fibers," J. Opt. A 3, 429-439 (2001).
[CrossRef]

Limberger, H.

Malo, B.

K. O. Hill, F. Bilodeau, B. Malo, and D. C. Johnson, "Birefringent photosensitivity in monomode optical fibre: application to external writing of rocking filters," Electron. Lett. 27, 1548-1550 (1991).
[CrossRef]

Meltz, G.

G. Meltz and W. W. Morey, "Bragg grating formation and germanosilicate fiber photosensitivity," in International workshop on photoinduced self-organization effects in optical fiber, Proc. Soc. Photo-Opt.Instrum. Eng. 1516, 185-199 (1991).

Mizrahi, V.

Morey, W. W.

G. Meltz and W. W. Morey, "Bragg grating formation and germanosilicate fiber photosensitivity," in International workshop on photoinduced self-organization effects in optical fiber, Proc. Soc. Photo-Opt.Instrum. Eng. 1516, 185-199 (1991).

Muriel, M. A.

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

Mussi, G.

J. von der Weid, R. Passy, G. Mussi, and N. Gisin, "On the characterization of optical network componenents with optical frequency domain reflectometry," IEEE J. Lightwave Technol. 15, 1131-1141 (1997).
[CrossRef]

Noe, R.

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitunal structure characterization of fiber Bragg gratings," IEEE J. Lightwave Technol. 16, 2435-2442 (1998).
[CrossRef]

Oberson, P.

P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
[CrossRef]

Ohba, R.

S. Kakuma, K. Ohmura, and R. Ohba, "Improved uncertainty of optical frequency domain reflectometry based length measurement by linearizing the frequency chirping of a laser diode," Opt. Rev. 10, 182-183 (2003).
[CrossRef]

Ohmura, K.

S. Kakuma, K. Ohmura, and R. Ohba, "Improved uncertainty of optical frequency domain reflectometry based length measurement by linearizing the frequency chirping of a laser diode," Opt. Rev. 10, 182-183 (2003).
[CrossRef]

Passy, R.

J. von der Weid, R. Passy, G. Mussi, and N. Gisin, "On the characterization of optical network componenents with optical frequency domain reflectometry," IEEE J. Lightwave Technol. 15, 1131-1141 (1997).
[CrossRef]

Pereira, S.

Poumellec, B.

F. Kherbouche and B. Poumellec, "UV-induced stress fields during Bragg grating inscription in optical fibers," J. Opt. A 3, 429-439 (2001).
[CrossRef]

Ribordy, G.

P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
[CrossRef]

Rønnekleiv, E.

E. Rønnekleiv, "Frequency and Intensity Noise of Single Frequency Fiber Bragg Grating Lasers," Opt. Fiber Technol. 7, 206-235 (2001).
[CrossRef]

Sahlgren, B.

A. Asseh, H. Storøy, B. Sahlgren, S. Sandgren, and R. Stubbe, "A writing technique for long fiber bragg gratings with complex reflectivity profiles," IEEE J. Lightwave Technol. 15, 1419-1423 (1997).
[CrossRef]

Salathe, R.

Sandel, D.

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitunal structure characterization of fiber Bragg gratings," IEEE J. Lightwave Technol. 16, 2435-2442 (1998).
[CrossRef]

Sandgren, S.

A. Asseh, H. Storøy, B. Sahlgren, S. Sandgren, and R. Stubbe, "A writing technique for long fiber bragg gratings with complex reflectivity profiles," IEEE J. Lightwave Technol. 15, 1419-1423 (1997).
[CrossRef]

Sipe, J. E.

Skaar, J.

O. Waagaard and J. Skaar, "Synthesis of birefringent reflective gratings," J. Opt. Soc. Am. A 21, 1207-1220 (2004).
[CrossRef]

J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Slusher, R. E.

Soller, B.

Spalter, S.

Storøy, H.

A. Asseh, H. Storøy, B. Sahlgren, S. Sandgren, and R. Stubbe, "A writing technique for long fiber bragg gratings with complex reflectivity profiles," IEEE J. Lightwave Technol. 15, 1419-1423 (1997).
[CrossRef]

Stubbe, R.

A. Asseh, H. Storøy, B. Sahlgren, S. Sandgren, and R. Stubbe, "A writing technique for long fiber bragg gratings with complex reflectivity profiles," IEEE J. Lightwave Technol. 15, 1419-1423 (1997).
[CrossRef]

Ulrich, R.

W. Eickhoff and R. Ulrich, "Optical frequency-domain reflectometry in single-mode fiber," Applied Physics Letters 39, 693-695 (1981).
[CrossRef]

von der Weid, J.

J. von der Weid, R. Passy, G. Mussi, and N. Gisin, "On the characterization of optical network componenents with optical frequency domain reflectometry," IEEE J. Lightwave Technol. 15, 1131-1141 (1997).
[CrossRef]

Waagaard, O.

O. Waagaard, "Spatial characterization of strong fiber Bragg gratings using thermal chirp and optical-frequency-domain reflectometry," IEEE J. Lightwave Technol. 23, 909-914 (2005).
[CrossRef]

O. Waagaard and J. Skaar, "Synthesis of birefringent reflective gratings," J. Opt. Soc. Am. A 21, 1207-1220 (2004).
[CrossRef]

Waagaard, O. H.

J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
[CrossRef]

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Wolfe, M.

Yang, C.-C.

Zervas, M. N.

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

Appl. Opt.

Applied Physics Letters

W. Eickhoff and R. Ulrich, "Optical frequency-domain reflectometry in single-mode fiber," Applied Physics Letters 39, 693-695 (1981).
[CrossRef]

Electron. Lett.

K. O. Hill, F. Bilodeau, B. Malo, and D. C. Johnson, "Birefringent photosensitivity in monomode optical fibre: application to external writing of rocking filters," Electron. Lett. 27, 1548-1550 (1991).
[CrossRef]

IEEE J. Lightwave Technol.

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitunal structure characterization of fiber Bragg gratings," IEEE J. Lightwave Technol. 16, 2435-2442 (1998).
[CrossRef]

U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," IEEE J. Lightwave Technol. 11, 1377-1384 (1993).
[CrossRef]

J. von der Weid, R. Passy, G. Mussi, and N. Gisin, "On the characterization of optical network componenents with optical frequency domain reflectometry," IEEE J. Lightwave Technol. 15, 1131-1141 (1997).
[CrossRef]

O. Waagaard, "Spatial characterization of strong fiber Bragg gratings using thermal chirp and optical-frequency-domain reflectometry," IEEE J. Lightwave Technol. 23, 909-914 (2005).
[CrossRef]

A. Asseh, H. Storøy, B. Sahlgren, S. Sandgren, and R. Stubbe, "A writing technique for long fiber bragg gratings with complex reflectivity profiles," IEEE J. Lightwave Technol. 15, 1419-1423 (1997).
[CrossRef]

IEEE J. Quantum Electron.

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

J. Skaar and O. H. Waagaard, "Design and characterization of finite length fiber gratings," IEEE J. Quantum Electron. 39, 1238-1245 (2003).
[CrossRef]

IEEE Photon. Technol. Lett.

P. Oberson, B. Hutter, O. Guinnard, L. Guinnard, G. Ribordy, and N. Gisin, "Optical frequency domain reflectometry with a narrow linwidth fiber laser," IEEE Photon. Technol. Lett. 12, 867-869 (2000).
[CrossRef]

Instrum. Eng.

G. Meltz and W. W. Morey, "Bragg grating formation and germanosilicate fiber photosensitivity," in International workshop on photoinduced self-organization effects in optical fiber, Proc. Soc. Photo-Opt.Instrum. Eng. 1516, 185-199 (1991).

J. Opt. A

F. Kherbouche and B. Poumellec, "UV-induced stress fields during Bragg grating inscription in optical fibers," J. Opt. A 3, 429-439 (2001).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Express

Opt. Fiber Technol.

E. Rønnekleiv, "Frequency and Intensity Noise of Single Frequency Fiber Bragg Grating Lasers," Opt. Fiber Technol. 7, 206-235 (2001).
[CrossRef]

Opt. Lett.

Opt. Rev.

S. Kakuma, K. Ohmura, and R. Ohba, "Improved uncertainty of optical frequency domain reflectometry based length measurement by linearizing the frequency chirping of a laser diode," Opt. Rev. 10, 182-183 (2003).
[CrossRef]

Other

R. Azzam and N. Bashara, Ellipsometry and polarized light (North-Holland, 1977).

O. Waagaard, E. Rønnekleiv, and J.T. Kringlebotn, "Spatial characterization of strong fiber Bragg gatings," in Proceedings of SPIE, Fiber-Based Components Fabrication, Testing, and Connectorization, V. Pruneri, R. Dahlgren, and G. Sanger, eds., vol. 4943, pp. 16-24 (2003).

Luna Technologies white paper, "Optical vector network analyzer for single scan measurements of loss, group delay and polarization mode dispersion," http://www.lunatechnologies.com/products/ova/files/OVAwhitePaper.pdf (Luna Technologies, 2005).

Agilent Technologies white paper, "Agilent 81910A Photonic All-Parameter Analyzer User Guide," http://www.home.agilent.com/agilent/facet.jspx?kt=1&cc=US&lc=eng&k=81910 (Agilent, 2005).

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Figures (6)

Fig. 1.
Fig. 1.

Optical frequency domain reflectometry setup for measuring the reflection Jones matrix of a FBG. TLS: Tunable laser source.

Fig. 2.
Fig. 2.

Optical frequency domain reflectometry of a FBG’s reflection Jones matrix. DFB-FL: Distributed-feedback fiber laser; LD: Diode pump laser; EDFA: Erbium doped fiber amplifier; TrigIF: Trigger interferometer; D1-4: Detectors; PolIF: Polarization modulation interferometer; PC1-2: Manual polarization controllers; FRM1-2: Faraday rotation mirrors; ADC: Analog-to-digital converter (NI-6052); PLD: Programmable logic device; Cmp: Comparator; PID1-2: Proportional-integrate-derivate controllers; SR: Sweep rate; Ref1-2: Reference signals; LPF: low-pass filter.

Fig. 3.
Fig. 3.

Measured instantaneous sweep rate of a Ando AQ4320B TLS (blue), open-loop fiber laser sweep (green) and closed-loop fiber laser sweep (red). In the upper red graph, the variations is sweep rate of the closed-loop fiber sweep is zoomed, and refers to the right vertical axis.

Fig. 4.
Fig. 4.

Fourier transform of the measured response at detector D1.

Fig. 5.
Fig. 5.

Amplitude of extracted signal bands of ζ (left) and the amplitude of components of the impulse response matrix h (right).

Fig. 6.
Fig. 6.

Spatial characterization of an FBG written with varying uv-polarization. Top: Index modulation amplitudes and differential modulation amplitude. s and p indicates the positions with s- and p-polarization was used to fabricate the grating. Middle: Orientation angles of the first index modulation eigenmode and of the first birefringence eigenmode. Bottom: dc-index change.

Equations (41)

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E m ( t ) = k m E ̂ m e i 2 π ν ( t τ m ) = k m Φ d T Φ m T Φ m Φ s E ̂ s e i 2 π ν ( t τ m ) ,
E r ( t ) = k r E ̂ r e i 2 π ν ( t τ r ) = k r Φ d T Φ r T R ( ν ) Φ r Φ s E ̂ s e i 2 π ν ( t τ r ) ,
P r ( ν ) = k m 2 E m ( t ) E m ( t ) + k r 2 E r ( t ) E r ( t )
+ 2 k m k r Re { E m ( t ) E r ( t ) }
= k m 2 E ̂ m E ̂ m + k r 2 E ̂ r E ̂ r + 2 k m k r Re { E ̂ m E ̂ r e i 2 π ν τ 0 }
P i ( ν ) = E ̂ m E ̂ r e i 2 π ν τ 0
= E ̂ s Φ s Φ m Φ m * Φ r T R ( ν ) Φ r Φ s E ̂ s e i 2 π ν τ 0
= E ̂ s Φ o R ( ν ) Φ i E ̂ s e i 2 π ν τ 0 ,
P i ( ν ) = ( R ˜ 11 E 1 2 + R ˜ 12 E 1 * E 2 + R ˜ 21 E 2 * E 1 + R ˜ 22 E 2 2 ) e i 2 π ν τ 0
= C s T [ R ˜ 11 R ˜ 21 R ˜ 12 R ˜ 22 ] e i 2 π τ 0 ν ,
[ P i , 1 ( ν ) P i , 2 ( ν ) P i , 3 ( ν ) P i , 4 ( ν ) ] = [ C s , 1 C s , 2 C s , 3 C s , 4 ] T [ R ˜ 11 R ˜ 21 R ˜ 12 R ˜ 22 ] e i 2 π τ 0 ν ,
E ̂ t = k t Φ t T ( ν ) Φ r Φ s E ̂ s ,
P t ( ν ) = k t 2 E ̂ t E ̂ t = k t 2 E ̂ s Φ s Φ r T ( ν ) T ( ν ) Φ r Φ s E ̂ s
= k t 2 E ̂ s Φ i T ( ν ) T ( ν ) Φ i E ̂ s = k t 2 E ̂ s T ˜ ( ν ) T ˜ ( ν ) E ˜ s
R ˜ ( ν ) R ˜ ( ν ) + T ˜ ( ν ) T ˜ ( ν ) = I .
D = [ e i θ 0 0 e i θ ] ,
h ( τ ) = D * U h ˜ ( τ ) V D = [ h ̂ 11 h ̂ 12 e i 2 θ h ̂ 21 e i 2 θ h ̂ 22 ] ,
Re { P i ( k Δ ν + δ ν ( k ) } Re { P i ( k Δ ν ) } + d Re { P i ( k Δ ν ) } d ν δ ν ( k ) .
Δ P i , rms = d Re { P i ( k Δ ν ) } d ν 2 δ ν ( k ) 2 = d Re { P i ( k Δ ν ) } d ν 2 δ ν rms .
E s ( t ) = E ̂ s e i 2 π ν t = E ̂ 1 e i ( 2 π ν ( t τ 1 ) ) + E ̂ 2 e i ( 2 π ν ( t τ 2 ) ) + E ̂ 3 e i ( 2 π ν ( t τ 3 ) )
= k 1 Φ 1 e i ( 2 π ν ( t τ 1 ) ) ( e ̂ 1 + E ̂ a e i 2 π ν τ a + E ̂ b e i 2 π ν τ b ) ,
E ̂ a = Φ 1 E ̂ 2 = k a [ sin θ a e i α a cos θ a e i β a ] = [ s a c a ]
E ̂ b = Φ 1 E ̂ 3 = k b [ sin θ b e i α b cos θ b e i β b ] = [ s b c b ] .
C s = M [ 1 e i 2 π ν ( τ b τ a ) e i 2 π ν ( τ b τ a ) e i 2 π ν τ a e i 2 π ν τ a e i 2 π ν τ b e i 2 π ν τ b ] ,
M = [ 1 + s a 2 + s b 2 s a s b * s a * s b s a * s a s b * s b s a c a * + s b c b * s a c b * c a * s b c a * 0 c b * 0 s a * c a + s b * c b c a s b * s a * c b 0 c a 0 c b c a 2 + c b 2 c a c b * c a * c b 0 0 0 0 ] .
M = [ 1 0 0 0 0 0 0 0 0 0 k a e i β 0 k b e i β 0 0 0 0 0 k a e i β 0 k b e i β k a 2 + k b 2 k a k b e i 2 β k a k b e i 2 β 0 0 0 0 ] .
P i ( ν ) = [ 1 e i 2 π ν ( τ b τ a ) e i 2 π ν ( τ b τ a ) e i 2 π ν τ a e i 2 π ν τ a e i 2 π ν τ b e i 2 π ν τ b ] T M T [ R ˜ 11 ( ν ) R ˜ 21 ( ν ) R ˜ 12 ( ν ) R ˜ 22 ( ν ) ] e i 2 π τ 0 ν .
[ ζ ( τ τ 0 ) ζ ( τ τ 0 + ( τ b τ a ) ) ζ ( τ τ 0 ( τ b τ a ) ) ζ ( τ τ 0 + τ a ) ζ ( τ τ 0 τ a ) ζ ( τ τ 0 + τ b ) ζ ( τ τ 0 τ b ) ] = M T [ h ˜ 11 ( τ ) h ˜ 21 ( τ ) h ˜ 12 ( τ ) h ˜ 22 ( τ ) ] ,
P D 3 ( ν ) = k D 3 [ e ̂ 1 k c ( E ̂ a e i 2 π ν τ a + E ̂ b e i 2 π ν τ b ) ] [ e ̂ 1 k c ( E ̂ a e i 2 π ν τ a + E ̂ b e i 2 π ν τ b ) ]
= k D 3 [ 1 + k c 2 ( k a 2 + k b 2 + 2 Re { ( s a * s b + c a * c b ) e i 2 π ν ( τ b τ a ) } )
2 k c ( Re { s a e i 2 π ν τ a } + Re { s b e i 2 π ν τ b } ) ] ,
s a = ζ D 3 ( τ a ) ( k D 3 k c )
s b = ζ D 3 ( τ b ) ( k D 3 k c )
c a = k a 2 s a 2
c b = k b 2 s b 2
β = arg ( c a c b * ) 2 = arg ( ζ D 3 ( τ b τ a ) * k D 3 ζ D 3 ( τ a ) * ζ D 3 ( τ b ) ) 2 .
ζ D 3 ( τ b τ a ) 2 + k a 2 ζ D 3 ( τ b ) 2 + k b 2 ζ D 3 ( τ a ) 2
= k a 2 k b 2 ( 1 + k a 2 + k b 2 ) 2 + 2 ( 1 + k a 2 + k b 2 ) Re { ζ D 3 ( τ b τ a ) ζ D 3 ( τ a ) ζ D 3 * ( τ b ) } ,
n ac , y ( z ) = n ac , x ( z + ) = n ac , x ( z ) + d n ac , x ( z ) d z .
Φ ˜ as = V 2 Φ as V 2 = W * D ,
D = [ e i θ 0 0 e i θ det W ] ,

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