Abstract

A numerical investigation on how fiber Bragg grating fabrication conditions using the phase mask technique affect the harmonic components of the Bragg wavelength is presented. Both the properties of the phase mask and saturation effects are investigated to determine the underlying cause of the rise of various harmonic reflections other than the Bragg wavelength. Results are compared with published data by various authors.

© 2013 Optical Society of America

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  1. K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fibre waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
    [CrossRef]
  2. R. Kashyap, Fiber Bragg Gratings/Raman Kashyap(Academic, 1999).
  3. A. Othonos, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing/Andreas Othonos, Kyriacos Kalli (Artech, 1999).
  4. W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
    [CrossRef]
  5. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightw. Technol. 15, 1263–1276 (1997).
    [CrossRef]
  6. G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).
  7. J. Echevarria, A. Quintela, C. Jauregui, and J. M. Lopez-Higuera, “Uniform fiber Bragg grating first- and second-order diffraction wavelength experimental characterization for strain-temperature discrimination,” IEEE Photon. Technol. Lett. 13, 696–698 (2001).
    [CrossRef]
  8. B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Single-excimer-pulse writing of fiber gratings by use of a zero-order nulled phase mask: grating spectral response and visualization of index perturbations,” Opt. Lett. 18, 1277–1279 (1993).
    [CrossRef]
  9. C. M. Rollinson, S. A. Wade, N. M. Dragomir, G. W. Baxter, S. F. Collins, and A. Roberts, “Reflections near 1030 nm from 1540 nm fibre Bragg gratings: evidence of a complex refractive index structure,” Opt. Commun. 256, 310–318 (2005).
    [CrossRef]
  10. S. P. Yam, D. J. Kitcher, S. A. Wade, G. W. Baxter, and S. F. Collins, “Investigation of wavelength variations of fibre Bragg grating features using a chirped phase mask,” J. Opt. A 10, 055307 (2008).
    [CrossRef]
  11. S. P. Yam, Z. Brodzeli, B. P. Kouskousis, C. M. Rollinson, S. A. Wade, G. W. Baxter, and S. F. Collins, “Fabrication of a π-phase-shifted fiber Bragg grating at twice the Bragg wavelength with the standard phase mask technique,” Opt. Lett. 34, 2021–2023 (2009).
    [CrossRef]
  12. C. M. Rollinson, S. A. Wade, B. P. Kouskousis, D. J. Kitcher, G. W. Baxter, and S. F. Collins, “Variations of the growth of harmonic reflections in fiber Bragg gratings fabricated using phase masks,” J. Opt. Soc. Am. A 29, 1259–1268 (2012).
    [CrossRef]
  13. S. A. Wade, W. G. A. Brown, H. K. Bal, F. Sidiroglou, G. W. Baxter, and S. F. Collins, “Effect of phase mask alignment on fiber Bragg grating spectra at harmonics of the Bragg wavelength,” J. Opt. Soc. Am. A 29, 1597–1605 (2012).
    [CrossRef]
  14. J. D. Mills, C. W. J. Hillman, B. H. Blott, and W. S. Brocklesby, “Imaging of free-space interference patterns used to manufacture fiber Bragg gratings,” Appl. Opt. 39, 6128–6135 (2000).
    [CrossRef]
  15. C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. M. Ding, and X. L. Dai, “Multiple-beam interference patterns in optical fiber generated with ultrafast pulses and a phase mask,” Opt. Lett. 29, 1458–1460 (2004).
    [CrossRef]
  16. N. M. Dragomir, C. Rollinson, S. A. Wade, A. J. Stevenson, S. F. Collins, G. W. Baxter, P. M. Farrell, and A. Roberts, “Nondestructive imaging of a type I optical fiber Bragg grating,” Opt. Lett. 28, 789–791 (2003).
    [CrossRef]
  17. P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
    [CrossRef]
  18. B. P. Kouskousis, C. M. Rollinson, D. J. Kitcher, S. F. Collins, G. W. Baxter, S. A. Wade, N. M. Dragomir, and A. Roberts, “Quantitative investigation of the refractive-index modulation within the core of a fiber Bragg grating,” Opt. Express 14, 10332–10338 (2006).
    [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 3rd ed. (Pergamon, 1965), pp. xxviii, 808.
  20. T. Osuch and Z. Jaroszewicz, “Numerical analysis of apodized fiber Bragg gratings formation using phase mask with variable diffraction efficiency,” Opt. Commun. 284, 567–572 (2011).
    [CrossRef]
  21. R. J. Espejo, M. Svalgaard, and S. D. Dyer, “Characterizing fiber Bragg grating index profiles to improve the writing process,” IEEE Photon. Technol. Lett. 18, 2242–2244 (2006).
    [CrossRef]
  22. H. Patrick and S. L. Gilbert, “Growth of Bragg gratings produced by continuous-wave ultraviolet light in optical fiber,” Opt. Lett. 18, 1484–1486 (1993).
    [CrossRef]

2012 (2)

2011 (1)

T. Osuch and Z. Jaroszewicz, “Numerical analysis of apodized fiber Bragg gratings formation using phase mask with variable diffraction efficiency,” Opt. Commun. 284, 567–572 (2011).
[CrossRef]

2009 (1)

2008 (1)

S. P. Yam, D. J. Kitcher, S. A. Wade, G. W. Baxter, and S. F. Collins, “Investigation of wavelength variations of fibre Bragg grating features using a chirped phase mask,” J. Opt. A 10, 055307 (2008).
[CrossRef]

2006 (2)

2005 (1)

C. M. Rollinson, S. A. Wade, N. M. Dragomir, G. W. Baxter, S. F. Collins, and A. Roberts, “Reflections near 1030 nm from 1540 nm fibre Bragg gratings: evidence of a complex refractive index structure,” Opt. Commun. 256, 310–318 (2005).
[CrossRef]

2004 (1)

2003 (1)

2001 (1)

J. Echevarria, A. Quintela, C. Jauregui, and J. M. Lopez-Higuera, “Uniform fiber Bragg grating first- and second-order diffraction wavelength experimental characterization for strain-temperature discrimination,” IEEE Photon. Technol. Lett. 13, 696–698 (2001).
[CrossRef]

2000 (1)

1997 (2)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightw. Technol. 15, 1263–1276 (1997).
[CrossRef]

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).

1995 (1)

P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

1993 (3)

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fibre waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Albert, J.

Archambault, J. L.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).

Bal, H. K.

Baxter, G. W.

S. A. Wade, W. G. A. Brown, H. K. Bal, F. Sidiroglou, G. W. Baxter, and S. F. Collins, “Effect of phase mask alignment on fiber Bragg grating spectra at harmonics of the Bragg wavelength,” J. Opt. Soc. Am. A 29, 1597–1605 (2012).
[CrossRef]

C. M. Rollinson, S. A. Wade, B. P. Kouskousis, D. J. Kitcher, G. W. Baxter, and S. F. Collins, “Variations of the growth of harmonic reflections in fiber Bragg gratings fabricated using phase masks,” J. Opt. Soc. Am. A 29, 1259–1268 (2012).
[CrossRef]

S. P. Yam, Z. Brodzeli, B. P. Kouskousis, C. M. Rollinson, S. A. Wade, G. W. Baxter, and S. F. Collins, “Fabrication of a π-phase-shifted fiber Bragg grating at twice the Bragg wavelength with the standard phase mask technique,” Opt. Lett. 34, 2021–2023 (2009).
[CrossRef]

S. P. Yam, D. J. Kitcher, S. A. Wade, G. W. Baxter, and S. F. Collins, “Investigation of wavelength variations of fibre Bragg grating features using a chirped phase mask,” J. Opt. A 10, 055307 (2008).
[CrossRef]

B. P. Kouskousis, C. M. Rollinson, D. J. Kitcher, S. F. Collins, G. W. Baxter, S. A. Wade, N. M. Dragomir, and A. Roberts, “Quantitative investigation of the refractive-index modulation within the core of a fiber Bragg grating,” Opt. Express 14, 10332–10338 (2006).
[CrossRef]

C. M. Rollinson, S. A. Wade, N. M. Dragomir, G. W. Baxter, S. F. Collins, and A. Roberts, “Reflections near 1030 nm from 1540 nm fibre Bragg gratings: evidence of a complex refractive index structure,” Opt. Commun. 256, 310–318 (2005).
[CrossRef]

N. M. Dragomir, C. Rollinson, S. A. Wade, A. J. Stevenson, S. F. Collins, G. W. Baxter, P. M. Farrell, and A. Roberts, “Nondestructive imaging of a type I optical fiber Bragg grating,” Opt. Lett. 28, 789–791 (2003).
[CrossRef]

Bayon, J. F.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Bernage, P.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Bilodeau, F.

Blott, B. H.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 3rd ed. (Pergamon, 1965), pp. xxviii, 808.

Brady, G. P.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).

Brocklesby, W. S.

Brodzeli, Z.

Brown, W. G. A.

Collins, S. F.

C. M. Rollinson, S. A. Wade, B. P. Kouskousis, D. J. Kitcher, G. W. Baxter, and S. F. Collins, “Variations of the growth of harmonic reflections in fiber Bragg gratings fabricated using phase masks,” J. Opt. Soc. Am. A 29, 1259–1268 (2012).
[CrossRef]

S. A. Wade, W. G. A. Brown, H. K. Bal, F. Sidiroglou, G. W. Baxter, and S. F. Collins, “Effect of phase mask alignment on fiber Bragg grating spectra at harmonics of the Bragg wavelength,” J. Opt. Soc. Am. A 29, 1597–1605 (2012).
[CrossRef]

S. P. Yam, Z. Brodzeli, B. P. Kouskousis, C. M. Rollinson, S. A. Wade, G. W. Baxter, and S. F. Collins, “Fabrication of a π-phase-shifted fiber Bragg grating at twice the Bragg wavelength with the standard phase mask technique,” Opt. Lett. 34, 2021–2023 (2009).
[CrossRef]

S. P. Yam, D. J. Kitcher, S. A. Wade, G. W. Baxter, and S. F. Collins, “Investigation of wavelength variations of fibre Bragg grating features using a chirped phase mask,” J. Opt. A 10, 055307 (2008).
[CrossRef]

B. P. Kouskousis, C. M. Rollinson, D. J. Kitcher, S. F. Collins, G. W. Baxter, S. A. Wade, N. M. Dragomir, and A. Roberts, “Quantitative investigation of the refractive-index modulation within the core of a fiber Bragg grating,” Opt. Express 14, 10332–10338 (2006).
[CrossRef]

C. M. Rollinson, S. A. Wade, N. M. Dragomir, G. W. Baxter, S. F. Collins, and A. Roberts, “Reflections near 1030 nm from 1540 nm fibre Bragg gratings: evidence of a complex refractive index structure,” Opt. Commun. 256, 310–318 (2005).
[CrossRef]

N. M. Dragomir, C. Rollinson, S. A. Wade, A. J. Stevenson, S. F. Collins, G. W. Baxter, P. M. Farrell, and A. Roberts, “Nondestructive imaging of a type I optical fiber Bragg grating,” Opt. Lett. 28, 789–791 (2003).
[CrossRef]

Dai, X. L.

Ding, H. M.

Douay, M.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Dragomir, N. M.

Dyer, P. E.

P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

Dyer, S. D.

R. J. Espejo, M. Svalgaard, and S. D. Dyer, “Characterizing fiber Bragg grating index profiles to improve the writing process,” IEEE Photon. Technol. Lett. 18, 2242–2244 (2006).
[CrossRef]

Echevarria, J.

J. Echevarria, A. Quintela, C. Jauregui, and J. M. Lopez-Higuera, “Uniform fiber Bragg grating first- and second-order diffraction wavelength experimental characterization for strain-temperature discrimination,” IEEE Photon. Technol. Lett. 13, 696–698 (2001).
[CrossRef]

Espejo, R. J.

R. J. Espejo, M. Svalgaard, and S. D. Dyer, “Characterizing fiber Bragg grating index profiles to improve the writing process,” IEEE Photon. Technol. Lett. 18, 2242–2244 (2006).
[CrossRef]

Farley, R. J.

P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

Farrell, P. M.

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fibre waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Georges, T.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Giedl, R.

P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

Gilbert, S. L.

Grobnic, D.

Hill, K. O.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightw. Technol. 15, 1263–1276 (1997).
[CrossRef]

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Single-excimer-pulse writing of fiber gratings by use of a zero-order nulled phase mask: grating spectral response and visualization of index perturbations,” Opt. Lett. 18, 1277–1279 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fibre waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Hillman, C. W. J.

Jackson, D. A.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).

Jaroszewicz, Z.

T. Osuch and Z. Jaroszewicz, “Numerical analysis of apodized fiber Bragg gratings formation using phase mask with variable diffraction efficiency,” Opt. Commun. 284, 567–572 (2011).
[CrossRef]

Jauregui, C.

J. Echevarria, A. Quintela, C. Jauregui, and J. M. Lopez-Higuera, “Uniform fiber Bragg grating first- and second-order diffraction wavelength experimental characterization for strain-temperature discrimination,” IEEE Photon. Technol. Lett. 13, 696–698 (2001).
[CrossRef]

Johnson, D. C.

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Single-excimer-pulse writing of fiber gratings by use of a zero-order nulled phase mask: grating spectral response and visualization of index perturbations,” Opt. Lett. 18, 1277–1279 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fibre waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kalli, K.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings/Raman Kashyap(Academic, 1999).

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fibre waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kitcher, D. J.

Kouskousis, B. P.

Lopez-Higuera, J. M.

J. Echevarria, A. Quintela, C. Jauregui, and J. M. Lopez-Higuera, “Uniform fiber Bragg grating first- and second-order diffraction wavelength experimental characterization for strain-temperature discrimination,” IEEE Photon. Technol. Lett. 13, 696–698 (2001).
[CrossRef]

Lu, P.

Malo, B.

Meltz, G.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightw. Technol. 15, 1263–1276 (1997).
[CrossRef]

Mihailov, S. J.

Mills, J. D.

Niay, P.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Osuch, T.

T. Osuch and Z. Jaroszewicz, “Numerical analysis of apodized fiber Bragg gratings formation using phase mask with variable diffraction efficiency,” Opt. Commun. 284, 567–572 (2011).
[CrossRef]

Othonos, A.

A. Othonos, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing/Andreas Othonos, Kyriacos Kalli (Artech, 1999).

Patrick, H.

Quintela, A.

J. Echevarria, A. Quintela, C. Jauregui, and J. M. Lopez-Higuera, “Uniform fiber Bragg grating first- and second-order diffraction wavelength experimental characterization for strain-temperature discrimination,” IEEE Photon. Technol. Lett. 13, 696–698 (2001).
[CrossRef]

Reekie, L.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).

Roberts, A.

Rollinson, C.

Rollinson, C. M.

Sidiroglou, F.

Smelser, C. W.

Stevenson, A. J.

Svalgaard, M.

R. J. Espejo, M. Svalgaard, and S. D. Dyer, “Characterizing fiber Bragg grating index profiles to improve the writing process,” IEEE Photon. Technol. Lett. 18, 2242–2244 (2006).
[CrossRef]

Wade, S. A.

C. M. Rollinson, S. A. Wade, B. P. Kouskousis, D. J. Kitcher, G. W. Baxter, and S. F. Collins, “Variations of the growth of harmonic reflections in fiber Bragg gratings fabricated using phase masks,” J. Opt. Soc. Am. A 29, 1259–1268 (2012).
[CrossRef]

S. A. Wade, W. G. A. Brown, H. K. Bal, F. Sidiroglou, G. W. Baxter, and S. F. Collins, “Effect of phase mask alignment on fiber Bragg grating spectra at harmonics of the Bragg wavelength,” J. Opt. Soc. Am. A 29, 1597–1605 (2012).
[CrossRef]

S. P. Yam, Z. Brodzeli, B. P. Kouskousis, C. M. Rollinson, S. A. Wade, G. W. Baxter, and S. F. Collins, “Fabrication of a π-phase-shifted fiber Bragg grating at twice the Bragg wavelength with the standard phase mask technique,” Opt. Lett. 34, 2021–2023 (2009).
[CrossRef]

S. P. Yam, D. J. Kitcher, S. A. Wade, G. W. Baxter, and S. F. Collins, “Investigation of wavelength variations of fibre Bragg grating features using a chirped phase mask,” J. Opt. A 10, 055307 (2008).
[CrossRef]

B. P. Kouskousis, C. M. Rollinson, D. J. Kitcher, S. F. Collins, G. W. Baxter, S. A. Wade, N. M. Dragomir, and A. Roberts, “Quantitative investigation of the refractive-index modulation within the core of a fiber Bragg grating,” Opt. Express 14, 10332–10338 (2006).
[CrossRef]

C. M. Rollinson, S. A. Wade, N. M. Dragomir, G. W. Baxter, S. F. Collins, and A. Roberts, “Reflections near 1030 nm from 1540 nm fibre Bragg gratings: evidence of a complex refractive index structure,” Opt. Commun. 256, 310–318 (2005).
[CrossRef]

N. M. Dragomir, C. Rollinson, S. A. Wade, A. J. Stevenson, S. F. Collins, G. W. Baxter, P. M. Farrell, and A. Roberts, “Nondestructive imaging of a type I optical fiber Bragg grating,” Opt. Lett. 28, 789–791 (2003).
[CrossRef]

Walker, R. B.

Webb, D. J.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 3rd ed. (Pergamon, 1965), pp. xxviii, 808.

Xie, W. X.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Yam, S. P.

S. P. Yam, Z. Brodzeli, B. P. Kouskousis, C. M. Rollinson, S. A. Wade, G. W. Baxter, and S. F. Collins, “Fabrication of a π-phase-shifted fiber Bragg grating at twice the Bragg wavelength with the standard phase mask technique,” Opt. Lett. 34, 2021–2023 (2009).
[CrossRef]

S. P. Yam, D. J. Kitcher, S. A. Wade, G. W. Baxter, and S. F. Collins, “Investigation of wavelength variations of fibre Bragg grating features using a chirped phase mask,” J. Opt. A 10, 055307 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fibre waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. Echevarria, A. Quintela, C. Jauregui, and J. M. Lopez-Higuera, “Uniform fiber Bragg grating first- and second-order diffraction wavelength experimental characterization for strain-temperature discrimination,” IEEE Photon. Technol. Lett. 13, 696–698 (2001).
[CrossRef]

R. J. Espejo, M. Svalgaard, and S. D. Dyer, “Characterizing fiber Bragg grating index profiles to improve the writing process,” IEEE Photon. Technol. Lett. 18, 2242–2244 (2006).
[CrossRef]

IEEE Proc. Optoelectron. (1)

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Reekie, and J. L. Archambault, “Simultaneous measurement of strain and temperature using the first and second-order diffraction wavelengths of Bragg gratings,” IEEE Proc. Optoelectron. 144, 156–161 (1997).

J. Lightw. Technol. (1)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightw. Technol. 15, 1263–1276 (1997).
[CrossRef]

J. Opt. A (1)

S. P. Yam, D. J. Kitcher, S. A. Wade, G. W. Baxter, and S. F. Collins, “Investigation of wavelength variations of fibre Bragg grating features using a chirped phase mask,” J. Opt. A 10, 055307 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (4)

P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

C. M. Rollinson, S. A. Wade, N. M. Dragomir, G. W. Baxter, S. F. Collins, and A. Roberts, “Reflections near 1030 nm from 1540 nm fibre Bragg gratings: evidence of a complex refractive index structure,” Opt. Commun. 256, 310–318 (2005).
[CrossRef]

T. Osuch and Z. Jaroszewicz, “Numerical analysis of apodized fiber Bragg gratings formation using phase mask with variable diffraction efficiency,” Opt. Commun. 284, 567–572 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Other (3)

R. Kashyap, Fiber Bragg Gratings/Raman Kashyap(Academic, 1999).

A. Othonos, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing/Andreas Othonos, Kyriacos Kalli (Artech, 1999).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 3rd ed. (Pergamon, 1965), pp. xxviii, 808.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Intensity distribution produced inside the core region of a fiber during FBG fabrication using the phase mask technique, including the zeroth and ±1 diffraction orders of the phase mask. (b) Magnitude of the FFT of the intensity distribution, used to determine the expected harmonics, with the maxima and their associated periodicity identified.

Fig. 2.
Fig. 2.

(a) Intensity distribution produced inside the core region of a fiber during FBG fabrication using the phase mask technique, including the zeroth, ±1 and ±2 diffraction orders of the phase mask. (b) Magnitude of the FFT of the intensity distribution, used to determine the expected harmonics, with the maxima and their associated periodicity identified.

Fig. 3.
Fig. 3.

(a) Intensity distribution produced inside the core region of a fiber during FBG fabrication using the phase mask technique, including the zeroth, ±1, ±2, and ±3 diffraction orders of the phase mask. (b) Magnitude of the FFT of the intensity distribution, used to determine the expected harmonics, with the maxima and their associated periodicity identified.

Fig. 4.
Fig. 4.

(a) Intensity distribution produced inside the core region of a fiber during FBG fabrication using the phase mask technique, including the zeroth, ±1, ±2, ±3 and ±4 diffraction orders of the phase mask. (b) Magnitude of the FFT of the intensity distribution, used to determine the expected harmonics, with the maxima and their associated periodicity identified.

Fig. 5.
Fig. 5.

Saturation effects on the Bragg reflectance peak growth, where the values in the figures correspond to the grating period with the associated harmonic peak. Intensity distribution simulated for a FBG fabricated using the phase mask technique, including (a) the zeroth and ±1, (b) the zeroth, ±1, and ±2, (c) the zeroth, ±1, ±2, and ±3, and (d) the zeroth, ±1, ±2, ±3 and ±4 diffraction orders of the phase mask.

Tables (3)

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Table 1. Diffracted Orders Measured in the Far Field, where Λpm=1.06μm

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Table 2. Calculated Range across Grating in which Diffracted Orders Overlap Coherently

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Table 3. Summary of the Simulation Results and Comparison with Experimenta

Equations (3)

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λj=2jneffΛ,
E(x,z)=mCmexp(imGx)exp(ikmz),
u(x,z)=umax(x,z)(1exp(F(x,z)/F0(x,z))),

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