Abstract

Rouard’s method is used to model the spectral response of type I-IR gratings. Type I-IR gratings are shown to have a broader bandwidth and larger sideband suppression than would be expected from standard type I UV-written gratings. These properties are related to the nonlinear dependence of the index change on intensity. At higher intensities the spectral response indicates saturation of the index change growth rate.

© 2006 Optical Society of America

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  1. T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]
  2. R. Kashyap, Fiber Bragg Gratings (Academic, 1999).
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    [CrossRef]
  4. S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, "Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation," Opt. Lett. 28, 995-997 (2003).
    [CrossRef] [PubMed]
  5. A. Dragomir, D. N. Nikogosyan, K. A. Zagorulko, P. G. Kryukov, and E. M. Dianov, "Inscription of fiber Bragg gratings by ultraviolet femtosecond radiation," Opt. Lett. 28, 2171-2173 (2003).
    [CrossRef] [PubMed]
  6. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, "Direct writing of fibre Bragg gratings by femtosecond laser," Electron. Lett. 40, 1170-1172 (2004).
    [CrossRef]
  7. C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005).
    [CrossRef] [PubMed]
  8. C. W. Smelser, D. Grobnic, and S. J. Mihailov, "Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask," Opt. Lett. 29, 1730-1732 (2004).
    [CrossRef] [PubMed]
  9. 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, 1458-1460 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  15. D. Grobnic, S. J. Mihailov, and C. W. Smelser, "Higher order spectral response characteristics of fiber Bragg gratings made with ultrafast IR radiation and a phase mask," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), P43.
  16. C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Intensity dependence of the index modulation growth rate of type I-IR ultrafast fiber Bragg gratings," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), W1445.
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    [CrossRef]
  19. W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
    [CrossRef]

2005 (2)

2004 (5)

2003 (2)

2002 (1)

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

2001 (1)

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
[CrossRef]

2000 (1)

Z. Wang, G. Peng, and P. Chu, "Improved Rouard's method for fiber and waveguide gratings," Opt. Commun. 177, 245-250 (2000).
[CrossRef]

1997 (1)

T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

1995 (1)

1987 (1)

1985 (1)

Aközbek, N.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Becker, A.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Bennion, I.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, "Direct writing of fibre Bragg gratings by femtosecond laser," Electron. Lett. 40, 1170-1172 (2004).
[CrossRef]

Bowden, C. M.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Chin, S. L.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Chu, P.

Z. Wang, G. Peng, and P. Chu, "Improved Rouard's method for fiber and waveguide gratings," Opt. Commun. 177, 245-250 (2000).
[CrossRef]

Corkum, P. B.

Dai, X.

Dianov, E. M.

Ding, H.

Dragomir, A.

Dubov, M.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, "Direct writing of fibre Bragg gratings by femtosecond laser," Electron. Lett. 40, 1170-1172 (2004).
[CrossRef]

Erdogan, T.

T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

Franco, M.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
[CrossRef]

Grobnic, D.

C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, D. Grobnic, R. B. Walker, P. Lu, H. Ding, and J. Unruh, "Bragg gratings written in all-SiO2 and Ge-doped core fibers with 800-nm femtosecond radiation and a phase mask," J. Lightwave Technol. 22, 94-100 (2004).
[CrossRef]

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, 1458-1460 (2004).
[CrossRef] [PubMed]

D. Grobnic, C. W. Smelser, S. J. Mihailov, R. B. Walker, and P. Lu, "Fiber Bragg gratings with suppressed cladding modes made in SMF-28 with a femtosecond IR laser and a phase Mask," IEEE Photon. Technol. Lett. 16, 1864-1866 (2004).
[CrossRef]

C. W. Smelser, D. Grobnic, and S. J. Mihailov, "Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask," Opt. Lett. 29, 1730-1732 (2004).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, "Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation," Opt. Lett. 28, 995-997 (2003).
[CrossRef] [PubMed]

D. Grobnic, S. J. Mihailov, and C. W. Smelser, "Higher order spectral response characteristics of fiber Bragg gratings made with ultrafast IR radiation and a phase mask," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), P43.

C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Intensity dependence of the index modulation growth rate of type I-IR ultrafast fiber Bragg gratings," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), W1445.

Hall, D. G.

Henderson, G.

Kashyap, R.

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

Khrushchev, I.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, "Direct writing of fibre Bragg gratings by femtosecond laser," Electron. Lett. 40, 1170-1172 (2004).
[CrossRef]

Krug, P. A.

Kryukov, P. G.

Liu, W.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Lu, P.

Martinez, A.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, "Direct writing of fibre Bragg gratings by femtosecond laser," Electron. Lett. 40, 1170-1172 (2004).
[CrossRef]

Mihailov, S. J.

C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, D. Grobnic, R. B. Walker, P. Lu, H. Ding, and J. Unruh, "Bragg gratings written in all-SiO2 and Ge-doped core fibers with 800-nm femtosecond radiation and a phase mask," J. Lightwave Technol. 22, 94-100 (2004).
[CrossRef]

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, 1458-1460 (2004).
[CrossRef] [PubMed]

C. W. Smelser, D. Grobnic, and S. J. Mihailov, "Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask," Opt. Lett. 29, 1730-1732 (2004).
[CrossRef] [PubMed]

D. Grobnic, C. W. Smelser, S. J. Mihailov, R. B. Walker, and P. Lu, "Fiber Bragg gratings with suppressed cladding modes made in SMF-28 with a femtosecond IR laser and a phase Mask," IEEE Photon. Technol. Lett. 16, 1864-1866 (2004).
[CrossRef]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, "Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation," Opt. Lett. 28, 995-997 (2003).
[CrossRef] [PubMed]

D. Grobnic, S. J. Mihailov, and C. W. Smelser, "Higher order spectral response characteristics of fiber Bragg gratings made with ultrafast IR radiation and a phase mask," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), P43.

C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Intensity dependence of the index modulation growth rate of type I-IR ultrafast fiber Bragg gratings," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), W1445.

Mysyrowicz, A.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
[CrossRef]

Naumov, A.

Nikogosyan, D. N.

Peng, G.

Z. Wang, G. Peng, and P. Chu, "Improved Rouard's method for fiber and waveguide gratings," Opt. Commun. 177, 245-250 (2000).
[CrossRef]

Petit, S.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Prade, B.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
[CrossRef]

Rayner, D. M.

Smelser, C. W.

C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, D. Grobnic, R. B. Walker, P. Lu, H. Ding, and J. Unruh, "Bragg gratings written in all-SiO2 and Ge-doped core fibers with 800-nm femtosecond radiation and a phase mask," J. Lightwave Technol. 22, 94-100 (2004).
[CrossRef]

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, 1458-1460 (2004).
[CrossRef] [PubMed]

D. Grobnic, C. W. Smelser, S. J. Mihailov, R. B. Walker, and P. Lu, "Fiber Bragg gratings with suppressed cladding modes made in SMF-28 with a femtosecond IR laser and a phase Mask," IEEE Photon. Technol. Lett. 16, 1864-1866 (2004).
[CrossRef]

C. W. Smelser, D. Grobnic, and S. J. Mihailov, "Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask," Opt. Lett. 29, 1730-1732 (2004).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, "Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation," Opt. Lett. 28, 995-997 (2003).
[CrossRef] [PubMed]

D. Grobnic, S. J. Mihailov, and C. W. Smelser, "Higher order spectral response characteristics of fiber Bragg gratings made with ultrafast IR radiation and a phase mask," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), P43.

C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Intensity dependence of the index modulation growth rate of type I-IR ultrafast fiber Bragg gratings," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), W1445.

Stolte, R.

Sudrie, L.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
[CrossRef]

Ulrich, R.

Unruh, J.

Walker, R. B.

Wang, Z.

Z. Wang, G. Peng, and P. Chu, "Improved Rouard's method for fiber and waveguide gratings," Opt. Commun. 177, 245-250 (2000).
[CrossRef]

Weller-Brophy, L. A.

Zagorulko, K. A.

Electron. Lett. (1)

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, "Direct writing of fibre Bragg gratings by femtosecond laser," Electron. Lett. 40, 1170-1172 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

D. Grobnic, C. W. Smelser, S. J. Mihailov, R. B. Walker, and P. Lu, "Fiber Bragg gratings with suppressed cladding modes made in SMF-28 with a femtosecond IR laser and a phase Mask," IEEE Photon. Technol. Lett. 16, 1864-1866 (2004).
[CrossRef]

J. Lightwave Technol. (2)

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

Opt. Commun. (3)

Z. Wang, G. Peng, and P. Chu, "Improved Rouard's method for fiber and waveguide gratings," Opt. Commun. 177, 245-250 (2000).
[CrossRef]

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, "Study of damage in fused silica induced by ultra-short IR laser pulses," Opt. Commun. 191, 333-339 (2001).
[CrossRef]

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Other (3)

D. Grobnic, S. J. Mihailov, and C. W. Smelser, "Higher order spectral response characteristics of fiber Bragg gratings made with ultrafast IR radiation and a phase mask," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), P43.

C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Intensity dependence of the index modulation growth rate of type I-IR ultrafast fiber Bragg gratings," in Proceedings of Bragg Grating, Photosensitivity and Poling Topical Meeting (BGPP/ACOFT, 2005), W1445.

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

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Figures (11)

Fig. 1
Fig. 1

Reflection from three planes. The incident amplitude A inc undergoes reflections from the surfaces r 1 and r 2 . These two reflections can be treated as one reflection with a complex reflectivity ρ 2 .

Fig. 2
Fig. 2

Grating can be subdivided into a series of Fresnel reflections. The total complex reflectivity can be determined through an iterative process.

Fig. 3
Fig. 3

Schematic of the focusing arrangement. A cylindrical lens focuses the ultrafast beam through a phase mask, and the distance between the fiber and phase mask, d, can be adjusted to reduce the number of interfering phase-mask orders.

Fig. 4
Fig. 4

Two-beam intensity patterns as a function of phase-mask fiber distance. The peak amplitude, the width of the interference region, and the edge visibility are all reduced as the phase-mask fiber separation, d, is increased. The grating pitch is exaggerated for clarity.

Fig. 5
Fig. 5

Comparison between the linear (dotted curve) and the nonlinear (solid curve) index modulation profiles. If the index change in the medium depends nonlinearly on the interference field, then the grating effective length and the area under each peak become smaller. The grating pitches of the index modulation profile are exaggerated for clarity.

Fig. 6
Fig. 6

Rouard’s method used to model a UV-written grating. (a) A comparison between the experimental (dashed curve) and modeled (solid curve) curve for the UV-written grating. (b) The linear intensity profile that was used to model the grating response.

Fig. 7
Fig. 7

(a) Comparison between the experimentally observed type I-IR grating spectrum (dashed curve) and the modeled grating spectrum, assuming that the index change in the fiber depends linearly on the interference field intensity (solid curve). (b) Index modulation profile used in the modeled spectrum.

Fig. 8
Fig. 8

(a) Comparison between the experimentally observed (dashed curve) and the modeled spectra, assuming that the index change scales with intensity to the power of 5 (solid curve). (b) The index modulation profile used to model the spectrum.

Fig. 9
Fig. 9

(a) Comparison between the experimentally observed (dashed curve) and the modeled spectra, assuming that the index change scales with intensity to the power of 6 (solid curve). (b) The index modulation profile used to model the spectrum.

Fig. 10
Fig. 10

(a) Comparison of the spectrum of a grating written with an input energy of 1200 μ J (solid curve) and the modeled spectrum for a grating that depends on I 6 (dashed curve) and one based on Eq. (5) (dashed–dotted curve). (b) The spectral profile that best fits the 1200 μ J data.

Fig. 11
Fig. 11

Comparison of the coverage of the core at the edge of the grating structure to that at the center. The phase-mask pitch used here was 3.21 μ m to allow for a visible two-beam interference pattern under an optical microscope.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ρ 2 = r 1 + r 2 exp ( i δ ) 1 + r 1 r 2 exp ( i δ ) .
δ = k 2 d = 4 π n 2 λ o d ,
ρ i 1 = r i 2 + r i 1 exp ( i δ ) 1 + r i 2 r i 1 exp ( i δ ) .
I = pulse energy ( 2 ) ( % energy ± 1 orders ) 0.86 area ( pulse duration ) = 800 μ J ( 2 ) ( 0.728 ) ( 0.86 ) 3 × 10 4 cm 2 ( 125 fs ) = 2.7 × 10 13 W cm 2 .
Δ n norm = I 6 C + I 6 .

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