## Numerical model of a Q-switched double-clad fiber laser

Optics Express, Vol. 12, Issue 15, pp. 3554-3559 (2004)

http://dx.doi.org/10.1364/OPEX.12.003554

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### Abstract

The time-energy characteristics of a Q-switched neodymium-doped double-clad fiber laser are presented. Based on the proposed differential equations, a numerical model is developed to simulate this fiber laser. Using this model pulse duration and the energy of generated pulses can be predicted.

© 2004 Optical Society of America

## 1. Introduction

1. C.J. Koester and E. Snitzer, “Amplification in a fiber laser,” Appl. Optics **3**, 1182–1186 (1964). [CrossRef]

3. A.F. El-Sherif and T.A. King, “High-energy, high brightness Q-switched Tm^{3+}-doped fiber laser using an electro-optic modulator,” Opt. Commun. **218**, 337–344 (2003). [CrossRef]

4. Z.J. Chen, A.B. Grudinin, J. Porta, and J.D. Minelly, “Enhanced Q-switching in double clad fibre laser,” Opt. Lett. **23**, 454–456 (1998). [CrossRef]

5. C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, “Analytical model for rare-earth-doped fiber amplifiers and lasers,” IEEE J. Quantum Electron. **30**, 1817–1830 (1994). [CrossRef]

6. L. Xiao, P. Yan, M. Gong, W. Wei, and P. Ou, “An approximate analytic solution of strongly pumped Yb-doped double-clad fiber lasers without neglecting the scattering loss,” Opt. Commun. **230**, 401–410 (2004). [CrossRef]

7. I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. **17**, 891–897 (1999). [CrossRef]

## 2. Modelling of actively Q-switched fiber lasers

^{2}] and gain factor in an active medium k [cm

^{-1}]. Both quantities are functions of the time t and the position z.

### 2.1 Rate equations

^{+}and Jpropagating in the opposite direction (Fig. 1). In general, they are considered as mono-dimensional fluxes, i.e. for a plane wave J=J(z, t). The J

^{+}and J

^{-}circulate inside the optical cavity and interact through boundary conditions and active medium (amplifier). The description of such a problem will include two transport energy equations (describing e-m field in a laser cavity) and an equation describing gain evolution in a laser medium:

_{e}– gain coefficient of an active medium [cm

^{-1}], n=n

_{i}-n

_{j}– population inversion of active dopant [cm

^{-3}], i – upper laser level, j – lower laser level; σ

_{e}– stimulated emission cross section [cm

^{2}], ρm – material losses coefficient [cm

^{-1}], V=c/n – velocity of light propagation in an active medium. E

_{S}=hν/σ

_{e}is the saturation energy describing the amount of energy that can be stored in a laser [J/cm

^{2}].

### 2.2 Boundary conditions

_{1}and R

_{2}are the power reflectivities of the reflectors at z=0 and z=l

_{R}, respectively. T

_{S}is the transmission of the Q-switch. For the sake of simplicity an ideal unidirectional Q-modulator will be considered. The transmission characteristics (for the forward and backward direction) of this active element are expressed by: T

_{S}+(t)=0 (for t≤0) and T

_{S}+(t)=1 (for t>0). T

_{S}-(t)=1. In the range of 0<z<l

_{F}Eqs. (1)–(3) are valid, however, in the range of l

_{F}<z < l

_{R}only Eqs. (1)–(2) with right-hand sides equalling to zero are in force.

_{OUT}) and pulse energy are determined by:

_{p}is the initial value of a time interval comprising an output pulse.

### 2.3 Initial conditions

_{0}=0), a definite fluxes density distribution and a definite population inversion in an active medium exist inside the laser cavity. Therefore, Eqs. (1)–(3) have to be completed by suitable initial conditions.

_{0}=0 is inconvenient. In order to estimate their value it is necessary to take into consideration the laser cavity construction, relaxation processes and stimulated emission in a laser medium. The values of J

^{+}(z,0), J

^{-}(z,0) are not high in comparison with the maximum value of the output laser flux and they influence the parameters of generated pulses in a low extent. The initial values of the forward and backward photon fluxes can be expressed by:

_{g}– photon energy,

*τ*– fluorescence lifetime, Ω=π(NA/n

_{c})

^{2}– solid angle (n

_{c}– refractive index of the active core), l

_{F}– laser medium length.

_{a}is an effective absorption coefficient of the core at the pump wavelength, ρ

_{p}is a loss coefficient of the active fiber at the pump wavelength accounting for all loss mechanisms excluding resonant absorption described by α

_{a}, A

_{clad}is the cross-sectional area of the fiber inner cladding, P

_{p}(0) is the input pump power launched into the fiber at z=0 and f

_{r}is the repetition rate of the Q-switching process.

## 3. Simulation results

_{0}=3500 ppm, σ

_{e}=2×10

^{-24}m

^{2}, λ

_{p}=810 nm, τ=400 µs, ρ

_{m}=12 dB/km (2.76×10

^{-3}m

^{-1}), α

_{a}=170 dB/km (0.039 m

^{-1}), A

_{clad}=1.1×10

^{-7}m

^{2}, L

_{air}=0.2 m, R

_{1}=1, R

_{2}=0.1, NA=0.12. The length of the active optical fiber lF was changeable and ranged from 1 to 10 meters, repetition rate of losses switching f

_{r}was up to 10 kHz and pump power P

_{p}(0) equalled above 2 W. Some simulation results in Q-switching process are depicted in Figs. 2–4.

_{0}– ρm)l

_{F}is. These overmodulations are a result of 1) gain heterogeneity occurring in a laser cavity and 2) appearance of discrete elements (like Q-switch).

_{F}(k

_{0}– ρ

_{m}) for the fiber laser cavity length of 5.2 m (l

_{F}=5 m and L

_{air}=0.2 m). The pulse energy grows and pulse duration shortens as the initial gain k

_{0}increases. For the simulated 5 m-long fiber, the pulse duration ranged from 1080 ns to 50 ns whereas the pulse energy ranged from 110 µJ to 680 µJ. For instance, for 2l

_{F}(k

_{0}– ρ

_{m})=31, the pulse width equals 290 ns and pulse energy equals 0.18 mJ. When increasing the factor 2l

_{F}(k

_{0}– ρm) to the level of 40, it is possible to obtain 820 ns pulses with energy of 0.53 mJ. In analogous way, numerical calculations for different laser cavity length can be made.

## 4. Experimental verification of numerical simulation results

## 5. Conclusion

## References and links

1. | C.J. Koester and E. Snitzer, “Amplification in a fiber laser,” Appl. Optics |

2. | I.P. Alcock, A.C. Tropper, A.I. Ferguson, and D.C. Hanna, “Q-switched operation of a neodymium-doped monomode fibre laser,” Electron. Lett. |

3. | A.F. El-Sherif and T.A. King, “High-energy, high brightness Q-switched Tm |

4. | Z.J. Chen, A.B. Grudinin, J. Porta, and J.D. Minelly, “Enhanced Q-switching in double clad fibre laser,” Opt. Lett. |

5. | C. Barnard, P. Myslinski, J. Chrostowski, and M. Kavehrad, “Analytical model for rare-earth-doped fiber amplifiers and lasers,” IEEE J. Quantum Electron. |

6. | L. Xiao, P. Yan, M. Gong, W. Wei, and P. Ou, “An approximate analytic solution of strongly pumped Yb-doped double-clad fiber lasers without neglecting the scattering loss,” Opt. Commun. |

7. | I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. |

8. | J. Swiderski, A. Zajac, P. Konieczny, and M. Skorczakowski, “Q-switched double-clad fiber laser,” Opto-Electron. Rev.12 (to be published). |

**OCIS Codes**

(140.3510) Lasers and laser optics : Lasers, fiber

(140.3540) Lasers and laser optics : Lasers, Q-switched

**ToC Category:**

Research Papers

**History**

Original Manuscript: June 9, 2004

Revised Manuscript: July 19, 2004

Published: July 26, 2004

**Citation**

J. Swiderski, A. Zajac, P. Konieczny, and M. Skorczakowski, "Numerical model of a Q-switched double-clad fiber laser," Opt. Express **12**, 3554-3559 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3554

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### References

- C.J. Koester, E. Snitzer, �??Amplification in a fiber laser,�?? Appl. Opt. 3, 1182-1186 (1964). [CrossRef]
- I.P. Alcock, A.C. Tropper, A.I. Ferguson, D.C. Hanna, �??Q-switched operation of a neodymium-doped monomode fibre laser,�?? Electron. Lett. 272, 84-85 (1985).
- A.F. El-Sherif, T.A. King, �??High-energy, high brightness Q-switched Tm3+-doped fiber laser using an electro-optic modulator,�?? Opt. Commun. 218, 337-344 (2003). [CrossRef]
- Z.J. Chen, A.B. Grudinin, J. Porta, J.D. Minelly, �??Enhanced Q-switching in double clad fibre laser,�?? Opt. Lett. 23, 454-456 (1998). [CrossRef]
- C. Barnard, P. Myslinski, J. Chrostowski, M. Kavehrad, �??Analytical model for rare-earth-doped fiber amplifiers and lasers,�?? IEEE J. Quantum Electron. 30, 1817-1830 (1994). [CrossRef]
- L.Xiao, P. Yan, M. Gong, W. Wei, P. Ou, �??An approximate analytic solution of strongly pumped Yb-doped double-clad fiber lasers without neglecting the scattering loss,�?? Opt. Commun. 230, 401-410 (2004). [CrossRef]
- I. Kelson, A. Hardy, �??Optimization of strongly pumped fiber lasers,�?? J. Lightwave Technol. 17, 891-897 (1999). [CrossRef]
- J. Swiderski, A. Zajac, P. Konieczny, M. Skorczakowski, �??Q-switched double-clad fiber laser,�?? Opto-Electron. Rev. 12 (to be published).

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