Abstract

We present numerical modeling based on a combination of the Bidirectional Beam Propagation Method and Finite Element Method that completely describes the wavelength spectra of point by point femtosecond laser inscribed fiber Bragg gratings, showing excellent agreement with experiment. We have investigated the dependence of different spectral parameters such as insertion loss, all dominant cladding and ghost modes and their shape relative to the position of the fiber Bragg grating in the core of the fiber. Our model is validated by comparing model predictions with experimental data and allows for predictive modeling of the gratings. We expand our analysis to more complicated structures, where we introduce symmetry breaking; this highlights the importance of centered gratings and how maintaining symmetry contributes to the overall spectral quality of the inscribed Bragg gratings. Finally, the numerical modeling is applied to superstructure gratings and a comparison with experimental results reveals a capability for dealing with complex grating structures that can be designed with particular wavelength characteristics.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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(12), 995–997 (2003).
    [CrossRef] [PubMed]
  2. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
    [CrossRef]
  3. G. D. Marshall, M. Ams, and M. J. Withford, “Point by point femtosecond laser inscription of fibre and waveguide Bragg gratings for photonics device fabrication,” Proc. 2nd Pacific International Conference on Application of Lasers and Optics, 360–362 (2006).
  4. Y. Lai, K. Zhou, K. Sugden, and I. Bennion, “Point-by-point inscription of first-order fiber Bragg grating for C band applications,” Opt. Express 15(26), 18318–18325 (2007).
    [CrossRef] [PubMed]
  5. T. Geernaert, K. Kalli, C. Koutsides, M. Komodromos, T. Nasilowski, W. Urbanczyk, J. Wojcik, F. Berghmans, and H. Thienpont, “Point-by-point fiber Bragg grating inscription in free-standing step-index and photonic crystal fibers using near-IR femtosecond laser,” Opt. Lett. 35(10), 1647–1649 (2010).
    [CrossRef] [PubMed]
  6. A. Arigiris, M. Konstantaki, A. Ikiades, D. Chronis, P. Florias, K. Kallimani, and G. Pagiatakis, “Fabrication of high-reflectivity superimposed multiple-fiber Bragg gratings with unequal wavelength spacing,” Opt. Lett. 27(15), 1306 (2002).
    [CrossRef]
  7. M. Harumoto, M. Shigehara, and H. Suganuma, “A novel superimposed sampled long-period fiber grating,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper BThC16.
  8. B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30(19), 1620–1622 (1994).
    [CrossRef]
  9. N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3634–3646 (1997).
    [CrossRef]
  10. H. Rao, R. Scarmozzino, and R. M. Osgood, “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11(7), 830–832 (1999).
    [CrossRef]
  11. L. Vincetti, A. Cucinotta, S. Selleri, and M. Zoboli, “Three-dimensional finite-element beam propagation method: assessments and developments,” J. Opt. Soc. Am. A 17(6), 1124–1131 (2000).
    [CrossRef]
  12. J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
    [CrossRef]
  13. F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31(11), 899–901 (1995).
    [CrossRef]

2010

2007

2004

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
[CrossRef]

2003

2002

2000

1999

H. Rao, R. Scarmozzino, and R. M. Osgood, “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11(7), 830–832 (1999).
[CrossRef]

1997

N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3634–3646 (1997).
[CrossRef]

1996

J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
[CrossRef]

1995

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31(11), 899–901 (1995).
[CrossRef]

1994

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30(19), 1620–1622 (1994).
[CrossRef]

Arigiris, A.

Bennion, I.

Y. Lai, K. Zhou, K. Sugden, and I. Bennion, “Point-by-point inscription of first-order fiber Bragg grating for C band applications,” Opt. Express 15(26), 18318–18325 (2007).
[CrossRef] [PubMed]

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
[CrossRef]

J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
[CrossRef]

Berghmans, F.

Broderick, N. G. R.

N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3634–3646 (1997).
[CrossRef]

Chow, J.

J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
[CrossRef]

Chronis, D.

Cucinotta, A.

de Sterke, C. M.

N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3634–3646 (1997).
[CrossRef]

Dhosi, G.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31(11), 899–901 (1995).
[CrossRef]

Ding, H.

Dubov, M.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
[CrossRef]

Eggleton, B.

J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
[CrossRef]

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31(11), 899–901 (1995).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30(19), 1620–1622 (1994).
[CrossRef]

Florias, P.

Geernaert, T.

Grobnic, D.

Henderson, G.

Ibsen, M.

J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
[CrossRef]

Ikiades, A.

Kalli, K.

Kallimani, K.

Khrushchev, I.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
[CrossRef]

Komodromos, M.

Konstantaki, M.

Koutsides, C.

Krug, P. A.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31(11), 899–901 (1995).
[CrossRef]

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30(19), 1620–1622 (1994).
[CrossRef]

Lai, Y.

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(19), 1170–1172 (2004).
[CrossRef]

Mihailov, S. J.

Nasilowski, T.

Osgood, R. M.

H. Rao, R. Scarmozzino, and R. M. Osgood, “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11(7), 830–832 (1999).
[CrossRef]

Ouellette, F.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31(11), 899–901 (1995).
[CrossRef]

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30(19), 1620–1622 (1994).
[CrossRef]

Pagiatakis, G.

Poladian, L.

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30(19), 1620–1622 (1994).
[CrossRef]

Rao, H.

H. Rao, R. Scarmozzino, and R. M. Osgood, “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11(7), 830–832 (1999).
[CrossRef]

Scarmozzino, R.

H. Rao, R. Scarmozzino, and R. M. Osgood, “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11(7), 830–832 (1999).
[CrossRef]

Selleri, S.

Smelser, C. W.

Stephens, T.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31(11), 899–901 (1995).
[CrossRef]

Sugden, K.

Y. Lai, K. Zhou, K. Sugden, and I. Bennion, “Point-by-point inscription of first-order fiber Bragg grating for C band applications,” Opt. Express 15(26), 18318–18325 (2007).
[CrossRef] [PubMed]

J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
[CrossRef]

Thienpont, H.

Town, G.

J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
[CrossRef]

Unruh, J.

Urbanczyk, W.

Vincetti, L.

Walker, R. B.

Wojcik, J.

Zhou, K.

Zoboli, M.

Electron. Lett.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
[CrossRef]

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30(19), 1620–1622 (1994).
[CrossRef]

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31(11), 899–901 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

H. Rao, R. Scarmozzino, and R. M. Osgood, “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. 11(7), 830–832 (1999).
[CrossRef]

J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in an erbium-doped fibre laser using in-fibre comb filters,” IEEE Photon. Technol. Lett. 8(1), 60–62 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 3634–3646 (1997).
[CrossRef]

Other

G. D. Marshall, M. Ams, and M. J. Withford, “Point by point femtosecond laser inscription of fibre and waveguide Bragg gratings for photonics device fabrication,” Proc. 2nd Pacific International Conference on Application of Lasers and Optics, 360–362 (2006).

M. Harumoto, M. Shigehara, and H. Suganuma, “A novel superimposed sampled long-period fiber grating,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper BThC16.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Intensity mode profile (arbitrary units) and effective refractive index calculated with FEM. Effective refractive index for λ = 1550 nm is 1.444602.

Fig. 2
Fig. 2

Typical experimentally measured and simulated spectra showing excellent agreement in the number of cladding modes and their wavelength positions. The simulation resolution set to be equal with experimental measurements resolution.

Fig. 5
Fig. 5

Grating spectra for different offsets from the center of the core, where the label refers to offset in microns (inset: cladding mode structure with greater clarity). Core radius was 4.15 microns.

Fig. 3
Fig. 3

Experimental and simulated results for a non-centered Bragg grating (traces offset for clarity).

Fig. 4
Fig. 4

(a) Simulated transmission spectrum of superimposed gratings (inset: relative core positions of modeled FBGs). (b) Experimental spectrum.

Fig. 6
Fig. 6

Different structures with lower (a) and higher (b) symmetry. Gratings in the cladding partially reflect light back to the core.

Fig. 7
Fig. 7

Centered grating compared with symmetric and asymmetric distortion, showing the centered grating response (black), an offset grating displaced by 5 microns (red) with a characteristic ghost mode and a third similar grating placed on the opposite side of the core–cladding interface (green) without the appearance of the ghost mode.

Fig. 8
Fig. 8

Grating notch depth as a function of the position of the grating in the fiber core. Red line is a Gaussian fit to the results.

Fig. 9
Fig. 9

(a) Index profile of an axially tilted grating. (b) Spectra for different grating angles (degree of axial tilt).

Fig. 10
Fig. 10

(a) Index profile of a superstructure fiber Bragg grating. (b) Experimental and theoretical reflection spectrum from the SFG.

Equations (4)

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

2 φ x 2 + 2 φ y 2 + 2 φ z 2 + k ( x , y , z ) 2 φ = 0
φ ( x , y , z ) = u ( x , y , z ) e i k z
( u o u t + u o u t ) = M ( u i n + u i n )
G r a t i n g N o t c h D e p t h = A + B C π 2 exp ( 2 ( x D C ) 2 ) A = 0.8575 , B = 0.55887 , C = 3.85936 , D = 4.83831

Metrics