High-accuracy fiber optical microphone in a DBR fiber laser based on a nanothick silver diaphragm by self-mixing technique

Zhengting Du; Liang Lu; Wenhua Zhang; Bo Yang; Shuang Wu; Yunhe Zhao; Feng Xu; Zhiping Wang; Huaqiao Gui; Jianguo Liu; Benli Yu

doi:10.1364/OE.21.030580

Abstract

A high-accuracy fiber optical microphone (FOM) is first applied by self-mixing technique in a DBR fiber laser based on a nanothick silver diaphragm. The nanothick silver diaphragm fabricated by the convenient and low cost electroless plating method is functioned as sensing diaphragm due to critically susceptible to the air vibration. Simultaneously, micro-vibration theory model of self-mixing interference fiber optical microphone is deduced based on quasi-analytical method. The dynamic property to frequencies and amplitudes are experimentally carried out to characterize the fabricated FOM and also the reproduced sound of news and music can clearly meet the ear of the people which shows the technique proposed in this paper guarantee steady, high signal-noise ratio operation and outstanding accuracy in the DBR fiber laser which is potential to medical and security applications such as real-time voice reproduction for throat and voiceprint verification.

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References

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Author
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Publication

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).
J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).
H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).
J. H. Churnside, “Laser Doppler velocimetry by modulating a CO2 laser with backscattered light,” Appl. Opt. 23(1), 61–66 (1984).
[Crossref] [PubMed]
L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).
W. M. Wang, W. J. Boyle, K. T. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[Crossref] [PubMed]
Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).
L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]
F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]
E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]
I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. 17(5), 891–897 (1999).
[Crossref]
M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997).
[Crossref]
L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er3+–Yb3+ codoped distributed Bragg reflector fiber laser for remote sensing applications up to 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]
J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

2013 (1)

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

2012 (3)

L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er3+–Yb3+ codoped distributed Bragg reflector fiber laser for remote sensing applications up to 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

2011 (1)

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

2010 (2)

J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

2006 (1)

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

2005 (1)

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

2003 (1)

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]

1999 (1)

I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. 17(5), 891–897 (1999).
[Crossref]

1997 (1)

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997).
[Crossref]

Bucaro, J. A.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Cao, Z.

L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er3+–Yb3+ codoped distributed Bragg reflector fiber laser for remote sensing applications up to 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

Churnside, J. H.

J. H. Churnside, “Laser Doppler velocimetry by modulating a CO2 laser with backscattered light,” Appl. Opt. 23(1), 61–66 (1984).
[Crossref] [PubMed]

Dai, J.

L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er3+–Yb3+ codoped distributed Bragg reflector fiber laser for remote sensing applications up to 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

Du, K. Z.

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Du, Z.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Grattan, K. T.

W. M. Wang, W. J. Boyle, K. T. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[Crossref] [PubMed]

Gui, H.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Hardy, A.

I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. 17(5), 891–897 (1999).
[Crossref]

Hardy, A. A.

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]

Houston, B. H.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Jarzynski, J.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Karasek, M.

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997).
[Crossref]

Kelson, I.

I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. 17(5), 891–897 (1999).
[Crossref]

Koh, L. M.

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

Konle, H. J.

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

Lagakos, N.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Li, C.

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

Lu, L.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er3+–Yb3+ codoped distributed Bragg reflector fiber laser for remote sensing applications up to 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Lu, W.

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

Mohanty, L.

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

Pacheco, G. M.

J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

Palmer, A. W.

W. M. Wang, W. J. Boyle, K. T. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[Crossref] [PubMed]

Paschereit, C. O.

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

Ren, D.

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

Rohle, I. R.

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

Sakamoto, J. M. S.

J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

Shi, X.

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

Tjin, S. C.

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

Wang, R.

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

Wang, W. M.

W. M. Wang, W. J. Boyle, K. T. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[Crossref] [PubMed]

Xu, F.

L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er3+–Yb3+ codoped distributed Bragg reflector fiber laser for remote sensing applications up to 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

Yahel, E.

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]

Yang, B.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Yang, J.

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

Yu, B.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er3+–Yb3+ codoped distributed Bragg reflector fiber laser for remote sensing applications up to 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Zalalutdinov, M.

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

Zhai, L.

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Zhang, W.

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Appl. Opt. (2)

J. H. Churnside, “Laser Doppler velocimetry by modulating a CO2 laser with backscattered light,” Appl. Opt. 23(1), 61–66 (1984).
[Crossref] [PubMed]

W. M. Wang, W. J. Boyle, K. T. Grattan, and A. W. Palmer, “Self-mixing interference in a diode laser: experimental observations and theoretical analysis,” Appl. Opt. 32(9), 1551–1558 (1993).
[Crossref] [PubMed]

Appl. Phys. B (1)

Z. Du, L. Lu, W. Zhang, B. Yang, H. Gui, and B. Yu, “Measurement of the velocity inside an all-fiber DBR laser by self-mixing technique,” Appl. Phys. B 113, 153–158 (2013).

Appl. Phys. Lett. (1)

L. Mohanty, L. M. Koh, and S. C. Tjin, “Fiber Bragg grating microphone system,” Appl. Phys. Lett. 89, 161109 (2006).

IEEE J. Quantum Electron. (2)

E. Yahel and A. A. Hardy, “Modeling and optimization of short Er3+–Yb3+ codoped fiber lasers,” IEEE J. Quantum Electron. 39(11), 1444–1451 (2003).
[Crossref]

M. Karasek, “Optimum design of Er3+-Yb3+ codoped fibers for large-signal high-pump-power applications,” IEEE J. Quantum Electron. 33(10), 1699–1705 (1997).
[Crossref]

IEEE Photonics Technol. Lett. (1)

L. Lu, Z. Cao, J. Dai, F. Xu, and B. Yu, “Self-mixing signal in Er3+–Yb3+ codoped distributed Bragg reflector fiber laser for remote sensing applications up to 20Km,” IEEE Photonics Technol. Lett. 24(5), 392–394 (2012).
[Crossref]

J. Acoust. Soc. Am. (1)

J. A. Bucaro, N. Lagakos, B. H. Houston, J. Jarzynski, and M. Zalalutdinov, “Miniature, high performance, low-cost fiber optic microphone,” J. Acoust. Soc. Am. 118(3), 1406–1413 (2005).
[Crossref]

J. Lightwave Technol. (1)

I. Kelson and A. Hardy, “Optimization of strongly pumped fiber lasers,” J. Lightwave Technol. 17(5), 891–897 (1999).
[Crossref]

Meas. Sci. Technol. (1)

H. J. Konle, C. O. Paschereit, and I. R. Rohle, “A fiber-optical microphone based on a Fabry-Perot interferometer applied for thermo-acoustic measurements,” Meas. Sci. Technol. 21, 015302 (2010).

Opt. Commun. (1)

L. Lu, L. Zhai, K. Z. Du, and B. Yu, “Study on self-mixing interference using Er3+–Yb3+ codoped distributed Bragg reflector fiber laser with different pump power current,” Opt. Commun. 284(24), 5781–5785 (2011).
[Crossref]

Opt. Express (1)

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, and B. Yu, “A self-mixing interference measurement system of a fiber ring laser with narrow linewidth,” Opt. Express 20(8), 8598–8607 (2012).

Opt. Lett. (1)

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

Phys. Proc. (1)

J. M. S. Sakamoto and G. M. Pacheco, “Theory and experiment for single lens fiber optical microphone,” Phys. Proc. 3, 651–658, (2010).

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Fig. 1 The principle of SMI output power based on the Boundary conditional equations.

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Fig. 2 The typical simulated result by quasi-analytical method (Upper trace: vibration signal of external target, Lower trace: self-mixing interference signal).

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Fig. 3 Experimental setup of fiber optical microphone based on self-mixing in DBR fiber laser.

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Fig. 4 The linewidth of DBR fiber laser measured by optical analyzer.

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Fig. 5 The power spectrum of DBR fiber laser at different times.

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Fig. 6 Schematic of the test setup for characterization of the fiber optical microphone by self-mixing technique.

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Fig. 7 Measured signal at 820 Hz with 1mVrms. Left curve from the reference microphone links to the input1 of the Module Panel and right curve from the fiber optical microphone refers to the input2.

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Fig. 8 Measured SNR-frequency response of SMI-FOM and RM.

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Fig. 9 Measured SNR-amplitude response of SMI-FOM and RM at different gain amplitude.

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Fig. 10 the power spectrums of SMI-FOM and RM at different times.

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Tables (1)

Table 1 The parameters used for the DBR fiber laser

View Table

Equations (7)

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

P_{L}^{o u t} = P_{L}^{i n} e^{- α_{s} L + P_{s}^{a b s} / P_{s s} + P_{p}^{a b s} / P_{s s}}

P_{R}^{o u t} = P_{R}^{i n} e^{- α_{s} L + P_{s}^{a b s} / P_{s s} + P_{p}^{a b s} / P_{s s}}

P_{L}^{i n} = ε_{2} [ε_{2} R_{2} P_{R}^{o u t} + (1 - R_{2}) P_{s e e d}]

P_{R}^{i n} = ε_{1}^{2} R_{1} P_{L}^{o u t}

P_{R}^{o u t} = ε_{1}^{2} R_{1} ε_{2} [ε_{2} R_{2} P_{R}^{o u t} + (1 - R_{2}) P_{s e e d}] e^{-2 α_{s} L + 2 P_{s}^{a b s} / P_{s s} + 2 P_{p}^{a b s} / P_{s s}}

L_{e x t} (t) = L_{0} +A \cos {(ω}_{0} t)

P_{L a s e r} = ε_{1} {(1-R}_{1}) P_{R}^{o u t} e^{-(- \partial_{s} L + P_{s}^{a b s} / P_{s s} + P_{p}^{a b s} / P_{s s})}

Parameter	Value
λ: the oscillation wavelength of signal	1550 nm
σ_saEY: the absorption cross-section	3 × 10⁻²⁵ m²
σ_seEY: the emission cross-section	1 × 10⁻²⁵ m²
α_s: the scattering l osses for the signal	0.75 × 10⁻³ m⁻¹
Г_s: the power filling factor which represent the fraction of the signal amplified in the core	0.82
a^eff: the effective core area of signal light	1.5 × 10⁻¹¹ m²
L: the length of EYDF	0.1m
τ_Er: spontaneous lifetime	10.8 × 10⁻³ s
ε₁: attenuation factor	0.9
ε₂: attenuation factor	0.9
r₁: the reflectivity at the end of FBG1	0.87
r₂: the reflectivity at the end of FBG2	0.9
r₃: is the reflectivity of the external target face	0.001
f₀: frequency of driving signal launched on the external target	420 Hz
A: amplitude of driving signal	1.55 × 10⁻¹⁰ m

Abstract

References

2013 (1)

2012 (3)

2011 (1)

2010 (2)

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Gui, H.

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