Abstract

We have studied the effect of waveguide alignment on the reflection spectrum of Bragg gratings fabricated using a multiple order phase mask. We have demonstrated that splitting of certain Bragg peaks observed in earlier experiments reported in literature is caused by formation of the gratings with different periodicities in the waveguide tilted with respect to the phase mask plane due to the interference of non-symmetrical diffraction orders. Analytical expressions for spectral separation of the split peaks have been derived and verified against the experimental data recently presented in literature. The analytical predictions were also confirmed by numerical simulations of intensity distributions behind the multiple order diffraction grating and its projection on the tilted waveguide.

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  1. K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett.32(10), 647–649 (1978).
    [CrossRef]
  2. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.62(10), 1035–1037 (1993).
    [CrossRef]
  3. G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett.14(15), 823–825 (1989).
    [CrossRef] [PubMed]
  4. K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
    [CrossRef]
  5. P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, and D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193nm ArF laser,” Electron. Lett.30(11), 860–862 (1994).
    [CrossRef]
  6. Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” IEEE Photon. Technol. Lett.11(3), 352–354 (1999).
    [CrossRef]
  7. G. Statkiewicz-Barabach, K. Tarnowski, D. Kowal, P. Mergo, and W. Urbanczyk, “Fabrication of multiple Bragg gratings in microstructured polymer fibers using a phase mask with several diffraction orders,” Opt. Express21(7), 8521–8534 (2013).
    [CrossRef] [PubMed]
  8. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
    [CrossRef]
  9. S. P. Yam, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Occurrence of features of fiber bragg grating spectra having a wavelength corresponding to the phase mask periodicity,” J. Electron. Sci. Technol.6, 458–461 (2008).
  10. 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(33), 6128–6135 (2000).
    [CrossRef] [PubMed]
  11. H. F. Talbot, “Facts relating to optical science,” Philos. Mag.9, 401–407 (1836).
  12. 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(10), 789–791 (2003).
    [CrossRef] [PubMed]
  13. Z. F. Zhang, C. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” Photon. Technol. Lett.22(21), 1562–1564 (2010).
    [CrossRef]
  14. 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(15), 1277–1279 (1993).
    [CrossRef] [PubMed]
  15. P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun.115(3-4), 327–334 (1995).
    [CrossRef]
  16. C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, “Multiple-beam interference patterns in optical fiber generated with ultrafast pulses and a phase mask,” Opt. Lett.29(13), 1458–1460 (2004).
    [CrossRef] [PubMed]
  17. 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(4-6), 310–318 (2005).
    [CrossRef]
  18. 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. A29(7), 1259–1268 (2012).
    [CrossRef] [PubMed]
  19. 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(13), 2021–2023 (2009).
    [CrossRef] [PubMed]
  20. 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. A29(8), 1597–1605 (2012).
    [CrossRef] [PubMed]

2013 (1)

2012 (2)

2010 (1)

Z. F. Zhang, C. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” Photon. Technol. Lett.22(21), 1562–1564 (2010).
[CrossRef]

2009 (1)

2008 (1)

S. P. Yam, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Occurrence of features of fiber bragg grating spectra having a wavelength corresponding to the phase mask periodicity,” J. Electron. Sci. Technol.6, 458–461 (2008).

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(4-6), 310–318 (2005).
[CrossRef]

2004 (1)

2003 (1)

2000 (1)

1999 (1)

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” IEEE Photon. Technol. Lett.11(3), 352–354 (1999).
[CrossRef]

1997 (1)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

1995 (1)

P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun.115(3-4), 327–334 (1995).
[CrossRef]

1994 (1)

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, and D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193nm ArF laser,” Electron. Lett.30(11), 860–862 (1994).
[CrossRef]

1993 (2)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.62(10), 1035–1037 (1993).
[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(15), 1277–1279 (1993).
[CrossRef] [PubMed]

1990 (1)

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
[CrossRef]

1989 (1)

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett.32(10), 647–649 (1978).
[CrossRef]

1836 (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag.9, 401–407 (1836).

Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.62(10), 1035–1037 (1993).
[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(15), 1277–1279 (1993).
[CrossRef] [PubMed]

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. A29(8), 1597–1605 (2012).
[CrossRef] [PubMed]

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. A29(7), 1259–1268 (2012).
[CrossRef] [PubMed]

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(13), 2021–2023 (2009).
[CrossRef] [PubMed]

S. P. Yam, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Occurrence of features of fiber bragg grating spectra having a wavelength corresponding to the phase mask periodicity,” J. Electron. Sci. Technol.6, 458–461 (2008).

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(4-6), 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(10), 789–791 (2003).
[CrossRef] [PubMed]

Bilodeau, F.

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(15), 1277–1279 (1993).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.62(10), 1035–1037 (1993).
[CrossRef]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
[CrossRef]

Blott, B. H.

Brocklesby, W. S.

Brodzeli, Z.

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(13), 2021–2023 (2009).
[CrossRef] [PubMed]

S. P. Yam, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Occurrence of features of fiber bragg grating spectra having a wavelength corresponding to the phase mask periodicity,” J. Electron. Sci. Technol.6, 458–461 (2008).

Brown, W. G. A.

Byron, K. C.

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, and D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193nm ArF laser,” Electron. Lett.30(11), 860–862 (1994).
[CrossRef]

Chu, P. L.

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” IEEE Photon. Technol. Lett.11(3), 352–354 (1999).
[CrossRef]

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. A29(7), 1259–1268 (2012).
[CrossRef] [PubMed]

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. A29(8), 1597–1605 (2012).
[CrossRef] [PubMed]

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(13), 2021–2023 (2009).
[CrossRef] [PubMed]

S. P. Yam, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Occurrence of features of fiber bragg grating spectra having a wavelength corresponding to the phase mask periodicity,” J. Electron. Sci. Technol.6, 458–461 (2008).

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(4-6), 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(10), 789–791 (2003).
[CrossRef] [PubMed]

Dai, X.

Ding, H.

Dragomir, N. M.

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(4-6), 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(10), 789–791 (2003).
[CrossRef] [PubMed]

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(3-4), 327–334 (1995).
[CrossRef]

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, and D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193nm ArF laser,” Electron. Lett.30(11), 860–862 (1994).
[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(3-4), 327–334 (1995).
[CrossRef]

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, and D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193nm ArF laser,” Electron. Lett.30(11), 860–862 (1994).
[CrossRef]

Farrell, P. M.

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett.32(10), 647–649 (1978).
[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(3-4), 327–334 (1995).
[CrossRef]

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, and D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193nm ArF laser,” Electron. Lett.30(11), 860–862 (1994).
[CrossRef]

Glenn, W. H.

Grobnic, D.

Hill, K. O.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.62(10), 1035–1037 (1993).
[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(15), 1277–1279 (1993).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett.32(10), 647–649 (1978).
[CrossRef]

Hillman, C. W. J.

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.62(10), 1035–1037 (1993).
[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(15), 1277–1279 (1993).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett.32(10), 647–649 (1978).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett.32(10), 647–649 (1978).
[CrossRef]

Kitcher, D. J.

Kouskousis, B. P.

Kowal, D.

Lu, P.

Malo, B.

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(15), 1277–1279 (1993).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.62(10), 1035–1037 (1993).
[CrossRef]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
[CrossRef]

Meltz, G.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett.14(15), 823–825 (1989).
[CrossRef] [PubMed]

Mergo, P.

Mihailov, S. J.

Mills, J. D.

Morey, W. W.

Peng, G. D.

Z. F. Zhang, C. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” Photon. Technol. Lett.22(21), 1562–1564 (2010).
[CrossRef]

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” IEEE Photon. Technol. Lett.11(3), 352–354 (1999).
[CrossRef]

Reid, D.

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, and D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193nm ArF laser,” Electron. Lett.30(11), 860–862 (1994).
[CrossRef]

Roberts, A.

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(4-6), 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(10), 789–791 (2003).
[CrossRef] [PubMed]

Rollinson, C.

Rollinson, C. M.

Sidiroglou, F.

Skinner, I.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
[CrossRef]

Smelser, C. W.

Statkiewicz-Barabach, G.

Stevenson, A. J.

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science,” Philos. Mag.9, 401–407 (1836).

Tao, X. M.

Z. F. Zhang, C. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” Photon. Technol. Lett.22(21), 1562–1564 (2010).
[CrossRef]

Tarnowski, K.

Urbanczyk, W.

Vineberg, K. A.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
[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. A29(7), 1259–1268 (2012).
[CrossRef] [PubMed]

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. A29(8), 1597–1605 (2012).
[CrossRef] [PubMed]

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(13), 2021–2023 (2009).
[CrossRef] [PubMed]

S. P. Yam, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Occurrence of features of fiber bragg grating spectra having a wavelength corresponding to the phase mask periodicity,” J. Electron. Sci. Technol.6, 458–461 (2008).

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(4-6), 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(10), 789–791 (2003).
[CrossRef] [PubMed]

Walker, R. B.

Wang, G. F.

Z. F. Zhang, C. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” Photon. Technol. Lett.22(21), 1562–1564 (2010).
[CrossRef]

Wu, B.

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” IEEE Photon. Technol. Lett.11(3), 352–354 (1999).
[CrossRef]

Xiong, Z.

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” IEEE Photon. Technol. Lett.11(3), 352–354 (1999).
[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(13), 2021–2023 (2009).
[CrossRef] [PubMed]

S. P. Yam, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Occurrence of features of fiber bragg grating spectra having a wavelength corresponding to the phase mask periodicity,” J. Electron. Sci. Technol.6, 458–461 (2008).

Zhang, C.

Z. F. Zhang, C. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” Photon. Technol. Lett.22(21), 1562–1564 (2010).
[CrossRef]

Zhang, Z. F.

Z. F. Zhang, C. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” Photon. Technol. Lett.22(21), 1562–1564 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett.32(10), 647–649 (1978).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett.62(10), 1035–1037 (1993).
[CrossRef]

Electron. Lett. (2)

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett.26(16), 1270–1272 (1990).
[CrossRef]

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, and D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193nm ArF laser,” Electron. Lett.30(11), 860–862 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” IEEE Photon. Technol. Lett.11(3), 352–354 (1999).
[CrossRef]

J. Electron. Sci. Technol. (1)

S. P. Yam, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Occurrence of features of fiber bragg grating spectra having a wavelength corresponding to the phase mask periodicity,” J. Electron. Sci. Technol.6, 458–461 (2008).

J. Lightwave Technol. (1)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

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

Opt. Commun. (2)

P. E. Dyer, R. J. Farley, and R. Giedl, “Analysis of grating formation with excimer laser irradiated phase masks,” Opt. Commun.115(3-4), 327–334 (1995).
[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(4-6), 310–318 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Philos. Mag. (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag.9, 401–407 (1836).

Photon. Technol. Lett. (1)

Z. F. Zhang, C. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” Photon. Technol. Lett.22(21), 1562–1564 (2010).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Interference patterns behind the phase mask: (a) calculated only for the ± 1st diffraction orders, (b) for the 0th and the ± 1st diffraction orders, (c) for the 0th, the ± 1st and the ± 2nd diffraction orders. The phase mask of a period Λd = 1.0703 μm is parallel to x-coordinates. After [20] the diffraction efficiencies of the 0th, the ± 1st and the ± 2nd orders are equal to 4.1%, 44.3%, 3.7%, respectively. The incidence beam is parallel to z-coordinates.

Fig. 2
Fig. 2

Wave vectors of incident and diffracted beams. (K) represents the inverse vector of the phase mask, while s and t indicate unit vector tangential and normal to the waveguide surface, respectively. The red arrows indicate corresponding differences between the wave vectors of diffracted beams.

Fig. 3
Fig. 3

Wave vectors of incident and diffracted beams. (K) represents the inverse vector of the phase mask, km are wave vectors of diffracted beams, s and t are unit vectors respectively tangential and normal to the waveguide’s top surface, while r is normal to s and t. Simultaneously s represents the direction of mode propagation in the considered waveguide.

Fig. 4
Fig. 4

Results of numerical simulations: (a) waveguide parallel to the phase mask (φ = 0), mode field diameter 4 μm; (b) tilted waveguide (φ = 0.1°), mode field diameter 4 μm; (c) tilted waveguide (φ = 0.1°), mode field diameter 1 μm. From left to right: refractive index change in the core of the planar waveguide weighted with Gaussian mode intensity distribution plotted in (s, t) coordinates; modulation of effective refractive index obtained by integration of previous plot along t direction (only first two cycles are shown); spatial frequencies present in grating (absolute value of Fourier transform indicating relative strength of respective periodicities). Each peak is denoted with corresponding Bragg wavelength of the first order reflection. Split peaks for spatial frequencies 1/Λd and 2/Λd labeled with interfering diffraction orders.

Fig. 5
Fig. 5

Reflection coefficient calculated using a finite element method at around 2λB for 2.20 mm long grating inscribed in narrow silica waveguide tilted by φ = 0.1° during inscription process.

Equations (26)

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λ B =2 n eff Λ,
( k m kmK )× z ^ =0,
k 1 =[ K,0, k 2 K 2 ],
k 0 =[ 0,0,k ],
k +1 =[ K,0, k 2 K 2 ],
s=[ cosφ,0,sinφ ],
Λ m,q = 2π k m,q s = 2π k m,q ,
k 1,0 s= k 0,+1 s.
Λ 1,+1 = 1 cosφ Λ d 2 , Λ 1,0 = Λ d cosφκsinφ , Λ 0,+1 = Λ d cosφ+κsinφ ,
κ= k K ( k K ) 2 1 = Λ d λ UV ( Λ d λ UV ) 2 1 .
κ= Λ d Λ T ,
Λ T = 2π k k 2 K 2 .
λ B ( φ )=2 n eff ( λ B ( φ ) ) 1 cosφ Λ d 2 .
Δ λ B ( φ )= λ B ( φ ) λ B | φ=0 = n eff N eff λ B | φ=0 cosφ ,
λ 0,+1 ( φ )=2 n eff ( λ 0,+1 ) Λ d cosφκsinφ
λ -1,0 ( φ )=2 n eff ( λ -1,0 ) Λ d cosφ+κsinφ .
Δλ( φ )= λ ( 2 ) n eff N eff ( 2κsinφ cos 2 φ κ 2 sin 2 φ ),
λ ( 2 ) = λ -1,0 | φ=0 = λ 0,+1 | φ=0 =2 n eff ( λ ( 2 ) ) Λ d 2 λ B
Δλ( φ ) λ ( 2 ) n eff N eff 2κφ,
Δλ( φ )2 λ ( 2 ) κφ,
k=[ ksinαcosβ,ksinαsinβ,kcosα ],
k m =[ ksinαcosβ+mK,ksinαsinβ, k 2 ( ksinαsinβ ) 2 ( ksinαcosβ+mK ) 2 ],
s=[ cosφcosθ,cosφsinθ,sinφ ].
Λ m,q = Λ d | ( mq )cosφcosθsinφ[ κ m κ q ] | ,
κ m = ( k K ) 2 ( k K sinαsinβ ) 2 ( k K sinαcosβ+m ) 2 .
Λ m,q = Λ d | ( mq )cosθ | ,

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