## Results and comparison of a cladding pumped fiber simulation using a decagon-shaped fiber

Optics Express, Vol. 11, Issue 7, pp. 830-837 (2003)

http://dx.doi.org/10.1364/OE.11.000830

Acrobat PDF (122 KB)

### Abstract

This paper presents a simulation technique developed to concurrently model the pump and laser power evolution in a cladding pumped rare-earth doped fiber. The simulation technique uses a series of scaling factors to dramatically decrease simulation run-times, while maintaining accuracy. This approach differs from previous methods in that it can simulate arbitrary pump cladding shapes. The results of the simulation are validated using a decagon-shaped cladding pumped, ytterbium doped fiber. Good correlation is found between the simulated and experimental pump evolution and conversion efficiency.

© 2003 Optical Society of America

## 1. Introduction

_{1m}[2] modes have energy at the center of the waveguide, once the rare-earth doped core absorbs this energy, only outer skew modes will exist. These skew modes can be perturbed by unintended index variations, stresses, and core-clad interface defects which scatter or refract the skew modes, increasing the probability of interaction with the core. Such perturbations can also cause leakage of the single-mode laser light, given the rare-earth doped core typically has a weaker guiding condition than the pump clad. With modern fiber manufacturing processes, most undesirable fiber defects such as point defects, unintended index variations, etc., that could scatter higher order mode energy towards the rare-earth doped core are avoided, creating the need for a intentional, controllable scattering mechanism. Solutions to this problem included rectangular shaped pump clads [3], hexagons [4] and concave polygons [5]. The last two shapes help to maximize the useful surface area being pumped, ease coupling to standard fibers, and simplify the fiber manufacturing process.

7. L. Qiao and J. Wang, “A modified ray-optic method for arbitrary dielectric waveguides,” IEEE J. Quantum Electron. , **28**, 2721–2727, (1992). [CrossRef]

8. M. Feit and J. Fleck, “Light propagation in graded index optical fibers” Appl. Opt. , **17**, 3990–3998, (1978). [CrossRef] [PubMed]

9. D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B. , **19**, 1259–1263, (2002). [CrossRef]

10. D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B. , **19**, 1304–1309, (2002). [CrossRef]

11. L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett. , **11**, 739–741, (1986). [CrossRef]

12. A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Comm. , **132**, 511–518, (1996). [CrossRef]

## 2. Model Development

_{at}is given by [14]:

_{rad,2→1}is the radiative decay rate from the upper to the lower lasing levels, Δω

_{a}is the atomic linewidth, ω

_{a}is the material resonance frequency, and g

_{1}and g

_{2}are the levels of degeneracy for the lower and upper lasing state energy levels. N

_{1}and N

_{2}, the populations of the lower and upper levels of the lasing transition, are a function of the energy density of the pump in the rare -earth doped core, as well as the laser energy evolution of the length of the fiber. The susceptibility can be separated into atomic phase shift and amplitude components through χ

_{at}=χ′+jχ″, χ″ is responsible for either loss or gain in the material. The mid-band value of the susceptibility is given by [14]:

_{1}and N

_{2}as a function of length along the fiber are calculated at each sampled point using solutions to the laser rate equations, which include the signal intensity in the rare-earth doped core and the pump intensity in the core. The rate equations used in this model are for a three-level lasing system, this allows the behavior of ytterbium, which in silica exhibits both quas i-three level behavior dependant on the lasing transition, to be modeled. The propagation and material dynamics are calculated in a stepwise manner that assumes that the propagation and material dynamics can be treated separately given small (sub-wavelength) step sizes. Two elements must be considered, the change in amplitude distribution and phase as a function of propagation, and the change in amplitude as a function of absorption (pump energy) or emission (core energy). The propagation technique used assumed that the paraxial condition holds – which is the case for the fiber modeled. The Fresnel approximation, which simplifies the description of the field, and the slowly varying envelope approximation are used to reduce the propagation equation to:

_{13}, for each array point must be calculated – the pump rate for any given array point is given by σ

_{p}

*I*

_{p}/

*h*ν

_{p}, where σ

_{p}is the pump absorption cross section in the core, I

_{p}is the pump intensity at any array point, and ν

_{p}is the frequency of the pump light. For the “signal” in the rare-earth doped core, the emission cross section probability, W

_{e}, is given by σ

_{e}

*I*

_{s}/

*h*ν

_{s}, and the absorption cross section probability, W

_{a}, is given by σ

_{a}

*I*

_{s}/

*h*ν

_{s}, where the σ

_{a},

_{e}is the signal absorption/emission cross section in the core, I

_{s}is the signal intensity at any array point, and ν

_{s}is the frequency of the signal light. The measured material properties were used in the model. The value used for σ

_{p}was 1.5×10

^{-21}cm

^{2}, σ

_{e}=1.3×10

^{-20}cm

^{2}, and σ

_{a}=5.8×10

^{-21}cm

^{2}. Given these terms, the population difference, ΔN, for a degenerate transition is given by:

_{1}=4, g

_{2}=3. N

_{0}is the ion density in the doped core, which was set at 4.4×10

^{19}cm

^{-3}. From [14], χ″ at mid-band is given by χ″=ΔNσ

_{e}λ/2π, where σ

_{e}is given by (1/2π)(γ

_{rad}/Δω

_{a})λ

^{2}. Stepping a small distance Δz=z-z

_{0}, the change in the magnitude of the input electric field, Ein as a function of material dynamics can now be given by;

_{fiber}can be scaled by varying the small-signal core absorption α

_{core}as well as the core and cladding area.

_{core}/A

_{clad}ratio, the size of the arrays being propagated can be decreased, reducing the overall simulation time. Reduction of the core and cladding diameter must be accompanied by a reduction of the pump and lasing wavelength in the model in order to preserve the modal behavior of the waveguides. The number of modes in the clad, thus the modal distribution is directly proportional to the ratio of the square of the clad radius and the wavelength of light being propagated. As the core radius decreases, the wavelength of light in the core must also be decreased in order to maintain the single-mode guiding condition. The model uses Fourier transform techniques for propagating the wave front – as the point density goes as 2

^{n}, it becomes important to carefully pick the array size – a 256×256 array requires 65,536 Fourier transforms per step, while the next density, 512×512, requires 262,144 Fourier transforms. The fiber being modeled is nominally 230 microns in diameter, with an 8-micron diameter core. At the Nyquist limit, it would require over 4 million Fourier transforms per step to properly propagate the field in both the core and clad. Using the scaling of the core/clad ratio, combined with scaling of the core absorption coefficient allowed for much shorter simulation times. In the simulation results shown below, a device with scale lengths up to 80 meters in length was simulated in less than 12 hours of run time on a current Pentium class personal computer.

## 3. Model results

^{-1}. As was mentioned in Section 2, a scaling factor, based on Eq. (8) was used to scale the model results to the experimental fiber. For the simulation a cladding diameter (circle inscribed into the decagon) of 18.4 µm was used. The core diameter was reduced to 0.64 µm to maintain the same core to cladding area ratio. In order to maintain the same capture area of the core, the pump and lasing wavelengths were scaled down to maintain the single-mode condition in the rare-earth doped core. The pump clad numerical aperture was set to 0.48. In the experimental measurements, the pump beam from a fiber coupled laser diode with a 600 um 0.22 NA fiber was coupled into a 230 um 0.48 NA fiber, which was run through a Newport mode scrambler to assure proper mode mixing. The output of this fiber was collimated, and then launched into the double-clad fiber using a 0.45 NA molded aspherical lens – the fiber was positioned until the laser power out was maximized. In the model a flattop beam that filled the aperture was used. In this model, the fiber shape is used to randomize the modes to increase the cladding pumped absorption per unit length – this randomization effect also acted to minimize any difference between simulation and model depending on fiber launch conditions. The core absorption rate in the model was also increased, once again to use the scaling described in Eq. (8). The total scaling factor for the core and cladding areas, and the core absorption rate was 500. Figure 1 shows the simulated evolution of the pump power and lasing power over the lengths modeled.

## 4. Experimental fiber

^{-1}– this was measured at 918 nm, the nominal pump wavelength of the measurement setup used.

## 5. Comparison of simulation data to experimental data

## 6. Conclusion

15. H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb^{3+}-doped silica fibre lasers in the 1 µm region,” Electron. Lett. , **30**, 863–864, (1994). [CrossRef]

## Acknowledgements

## References and Links

1. | E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B.C. McCollum, “Double-clad offset core Nd fiber laser,”in |

2. | A. White and S. Grubb, |

3. | H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, and T. Haw, “Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,” in |

4. | M. Muendel, “Optical fiber structure for efficient use of pump power,” US Patent # 5,533,563, 1996. |

5. | D. DiGiovanni, “Method of making a cladding pumped fiber structure,” US Patent # 5,873,923, 1999. |

6. | M. Muendel, “Optimal inner cladding shapes for double-clad fiber lasers,” in |

7. | L. Qiao and J. Wang, “A modified ray-optic method for arbitrary dielectric waveguides,” IEEE J. Quantum Electron. , |

8. | M. Feit and J. Fleck, “Light propagation in graded index optical fibers” Appl. Opt. , |

9. | D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B. , |

10. | D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B. , |

11. | L. Thylen, E. Wright, G. Stegeman, C. Seaton, and J. Moloney, “Beam propagation method analysis of a nonlinear directional coupler,” Optics Lett. , |

12. | A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Comm. , |

13. | B. Kerrinckx, P. Even, and D. Pureur, “New theoretical model of ytterbium-doped double-clad fiber for laser application,” in |

14. | A. Siegman, |

15. | H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, and A. Tropper, “Operation of cladding pumped Yb |

**OCIS Codes**

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

(140.3510) Lasers and laser optics : Lasers, fiber

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 17, 2003

Revised Manuscript: April 1, 2003

Published: April 7, 2003

**Citation**

David Young and C. Roychoudhuri, "Results and comparison of a cladding pumped fiber simulation using a decagon-shaped fiber," Opt. Express **11**, 830-837 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-7-830

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### References

- E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, B.C. McCollum, �??Double-clad offset core Nd fiber laser,�?? in Proc. of Optical Fiber Sensors �??88, pp. PD5, (1988)
- A. White, S. Grubb, Optical Fiber Telecommunications IIIB, (Academic Press, 1997), Chap. 7
- H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N.M. Cho, T. Haw, �??Double-clad high brightness Nd fiber laser pumped by GaAlAs phased array,�?? in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1989). Pp. PD7
- M. Muendel, �??Optical fiber structure for efficient use of pump power,�?? US Patent # 5,533,563, 1996.
- D. DiGiovanni, �??Method of making a cladding pumped fiber structure,�?? US Patent # 5,873,923, 1999.
- M. Muendel, �??Optimal inner cladding shapes for double-clad fiber lasers,�?? in Conference on Lasers and Electro-Optics, Technical Digest, (Optical Society of America, Washington DC, 1996), pp. 209.
- L. Qiao, J. Wang, �??A modified ray-optic method for arbitrary dielectric waveguides,�?? IEEE J. Quantum Electron. 28, 2721-2727, (1992). [CrossRef]
- M. Feit, J. Fleck, �??Light propagation in graded index optical fibers,�?? Appl. Opt. 17, 3990-3998, (1978). [CrossRef] [PubMed]
- D. Kouznetsov, J. Moloney, �??Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,�?? J. Opt. Soc. Am. B 19, 1259-1263, (2002). [CrossRef]
- D. Kouznetsov, J. Moloney, �??Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,�?? J. Opt. Soc. Am. B 19, 1304-1309, (2002). [CrossRef]
- L. Thylen, E. Wright, G. Stegeman, C. Seaton, J. Moloney, �??Beam propagation method analysis of a nonlinear directional coupler,�?? Opt. Lett. 11, 739-741, (1986). [CrossRef]
- A. Liu, K. Ueda, �??The absorption characteristics of circular, offset, and rectangular double-clad fibers,�?? Opt. Commun. 132, 511-518, (1996). [CrossRef]
- B. Kerrinckx, P. Even, D. Pureur, �??New theoretical model of ytterbium-doped double-clad fiber for laser application,�?? in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2001). Pp. TuI3-1.
- A. Siegman, Lasers (University Science Books, 1986), Chap. 3, 7.
- H. Pask, J Archambault, D. Hanna, L. Reekie, P.St.J. Russell, J. Townsend, A. Tropper, �??Operation of cladding pumped Yb3+-doped silica fibre lasers in the 1 μm region,�?? Electron. Lett. 30, 863-864, (1994). [CrossRef]

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