## Numerical analysis of multiwavelength erbium-doped fiber ring laser exploiting four-wave mixing

Optics Express, Vol. 16, Issue 16, pp. 12397-12402 (2008)

http://dx.doi.org/10.1364/OE.16.012397

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### Abstract

In this paper, a model is proposed to study the behavior of four-wave mixing assisted multiwavelength erbium doped fiber ring laser based on the theoretical model of the multiple FWM processes and Gile’s theory of erbium-doped fiber. It is demonstrated that the mode competition can be effectively suppressed through FWM. The effect of phase matching, the nonlinear coefficient, the power in the cavity and the length of the nonlinear medium on output spectrum uniformity are also investigated.

© 2008 Optical Society of America

## 1. Introduction

1. A. Bellemare, A. Bellemare, M. Karasek, M. Rochette, S. A. L. S. Lrochelle, and M. A. T. M. Tetu, “Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU Tetu, frequency grid,” J. Lightw. Technol. **18**, 825–831 (2000). [CrossRef]

2. S. K. Kim, M. J. Chu, and J. H. Lee, “Wideband multiwavelength erbium-doped fiber ring Laser with Frequency Shifted Feedback,” Opt. Commun. **190**, 291–302 (2001). [CrossRef]

3. Z. X. Zhang, L. Zhan, and Y. X. Xia, “Tunable self-seeded multiwavelength Brillouin-erbium fiber laser with enhanced power efficiency,” Opt. Express **15**, 9731–9736 (2007). [CrossRef] [PubMed]

4. Y. Huang, L. Zhan, J. H. Ji, S. Y. Luo, and Y. Xia, “Multiwavelength self-seeded Brillouin-erbium fiber laser with 45-nm tunable range,” Opt. Commun. **281**, 452–456 (2008). [CrossRef]

5. X. H. Feng, H. Y. Tam, H. L. Liu, and P. K. A. Wai, “Multiwavelength erbium-doped fiber laser employing a nonlinear optical loop mirror,” Opt. Commun. **268**, 278–281 (2006). [CrossRef]

6. X. H. Feng, H. Y. Tam, and P. K. A. Wai, “Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation,” Opt. Express **14**, 8205–8210 (2006). [CrossRef] [PubMed]

7. C. L. Zhao, X. F. Yang, C. Lu, N. J. Hong, X. Guo, P. R. Chaudhuri, and X. Y. Dong, “Switchable muitiwavelength erbium-doped fiber lasers by using cascaded fiber laser Bragg gratings written in high birefringence fiber,” Opt. Commun. **230**, 313–317 (2004). [CrossRef]

8. Y. G. Liu, X. Y. Dong, P. Shum, S. Z. Yuan, G. Y. Kai, and X. Y. Dong, “Stable room-temperature multiwavelength lasing realization in ordinary erbium-doped fiber loop lasers,” Opt. Express **14**, 9293–9298 (2006). [CrossRef] [PubMed]

9. X. Liu, X. Yang, F. Lu, J. Ng, X. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express **13**, 142–147 (2005). [CrossRef] [PubMed]

## 2. Theoretical model

*x*direction. Therefore, the total electrical field can be represented as the sums of its various frequency components:

*A*(

_{n}*z*) is the complex amplitude.

*F*(

_{n}*x*,

*y*) is the normalized transverse field distribution of frequency

*ω*.

_{n}*β*(

*ω*) is the propagation factor. Substituting equations (1) into the general nonlinear optical wave equation, the power of each frequency component after FWM can be described as [17]:

_{n}*γ*is nonlinear coefficient approximated as independent of frequency, since the frequency shift is slight compared with frequency itself. Δ

*β*=

_{ijk}*β*(

*ω*)+

_{i}*β*(

*ω*)-2

_{j}*β*(

*ω*) is the propagation constant difference describing the phase mismatch of the quasi-degenerate FWM induced by material and waveguide dispersion. After Taylor expansion, it can be simplified as:

_{k}*β*

_{2}(

*ω*

_{0}) and

*β*

_{3}(

*ω*

_{0}) are second and third derivatives of the propagation constant at frequency

*ω*

_{0}. In most situation, only

*β*

_{2}(

*ω*

_{0}) needs to be considered except in the region near

*ω*

_{0}where the contribution of

*β*

_{3}(

*ω*

_{0}) is comparable with

*β*

_{2}(

*ω*

_{0}). Higher order derivatives of the propagation constant do little contribution to Δ

*β*, and therefore can be ignored. Ω is the frequency shift.

_{ijk}13. X. M. Liu, “Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers,” Opt. Commun. **260**, 554–559 (2006). [CrossRef]

*ω*=

_{n}*ω*+

_{m}*ω*and the third must satisfy

_{k}*ω*+

_{n}*ω*=2

_{m}*ω*. The first term describes Kerr effect. Letting

_{k}*A*(

_{n}*z*)=

*B*(

_{n}*z*)exp(

*iϕ*), the equation can be separated into:

_{n}*i*>1 can be simply described as:

*i*=1,

*P*

_{1}(

*ω*)=0.

*EDF*denotes the theoretical mode in Ref.[16].

*FWM*represents the effect of FWM described in previous passage.

*F*is the transmission spectrum of filter and

*L*is the total loss of the cavity.

## 3. Simulation results and analysis

^{2}/km. A 3-dB coupler is used for output. The total loss of the cavity is approximated to be 10dB. The period filter is simulated by the superposition of Gaussian band pass filters with central frequencies shifted by 0.8nm and full width at half maximum (FWHM) of 0.15 nm, covering 1540~1560nm.

*λ*=0.1

*nm*and substituted into the EDF model. However, it is unrealistic to consider all the frequency slots in the FWM model because the possible mixing products of 2000 frequency components are horrible. To reduce the calculation work, only the 26 modes obtained through the filter are considered. This simplification is reasonable because the power of other frequency components is so small that their contribution to the FWM process can be ignored.

11. A. L. Zhang, H. Liu, M. S. Demokan, and H. Y. Tam, “Stable and broad bandwidth multiwavelength fiber ring laser incorporating a highly nonlinear photonic crystal fiber,” IEEE Photon. Technol. Lett. **17**, 2535–2537 (2005). [CrossRef]

*δ*=Δ

*δ*+Δ

_{M}*δ*+Δ

_{W}*δ*, where Δ

_{NL}*δ*, Δ

_{M}*δ*and Δ

_{W}*δ*represents the phase mismatching induced by material dispersion, waveguide dispersion and nonlinear effects, respectively. In single mode fiber, the contribution of Δ

_{NL}*δ*can be ignored except in the region near the zero dispersion wavelength, when it becomes comparable with Δ

_{W}*δ*for identified polarized waves. To control Δ

_{M}*δ*into a tolerate value, the following methods can be adopted:

*a*. reducing Δ

*δ*and Δ

_{M}*δ*by using small frequency shifts.

_{NL}*b*. operating near the zero dispersion wavelength so that Δ

*δ*almost cancels Δ

_{W}*δ*and Δ

_{M}*δ*.

_{NL}*c*. operating in the abnormal group velocity dispersion (GVD) regime so that Δ

*δ*is negative and can be canceled by Δ

_{M}*δ*and Δ

_{W}*δ*[17]. For the MWEDFL, only the third method is applicable. That is why many reported FWM assisted MWEDFL operates in the region >1550nm [11

_{NL}11. A. L. Zhang, H. Liu, M. S. Demokan, and H. Y. Tam, “Stable and broad bandwidth multiwavelength fiber ring laser incorporating a highly nonlinear photonic crystal fiber,” IEEE Photon. Technol. Lett. **17**, 2535–2537 (2005). [CrossRef]

*γ*and increasing the length

*L*of the HNDSF [11

11. A. L. Zhang, H. Liu, M. S. Demokan, and H. Y. Tam, “Stable and broad bandwidth multiwavelength fiber ring laser incorporating a highly nonlinear photonic crystal fiber,” IEEE Photon. Technol. Lett. **17**, 2535–2537 (2005). [CrossRef]

*L*=1.2km,

*γ*=11/W/km and the pump power is 100mW, 200mW, 300mW and 400mW, respectively. When the pump power is 200mW, the output spectrum is flattened, as shown in Fig.3 (b). The number of wavelengths in 3-dB bandwidth exceeds twenty. However, when pump power increases to 300mW and 400mW, the flatness of the output spectrum is abated, because too much power is transferred to wavelength near 1550nm and 1570nm. The number of the wavelengths in 3-dB bandwidth reduces to 14 and 9, respectively, as shown in Fig.3(c) and (d). Similar phenomenon can be observed through increasing the nonlinear coefficient

*γ*. The output spectrums for

*P*=100mW,

*L*=1.2km

*γ*=20/W/km and 30/W/km are plotted in Fig.4. When

*γ*=20/W/km, 17 lasing lines in 3-dB bandwidth are obtained, as shown in Fig.4 (a), while the number reduces to 14 when

*γ*=30/W/km. Thus the pump power and the nonlinear coefficient need to be optimized in order to get satisfying output spectrum.

**17**, 2535–2537 (2005). [CrossRef]

12. L. Zhang, M. S. Demokan, and H. Y. Tam, “Room temperature multiwavelength erbium-doped fiber ring laser using a highly nonlinear photonic crystal fiber,” Opt. Commun. **260**, 670–674 (2006). [CrossRef]

**17**, 2535–2537 (2005). [CrossRef]

## 4. Conclusion

## References and links

1. | A. Bellemare, A. Bellemare, M. Karasek, M. Rochette, S. A. L. S. Lrochelle, and M. A. T. M. Tetu, “Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU Tetu, frequency grid,” J. Lightw. Technol. |

2. | S. K. Kim, M. J. Chu, and J. H. Lee, “Wideband multiwavelength erbium-doped fiber ring Laser with Frequency Shifted Feedback,” Opt. Commun. |

3. | Z. X. Zhang, L. Zhan, and Y. X. Xia, “Tunable self-seeded multiwavelength Brillouin-erbium fiber laser with enhanced power efficiency,” Opt. Express |

4. | Y. Huang, L. Zhan, J. H. Ji, S. Y. Luo, and Y. Xia, “Multiwavelength self-seeded Brillouin-erbium fiber laser with 45-nm tunable range,” Opt. Commun. |

5. | X. H. Feng, H. Y. Tam, H. L. Liu, and P. K. A. Wai, “Multiwavelength erbium-doped fiber laser employing a nonlinear optical loop mirror,” Opt. Commun. |

6. | X. H. Feng, H. Y. Tam, and P. K. A. Wai, “Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation,” Opt. Express |

7. | C. L. Zhao, X. F. Yang, C. Lu, N. J. Hong, X. Guo, P. R. Chaudhuri, and X. Y. Dong, “Switchable muitiwavelength erbium-doped fiber lasers by using cascaded fiber laser Bragg gratings written in high birefringence fiber,” Opt. Commun. |

8. | Y. G. Liu, X. Y. Dong, P. Shum, S. Z. Yuan, G. Y. Kai, and X. Y. Dong, “Stable room-temperature multiwavelength lasing realization in ordinary erbium-doped fiber loop lasers,” Opt. Express |

9. | X. Liu, X. Yang, F. Lu, J. Ng, X. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express |

10. | Y. G. Han, J. H. Lee, S. B. Lee, L. PotÌ, and A. Bogoni, “Novel multiwavelength erbium-doped fiber and Raman fiber ring lasers with continuous wavelength spacing tunability at room temperature,” J. Lightw. Technol. |

11. | A. L. Zhang, H. Liu, M. S. Demokan, and H. Y. Tam, “Stable and broad bandwidth multiwavelength fiber ring laser incorporating a highly nonlinear photonic crystal fiber,” IEEE Photon. Technol. Lett. |

12. | L. Zhang, M. S. Demokan, and H. Y. Tam, “Room temperature multiwavelength erbium-doped fiber ring laser using a highly nonlinear photonic crystal fiber,” Opt. Commun. |

13. | X. M. Liu, “Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers,” Opt. Commun. |

14. | X. M. Liu, X. Q. Zhou, and C. Lu, “Four-wave mixing assisted stability enhancement: theory, experiment and application,” Opt. Lett. |

15. | D. Chen, S. Qin, Y. Gao, and S. Gao, “Wavelength-spacing continuously tunable multiwavelength erbium-doped fiber laser based on DSF and MZI,” Electron. Lett. |

16. | M. Karasek and A. Bellemare, “Numerical analysis of multifrequency erbium-doped fiber ring laser employing periodic filter and frequency shifter,” IEE Proc. |

17. | G.P. Agrawal, |

**OCIS Codes**

(140.3500) Lasers and laser optics : Lasers, erbium

(140.3510) Lasers and laser optics : Lasers, fiber

(140.3560) Lasers and laser optics : Lasers, ring

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: May 27, 2008

Revised Manuscript: July 11, 2008

Manuscript Accepted: July 18, 2008

Published: August 1, 2008

**Citation**

Xiaochuan Xu, Yong Yao, and Deying Chen, "Numerical analysis of multiwavelength erbium-doped fiber ring laser exploiting four-wave mixing," Opt. Express **16**, 12397-12402 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-12397

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### References

- A. Bellemare, A. Bellemare, M. Karasek, M. Rochette, S. A. L. S. Lrochelle, and M. A. T. M. Tetu, "Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU Tetu, frequency grid," J. Lightwave Technol. 18, 825-831 (2000). [CrossRef]
- S. K. Kim, M. J. Chu, and J. H. Lee, "Wideband multiwavelength erbium-doped fiber ring Laser with Frequency Shifted Feedback," Opt. Commun. 190, 291-302 (2001). [CrossRef]
- Z. X. Zhang, L. Zhan, and Y. X. Xia, "Tunable self-seeded multiwavelength Brillouin-erbium fiber laser with enhanced power efficiency," Opt. Express 15, 9731-9736 (2007). [CrossRef] [PubMed]
- Y. Huang, L. Zhan, J. H. Ji, S. Y. Luo, and Y. Xia, "Multiwavelength self-seeded Brillouin-erbium fiber laser with 45-nm tunable range," Opt. Commun. 281, 452-456 (2008). [CrossRef]
- X. H. Feng, H. Y. Tam, H. L. Liu, and P. K. A. Wai, "Multiwavelength erbium-doped fiber laser employing a nonlinear optical loop mirror," Opt. Commun. 268, 278-281 (2006). [CrossRef]
- X. H. Feng, H. Y. Tam, and P. K. A. Wai, "Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation," Opt. Express 14, 8205-8210 (2006). [CrossRef] [PubMed]
- C. L. Zhao, X. F. Yang, C. Lu, N. J. Hong, X. Guo, P. R. Chaudhuri, and X. Y. Dong, "Switchable muiti-wavelength erbium-doped fiber lasers by using cascaded fiber laser Bragg gratings written in high birefringence fiber," Opt. Commun. 230, 313-317 (2004). [CrossRef]
- Y. G. Liu, X. Y. Dong, P. Shum, S. Z. Yuan, G. Y. Kai, and X. Y. Dong, "Stable room-temperature multi-wavelength lasing realization in ordinary erbium-doped fiber loop lasers," Opt. Express 14, 9293-9298 (2006). [CrossRef] [PubMed]
- X. Liu, X. Yang, F. Lu, J. Ng, X. Zhou, and C. Lu, "Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber, " Opt. Express 13, 142-147 (2005). [CrossRef] [PubMed]
- Y. G. Han, J. H. Lee, S. B. Lee, L. Pot�?, and A. Bogoni, "Novel multiwavelength erbium-doped fiber and Raman fiber ring lasers with continuous wavelength spacing tunability at room temperature," J. Lightwave Technol. 18, 2219-2225 (2007).
- A. L. Zhang, H. Liu, M. S. Demokan, and H. Y. Tam, "Stable and broad bandwidth multiwavelength fiber ring laser incorporating a highly nonlinear photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 2535-2537 (2005). [CrossRef]
- L. Zhang, M. S. Demokan, and H. Y. Tam, "Room temperature multiwavelength erbium-doped fiber ring laser using a highly nonlinear photonic crystal fiber," Opt. Commun. 260, 670-674 (2006). [CrossRef]
- X. M. Liu, "Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers," Opt. Commun. 260, 554-559 (2006). [CrossRef]
- X. M. Liu, X. Q. Zhou, and C. Lu, "Four-wave mixing assisted stability enhancement: theory, experiment and application," Opt. Lett. 30, 2257-2259 (2005). [CrossRef] [PubMed]
- D. Chen, S. Qin, Y. Gao, and S. Gao, "Wavelength-spacing continuously tunable multiwavelength erbium-doped fiber laser based on DSF and MZI," Electron. Lett. 43, 524-525 (2007). [CrossRef]
- M. Karasek and A. Bellemare, "Numerical analysis of multifrequency erbium-doped fiber ring laser employing periodic filter and frequency shifter," IEE Proc. 147, 115-119 (2002).
- G.P. Agrawal, Nonlinear Fiber Optics, 3rd (Academic, 2000).

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