Abstract

Relaxation oscillations in Er3+-doped and Yb3+/Er3+ co-doped fiber grating lasers were investigated. Intensity noise models were established for both cases in which the fluctuations of pump power and cavity loss were analyzed. Simulation indicates that the relaxation oscillation is induced by the pump power fluctuation, and fluctuation of the cavity loss can broaden the relaxation oscillation peak and enhance the amplitude. The relaxation oscillation of a laser with Er3+-doped fiber exhibits a lower frequency and larger amplitude than that of an Yb3+/Er3+ co-doped fiber grating laser. Distributed Bragg reflector fiber grating lasers with Er3+-doped fiber and Yb3+/Er3+ co-doped fiber were fabricated, and the relaxation oscillations were measured. For the former, the relaxation oscillation frequency is at the magnitude of several hundreds of kilohertz and lineally shifts toward the higher frequency with the pump power. For the latter, no obvious relaxation oscillation was measured.

© 2010 Optical Society of America

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  1. G. A. Ball and W. H. Glenn, “Design of single-mode linear-cavity erbium fiber laser utilizing Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
    [CrossRef]
  2. G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett 7, 613-615 (1991).
  3. M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445-1448 (1995).
    [CrossRef]
  4. T. Xu, F. Li, and Y. Liu, “Characteristic mode of distributed feedback fiber lasers,” Chin. J. Lasers 10, 1358-1362 (2007).
  5. P. Varming, J. Hubner, and M. Kristensen, “DFB fiber laser as source for optical communication systems,” in Conference on Optical Fiber Communication, Vol. 6 of 1997 Technical Digest Series (Optical Society of America, 1997), p.169.
  6. G. A. Cranch, G. Flockhart, and C. K. Kirkendall, “Distributed feedback fiber laser strain sensors,” IEEE Sens. J. 8, 1161-1172 (2008).
    [CrossRef]
  7. S. Goodman, S. Foster, J. V. Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L (2009).
  8. D. J. Hill, P. J. Nash, and D. A. Jack, “A fiber laser hydrophone array,” Proc. SPIE 3860, 55-66 (2005).
  9. B. Yu, S. Zhen, and J. Zhu, “Experimental study on low-noise fiber laser,” Acta Opt. Sin. 2, 217-220 (2006).
  10. X. Liang, S. Xiong, Y. Hu, Q. Yao, and L. N. Ma, “The impact of relative intensity noise on fiber optic hydrophone's PGC scheme,” Chin. J. Lasers 5, 716-721 (2008).
  11. G. A. Cranch, M. A. Englund, and C. K. Kirkendall, “Intensity noise characteristics of erbium-doped distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 39, 1579-1586 (2003).
    [CrossRef]
  12. S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43, 378-384 (2007).
    [CrossRef]
  13. B. Zhou, Y. Gao, and C. Chen, Laser Principles (National Defence Industry Press, 2002).
  14. C. R. Giles and Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271-282 (1991).
    [CrossRef]
  15. S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19-26 (1998).
  16. E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+-Yb3+ co-doped fiber lasers,” IEEE J. Quantum Electron. 39, 1444-1451 (2003).
    [CrossRef]
  17. L. N. Ma, Y. Hu, H. Luo, X. Zhang, and Z. Meng, “Acoustic pressure sensitivity of Yb3+/Er3+ co-doped DBR fiber laser hydrophone,” Chin. J. Lasers 6, 1473-1478 (2009).
  18. G. Hu, Y. Guo, X. Li, and Y. Wang, “Noise measuring methods of semiconductor lasers,” Semiconductor Technol. 1, 53-56(2001).

2009 (2)

S. Goodman, S. Foster, J. V. Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L (2009).

L. N. Ma, Y. Hu, H. Luo, X. Zhang, and Z. Meng, “Acoustic pressure sensitivity of Yb3+/Er3+ co-doped DBR fiber laser hydrophone,” Chin. J. Lasers 6, 1473-1478 (2009).

2008 (2)

X. Liang, S. Xiong, Y. Hu, Q. Yao, and L. N. Ma, “The impact of relative intensity noise on fiber optic hydrophone's PGC scheme,” Chin. J. Lasers 5, 716-721 (2008).

G. A. Cranch, G. Flockhart, and C. K. Kirkendall, “Distributed feedback fiber laser strain sensors,” IEEE Sens. J. 8, 1161-1172 (2008).
[CrossRef]

2007 (2)

T. Xu, F. Li, and Y. Liu, “Characteristic mode of distributed feedback fiber lasers,” Chin. J. Lasers 10, 1358-1362 (2007).

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43, 378-384 (2007).
[CrossRef]

2006 (1)

B. Yu, S. Zhen, and J. Zhu, “Experimental study on low-noise fiber laser,” Acta Opt. Sin. 2, 217-220 (2006).

2005 (1)

D. J. Hill, P. J. Nash, and D. A. Jack, “A fiber laser hydrophone array,” Proc. SPIE 3860, 55-66 (2005).

2003 (2)

G. A. Cranch, M. A. Englund, and C. K. Kirkendall, “Intensity noise characteristics of erbium-doped distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 39, 1579-1586 (2003).
[CrossRef]

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+-Yb3+ co-doped fiber lasers,” IEEE J. Quantum Electron. 39, 1444-1451 (2003).
[CrossRef]

2001 (1)

G. Hu, Y. Guo, X. Li, and Y. Wang, “Noise measuring methods of semiconductor lasers,” Semiconductor Technol. 1, 53-56(2001).

1998 (1)

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19-26 (1998).

1995 (1)

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445-1448 (1995).
[CrossRef]

1992 (1)

G. A. Ball and W. H. Glenn, “Design of single-mode linear-cavity erbium fiber laser utilizing Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
[CrossRef]

1991 (2)

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett 7, 613-615 (1991).

C. R. Giles and Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271-282 (1991).
[CrossRef]

Ball, G. A.

G. A. Ball and W. H. Glenn, “Design of single-mode linear-cavity erbium fiber laser utilizing Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
[CrossRef]

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett 7, 613-615 (1991).

Chen, C.

B. Zhou, Y. Gao, and C. Chen, Laser Principles (National Defence Industry Press, 2002).

Cranch, G. A.

G. A. Cranch, G. Flockhart, and C. K. Kirkendall, “Distributed feedback fiber laser strain sensors,” IEEE Sens. J. 8, 1161-1172 (2008).
[CrossRef]

G. A. Cranch, M. A. Englund, and C. K. Kirkendall, “Intensity noise characteristics of erbium-doped distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 39, 1579-1586 (2003).
[CrossRef]

De Geronimo, G.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19-26 (1998).

Desurvire,

C. R. Giles and Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271-282 (1991).
[CrossRef]

Englund, M. A.

G. A. Cranch, M. A. Englund, and C. K. Kirkendall, “Intensity noise characteristics of erbium-doped distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 39, 1579-1586 (2003).
[CrossRef]

Flockhart, G.

G. A. Cranch, G. Flockhart, and C. K. Kirkendall, “Distributed feedback fiber laser strain sensors,” IEEE Sens. J. 8, 1161-1172 (2008).
[CrossRef]

Foster, S.

S. Goodman, S. Foster, J. V. Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L (2009).

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43, 378-384 (2007).
[CrossRef]

Gao, Y.

B. Zhou, Y. Gao, and C. Chen, Laser Principles (National Defence Industry Press, 2002).

Giles, C. R.

C. R. Giles and Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271-282 (1991).
[CrossRef]

Glenn, W. H.

G. A. Ball and W. H. Glenn, “Design of single-mode linear-cavity erbium fiber laser utilizing Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
[CrossRef]

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett 7, 613-615 (1991).

Goodman, S.

S. Goodman, S. Foster, J. V. Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L (2009).

Guo, Y.

G. Hu, Y. Guo, X. Li, and Y. Wang, “Noise measuring methods of semiconductor lasers,” Semiconductor Technol. 1, 53-56(2001).

Hardy, A. A.

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+-Yb3+ co-doped fiber lasers,” IEEE J. Quantum Electron. 39, 1444-1451 (2003).
[CrossRef]

Hill, D. J.

D. J. Hill, P. J. Nash, and D. A. Jack, “A fiber laser hydrophone array,” Proc. SPIE 3860, 55-66 (2005).

Hu, G.

G. Hu, Y. Guo, X. Li, and Y. Wang, “Noise measuring methods of semiconductor lasers,” Semiconductor Technol. 1, 53-56(2001).

Hu, Y.

L. N. Ma, Y. Hu, H. Luo, X. Zhang, and Z. Meng, “Acoustic pressure sensitivity of Yb3+/Er3+ co-doped DBR fiber laser hydrophone,” Chin. J. Lasers 6, 1473-1478 (2009).

X. Liang, S. Xiong, Y. Hu, Q. Yao, and L. N. Ma, “The impact of relative intensity noise on fiber optic hydrophone's PGC scheme,” Chin. J. Lasers 5, 716-721 (2008).

Hubner, J.

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445-1448 (1995).
[CrossRef]

P. Varming, J. Hubner, and M. Kristensen, “DFB fiber laser as source for optical communication systems,” in Conference on Optical Fiber Communication, Vol. 6 of 1997 Technical Digest Series (Optical Society of America, 1997), p.169.

Jack, D. A.

D. J. Hill, P. J. Nash, and D. A. Jack, “A fiber laser hydrophone array,” Proc. SPIE 3860, 55-66 (2005).

Kirkendall, C. K.

G. A. Cranch, G. Flockhart, and C. K. Kirkendall, “Distributed feedback fiber laser strain sensors,” IEEE Sens. J. 8, 1161-1172 (2008).
[CrossRef]

G. A. Cranch, M. A. Englund, and C. K. Kirkendall, “Intensity noise characteristics of erbium-doped distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 39, 1579-1586 (2003).
[CrossRef]

Kristensen, M.

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445-1448 (1995).
[CrossRef]

P. Varming, J. Hubner, and M. Kristensen, “DFB fiber laser as source for optical communication systems,” in Conference on Optical Fiber Communication, Vol. 6 of 1997 Technical Digest Series (Optical Society of America, 1997), p.169.

Laporta, P.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19-26 (1998).

Li, F.

T. Xu, F. Li, and Y. Liu, “Characteristic mode of distributed feedback fiber lasers,” Chin. J. Lasers 10, 1358-1362 (2007).

Li, X.

G. Hu, Y. Guo, X. Li, and Y. Wang, “Noise measuring methods of semiconductor lasers,” Semiconductor Technol. 1, 53-56(2001).

Liang, X.

X. Liang, S. Xiong, Y. Hu, Q. Yao, and L. N. Ma, “The impact of relative intensity noise on fiber optic hydrophone's PGC scheme,” Chin. J. Lasers 5, 716-721 (2008).

Liu, Y.

T. Xu, F. Li, and Y. Liu, “Characteristic mode of distributed feedback fiber lasers,” Chin. J. Lasers 10, 1358-1362 (2007).

Luo, H.

L. N. Ma, Y. Hu, H. Luo, X. Zhang, and Z. Meng, “Acoustic pressure sensitivity of Yb3+/Er3+ co-doped DBR fiber laser hydrophone,” Chin. J. Lasers 6, 1473-1478 (2009).

Ma, L. N.

L. N. Ma, Y. Hu, H. Luo, X. Zhang, and Z. Meng, “Acoustic pressure sensitivity of Yb3+/Er3+ co-doped DBR fiber laser hydrophone,” Chin. J. Lasers 6, 1473-1478 (2009).

X. Liang, S. Xiong, Y. Hu, Q. Yao, and L. N. Ma, “The impact of relative intensity noise on fiber optic hydrophone's PGC scheme,” Chin. J. Lasers 5, 716-721 (2008).

Mendis, H.

S. Goodman, S. Foster, J. V. Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L (2009).

Meng, Z.

L. N. Ma, Y. Hu, H. Luo, X. Zhang, and Z. Meng, “Acoustic pressure sensitivity of Yb3+/Er3+ co-doped DBR fiber laser hydrophone,” Chin. J. Lasers 6, 1473-1478 (2009).

Milnes, M.

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43, 378-384 (2007).
[CrossRef]

Morey, W. W.

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett 7, 613-615 (1991).

Nash, P. J.

D. J. Hill, P. J. Nash, and D. A. Jack, “A fiber laser hydrophone array,” Proc. SPIE 3860, 55-66 (2005).

Sejka, M.

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445-1448 (1995).
[CrossRef]

Svelto, O.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19-26 (1998).

Taccheo, S.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19-26 (1998).

Tikhomirov, A.

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43, 378-384 (2007).
[CrossRef]

Varming, P.

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445-1448 (1995).
[CrossRef]

P. Varming, J. Hubner, and M. Kristensen, “DFB fiber laser as source for optical communication systems,” in Conference on Optical Fiber Communication, Vol. 6 of 1997 Technical Digest Series (Optical Society of America, 1997), p.169.

Velzen, J. V.

S. Goodman, S. Foster, J. V. Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L (2009).

Wang, Y.

G. Hu, Y. Guo, X. Li, and Y. Wang, “Noise measuring methods of semiconductor lasers,” Semiconductor Technol. 1, 53-56(2001).

Xiong, S.

X. Liang, S. Xiong, Y. Hu, Q. Yao, and L. N. Ma, “The impact of relative intensity noise on fiber optic hydrophone's PGC scheme,” Chin. J. Lasers 5, 716-721 (2008).

Xu, T.

T. Xu, F. Li, and Y. Liu, “Characteristic mode of distributed feedback fiber lasers,” Chin. J. Lasers 10, 1358-1362 (2007).

Yahel, E.

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+-Yb3+ co-doped fiber lasers,” IEEE J. Quantum Electron. 39, 1444-1451 (2003).
[CrossRef]

Yao, Q.

X. Liang, S. Xiong, Y. Hu, Q. Yao, and L. N. Ma, “The impact of relative intensity noise on fiber optic hydrophone's PGC scheme,” Chin. J. Lasers 5, 716-721 (2008).

Yu, B.

B. Yu, S. Zhen, and J. Zhu, “Experimental study on low-noise fiber laser,” Acta Opt. Sin. 2, 217-220 (2006).

Zhang, X.

L. N. Ma, Y. Hu, H. Luo, X. Zhang, and Z. Meng, “Acoustic pressure sensitivity of Yb3+/Er3+ co-doped DBR fiber laser hydrophone,” Chin. J. Lasers 6, 1473-1478 (2009).

Zhen, S.

B. Yu, S. Zhen, and J. Zhu, “Experimental study on low-noise fiber laser,” Acta Opt. Sin. 2, 217-220 (2006).

Zhou, B.

B. Zhou, Y. Gao, and C. Chen, Laser Principles (National Defence Industry Press, 2002).

Zhu, J.

B. Yu, S. Zhen, and J. Zhu, “Experimental study on low-noise fiber laser,” Acta Opt. Sin. 2, 217-220 (2006).

Acta Opt. Sin. (1)

B. Yu, S. Zhen, and J. Zhu, “Experimental study on low-noise fiber laser,” Acta Opt. Sin. 2, 217-220 (2006).

Appl. Phys. B (1)

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19-26 (1998).

Chin. J. Lasers (3)

L. N. Ma, Y. Hu, H. Luo, X. Zhang, and Z. Meng, “Acoustic pressure sensitivity of Yb3+/Er3+ co-doped DBR fiber laser hydrophone,” Chin. J. Lasers 6, 1473-1478 (2009).

X. Liang, S. Xiong, Y. Hu, Q. Yao, and L. N. Ma, “The impact of relative intensity noise on fiber optic hydrophone's PGC scheme,” Chin. J. Lasers 5, 716-721 (2008).

T. Xu, F. Li, and Y. Liu, “Characteristic mode of distributed feedback fiber lasers,” Chin. J. Lasers 10, 1358-1362 (2007).

Electron. Lett. (1)

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445-1448 (1995).
[CrossRef]

IEEE J. Quantum Electron. (3)

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+-Yb3+ co-doped fiber lasers,” IEEE J. Quantum Electron. 39, 1444-1451 (2003).
[CrossRef]

G. A. Cranch, M. A. Englund, and C. K. Kirkendall, “Intensity noise characteristics of erbium-doped distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 39, 1579-1586 (2003).
[CrossRef]

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43, 378-384 (2007).
[CrossRef]

IEEE Photon. Technol. Lett (1)

G. A. Ball, W. W. Morey, and W. H. Glenn, “Standing-wave monomode erbium fiber laser,” IEEE Photon. Technol. Lett 7, 613-615 (1991).

IEEE Sens. J. (1)

G. A. Cranch, G. Flockhart, and C. K. Kirkendall, “Distributed feedback fiber laser strain sensors,” IEEE Sens. J. 8, 1161-1172 (2008).
[CrossRef]

J. Lightwave Technol. (2)

C. R. Giles and Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271-282 (1991).
[CrossRef]

G. A. Ball and W. H. Glenn, “Design of single-mode linear-cavity erbium fiber laser utilizing Bragg reflectors,” J. Lightwave Technol. 10, 1338-1343 (1992).
[CrossRef]

Proc. SPIE (2)

S. Goodman, S. Foster, J. V. Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L (2009).

D. J. Hill, P. J. Nash, and D. A. Jack, “A fiber laser hydrophone array,” Proc. SPIE 3860, 55-66 (2005).

Semiconductor Technol. (1)

G. Hu, Y. Guo, X. Li, and Y. Wang, “Noise measuring methods of semiconductor lasers,” Semiconductor Technol. 1, 53-56(2001).

Other (2)

P. Varming, J. Hubner, and M. Kristensen, “DFB fiber laser as source for optical communication systems,” in Conference on Optical Fiber Communication, Vol. 6 of 1997 Technical Digest Series (Optical Society of America, 1997), p.169.

B. Zhou, Y. Gao, and C. Chen, Laser Principles (National Defence Industry Press, 2002).

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Figures (12)

Fig. 1
Fig. 1

Energy levels of Yb 3 + / Er 3 + co-doped fiber.

Fig. 2
Fig. 2

Simulated results of intensity noise in fiber grating lasers with (a)  Er 3 + -doped fiber and (b)  Yb 3 + / Er 3 + co-doped fiber.

Fig. 3
Fig. 3

Measurement system of relaxation oscillation.

Fig. 4
Fig. 4

Spectrum of Er 3 + -doped DBR fiber laser.

Fig. 5
Fig. 5

Laser output versus pumping power.

Fig. 6
Fig. 6

Measurement result of F-P interferometer.

Fig. 7
Fig. 7

Relaxation oscillation of Er 3 + -doped DBR fiber laser.

Fig. 8
Fig. 8

Relaxation oscillation frequency versus pumping power.

Fig. 9
Fig. 9

Spectrum of Yb 3 + / Er 3 + co-doped DBR fiber laser.

Fig. 10
Fig. 10

Laser output versus pumping power.

Fig. 11
Fig. 11

Measurement result of F-P interferometer.

Fig. 12
Fig. 12

Relaxation oscillation of Yb 3 + / Er 3 + co-doped DBR fiber laser.

Tables (2)

Tables Icon

Table 1 Er 3 + -Doped Fiber

Tables Icon

Table 2 Yb 3 + / Er 3 + Co-doped Fiber

Equations (11)

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

RIN = Δ P 2 / P 2 ( dB / Hz ) ,
d n 2 d t = ( W P + W a ) ( 1 n 2 ) n 2 ( W e + 1 τ 2 ) , d q d t = W e n 2 N 0 W e ( 1 n 2 ) N 0 q τ c ,
n 20 = r q a N 0 + 1 / τ c Δ r q N 0 , q 0 = τ c Δ r q ( W p 0 N 0 Δ r q ( r q a N 0 + 1 / τ c ) ( W p + 1 / τ 2 ) ) ,
d δ n 2 ( t ) d t = A 1 δ n 2 ( t ) A 3 δ q ( t ) + ( 1 n 20 ) δ W p ( t ) , d δ q ( t ) d t = A 4 δ n 2 ( t ) + ( A 3 N 0 + A 5 ) δ q ( t ) c q 0 n l e δ γ ( t ) ,
Δ Q ( s ) q 0 = H p ( f ) δ W P ( s ) W p 0 + H l ( f ) δ Γ ( s ) γ 0 ,
H p ( f ) = A 2 A 4 s 2 + A 1 s + A 3 A 4 ( A 3 N 0 + A 5 ) s ( A 3 N 0 + A 5 ) A 1 , H l ( f ) = A 5 ( s + A 1 ) s 2 + A 1 s + A 3 A 4 ( A 3 N 0 + A 5 ) s ( A 3 N 0 + A 5 ) A 1 ,
RIN ( f ) = | H p ( f ) | 2 δ W P ( f ) 2 W p 0 2 + | H l ( f ) | 2 δ Γ ( f ) 2 γ 0 2 .
d n y b 2 d t = W p ( 1 n y b 2 ) K t r n y b 2 ( 1 n e r 2 ) N e r n y b 2 τ y b , d n e r 2 d t = ( K t r n y b 2 N y b + W a ) ( 1 n e r 2 ) n e r 2 ( W e + 1 τ e r ) , d q d t = W e n e r 2 N e r W a ( 1 n e r 2 ) N e r q τ c ,
n e r 20 = r q a N e r + 1 τ c Δ r q N e r , n y b 20 = W p W p + K t r ( 1 n e r 20 ) N e r + 1 τ y b , q 0 = K t r ( 1 n e r 20 ) n y b 20 N y b n e r 20 / τ e r Δ r q n e r 20 r q a .
H p ( f ) = A 4 A 2 A 8 s ( s + A 1 ) ( s + A 7 ) A 6 A 8 s + A 3 A 4 ( A 1 + s ) ( A 3 N e r + A 5 ) [ ( s + A 1 ) ( s + A 7 ) A 6 A 8 ] , H l ( f ) = A 5 [ ( s + A 7 ) ( s + A 1 ) A 6 A 8 ] s ( s + A 1 ) ( s + A 7 ) A 6 A 8 s + A 3 A 4 ( A 1 + s ) ( A 3 N e r + A 5 ) [ ( s + A 1 ) ( s + A 7 ) A 6 A 8 ] ,
A 1 = W p 0 + K t r ( 1 n e r 20 ) N e r + 1 / τ y b , A 2 = ( 1 n y b 20 ) W p 0 / q 0 , A 3 = Δ r q n e r 20 r q a , A 4 = Δ r q q 0 N e r , A 5 = c γ 0 / n l e , A 6 = K t r n y b 20 N e r , A 7 = K t r n y b 20 N y b + Δ r q q 0 + 1 / τ e r , A 8 = K t r ( 1 n e r 20 ) N y b .

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