## Characterizing femtosecond laser inscribed Bragg grating spectra |

Optics Express, Vol. 19, Issue 1, pp. 342-352 (2011)

http://dx.doi.org/10.1364/OE.19.000342

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### 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

## 1. Introduction

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]

## 2. Simulation method

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]

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]

*k(x,y,z) = k*is the spatially dependent wavenumber, and the geometry of the problem is defined by the refractive index distribution

_{0}n(x,y,z)*n(x,y,z)*. To determine the launch field we use the slowly varying envelope approximation (with a slowly varying field

*u*proportional to the phase variation

*ϕ*) where the scalar field

*ϕ(x,y,z)*can be calculated along the propagation direction using [10

**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]

**11**(7), 830–832 (1999). [CrossRef]

*u*and

^{+}(x, y, z)*u*, respectively. In the uniform regions the forward and backward waves are decoupled, while the interfaces between these regions couple the forward and backward waves due to reflection. A transfer matrix approach is employed in which the individual matrices are differential operators. The transfer matrix problem, however, is formulated by assuming that both the forward and backward fields are known at the input of the structure, and an overall transfer matrix

^{−}(x, y, z)*M*describes the system as follows [10

**11**(7), 830–832 (1999). [CrossRef]

*n(x,y,z)*, and the input wave field,

*u(x,y,z = 0)*. From these, the physics dictates the wave field throughout the rest of the domain,

*u(x,y,z>0)*. Additional input is required in the form of numerical simulation parameters such as the finite computational domain,

*{x ∈ (x*,

_{min},x_{max})}*{y ∈ (y*, and

_{min},y_{max})}*{z ∈ (z*, the transverse grid sizes,

_{min},z_{max})}*Δx*and

*Δy*, and the longitudinal step size,

*Δz*. Clearly the calculation accuracy is determined by the computational spatial resolution, the error in the effective refractive index of the supported mode and the step in the wavelength domain.

## 3. Simulation and experimental results – a comparison

**11**(7), 830–832 (1999). [CrossRef]

_{eff}= 1.444602 with FEM and n

_{eff}= 1.444772 with BPM), their impact on the final solutions proves important. A comparison between the two computation methods shows a small deviation, with the FEM solutions closer to our experimental results. Finally, there is a significant reduction in the calculation time by using the FEM.

*u*) in the matrix problem (Eq. (3), whereas the BPM was used to solve the problem; this takes advantage of the strong points of each calculation method. Figure 2 shows a typical comparison between calculated and measured spectra in a fiber containing a Bragg grating. A first order grating was inscribed in the center of the core of a standard telecom fiber. For the inscription a femtosecond laser system (HighQ Laser Femtoregen IC335) emitting 300 fs pulses at 1035 nm and operating at a repetition rate of 1 kHz was used while the light was focused with a Mitutoyo, long working distance microscope objective ( × 50, NA 0.42). Key parameters of the grating such as the period and the size of the spots have been measured using an optical microscope. Those parameters are required for our analysis. The size of the core was set to be 8.3 μm and the period was 536 nm. The width of each spot was 1 μm and the length of the grating set to be 2 cm. As we can see from Fig. 2, the analysis predicts the exact number of the cladding modes with an average wavelength determination error of 0.05 nm, or 0.005%. Furthermore, the small average deviation between calculated and measured insertion loss (4.6 × 10

^{+}_{in}^{−3}dB) is indicative of the reliability of the predictions. Small deviations of the analysis compared with the experiment relate to the differences of the spot shape associated with the index change. Our model assumes that the spots are homogenous but in the fiber the refractive index change has an inhomogeneous distribution, because of the nonlinear laser pulse interaction with the material. The modulated refractive index amplitude of the model was set as 4 × 10

^{−4}to be in agreement with the measured value obtained from phase contrast microscopy and the application of the inverse Abel transform. Stronger refractive indices increase the reflectivity of the grating but at the some time give rise to far stronger cladding modes in the spectrum. For sensing applications where the quality of the grating is the dominant factor instead of the reflectivity, cladding mode suppression is very important. In the experimental work all gratings were recorded just above the non-linear threshold value so that we could make distinct optical microscopy measurements in order to unambiguously determine the refractive index value used in the modeling. We carefully controlled the femtosecond laser energy such that we have a near zero mean index change and a net positive modulated index change. This meant that the gratings were not particularly strong, but were of greatest relevance to sensing applications, with good spectral quality.

## 4. Analysis of more complicated structures

## 5. Superstructure fiber Bragg gratings

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]

## 6. Conclusion

## Acknowledgement

## References and links

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. |

2. | A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. |

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 |

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. |

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. |

7. | M. Harumoto, M. Shigehara, and H. Suganuma, “A novel superimposed sampled long-period fiber grating,” in |

8. | B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. |

9. | N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

10. | H. Rao, R. Scarmozzino, and R. M. Osgood, “A bidirectional beam propagation method for multiple dielectric interfaces,” IEEE Photon. Technol. Lett. |

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 |

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. |

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. |

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: October 27, 2010

Revised Manuscript: December 4, 2010

Manuscript Accepted: December 6, 2010

Published: December 22, 2010

**Citation**

C. Koutsides, K. Kalli, D. J. Webb, and L. Zhang, "Characterizing femtosecond laser inscribed Bragg grating spectra," Opt. Express **19**, 342-352 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-1-342

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### References

- 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]
- 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]
- 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).
- 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]
- 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]
- 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]
- 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.
- 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]
- 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]
- 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]
- 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]
- 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]

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