Abstract

A method of detecting mode hopping for single-longitudinal-mode (SLM) fiber ring lasers has been proposed and experimentally demonstrated. The method that is based on an unbalanced Michelson interferometer (MI) utilizing phase generated carrier modulation instantly transforms mode-hopping dynamics into steep phase changes of the interferometer. Multiform mode hops in an SLM erbium-doped fiber ring laser with an 18.6 MHz mode spacing have been detected exactly in real-time domain and discussed in detail. Numerical results show that the MI-based method has a high testing sensitivity for identifying mode hopping, which will play a significant role in evaluating the output stability of SLM fiber lasers.

© 2012 Optical Society of America

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References

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  1. M. Ohtsu, K.-Y. Liou, E. C. Burrows, C. A. Burrus, and G. Eisenstein, “A simple interferometric method for monitoring mode hopping in tunable external-cavity semiconductor lasers,” J. Lightwave Technol. 7, 68–76 (1989).
    [CrossRef]
  2. T. A. Heumier and J. L. Carlsten, “Detecting mode hopping in semiconductor lasers by monitoring intensity noise,” IEEE J. Quantum Electron. 29, 2756–2761 (1993).
    [CrossRef]
  3. L. Bager, “All-electronic suppression of mode hopping noise in diode lasers,” IEEE Photon. Technol. Lett. 2, 899–901 (1990).
    [CrossRef]
  4. D.-L. Cheng, T.-C. Yen, E.-C. Liu, and K.-L. Chuang, “Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback,” IEEE Photon. Technol. Lett. 16, 1435–1437 (2004).
    [CrossRef]
  5. Y. Cheng, J. T. Kringlebotn, W. H. Loh, R. I. Laming, and D. N. Payne, “Stable single-frequency traveling-wave fiber loop laser with integral saturable-absorber-based tracking narrow-band filter,” Opt. Lett. 20, 875–877 (1995).
    [CrossRef]
  6. A. Polynkin, P. Ploynkin, M. Mansuripur, and N. Peyghambarian, “Single-frequency fiber ring laser with 1 W output power at 1.5 μm,” Opt. Express 13, 3179–3184 (2005).
    [CrossRef]
  7. Z. Meng, G. Stewart, and G. Whitenett, “Stable single-mode operation of a narrow-linewidth, linearly polarized, erbium-fiber ring laser using a saturable absorber,” J. Lightwave Technol. 24, 2179–2183 (2006).
    [CrossRef]
  8. X. X. Yang, L. Zhan, Q. S. Shen, and Y. X. Xia, “High-power single-longitudinal-mode fiber laser with a ring Fabry-Perot resonator and a saturable absorber,” IEEE Photon. Technol. Lett. 20, 879–881 (2008).
    [CrossRef]
  9. J. L. Zhang, C.-Y. Yue, G. W. Schinn, W. R. L. Clements, and J. W. Y. Lit, “Stable single-mode compound-ring erbium-doped fiber laser,” J. Lightwave Technol. 14, 104–109 (1996).
    [CrossRef]
  10. X. F. Chen, J. P. Yao, F. Zeng, and Z. C. Deng, “Single-longitudinal-mode fiber ring laser employing an equivalent phase-shifted fiber Bragg grating,” IEEE Photon. Technol. Lett. 17, 1390–1392 (2005).
    [CrossRef]
  11. A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18, 1647–1653 (1982).
    [CrossRef]
  12. M. X. Ma, H. Y. Yang, P. Xu, Z. L. Hu, and Y. M. Hu, “Investigation on characteristics of mode hopping in ultra-narrow linewidth erbium-doped fiber ring laser under pump modulation,” Acta Optica Sinica 32, 0314002 (2012). (in Chinese)
    [CrossRef]
  13. R. Q. Hui and M. O’Sullivan, Fiber Optic Measurement Techniques (Elsevier, 2009).
  14. D. J. DeShazer, J. García-Ojalvo, and R. Roy, “Bursting dynamics of a fiber laser with an injected signal,” Phys. Rev. E 67, 036602 (2003).
    [CrossRef]
  15. R. J. Forster and N. Langford, “Longitudinal mode control of a narrow-linewidth fiber laser by use of the intrinsic birefringence of the fiber laser,” Opt. Lett. 21, 1679–1681 (1996).
    [CrossRef]
  16. I. McMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode, standing-wave, CW dye laser,” Phys. Rev. A 38, 820–832 (1988).
    [CrossRef]
  17. M. S. Kang, M. S. Lee, J. C. Yong, and B. Y. Kim, “Characterization of wavelength-tunable single-frequency fiber laser employing acousto-optic tunable filter,” J. Lightwave Technol. 24, 1812–1823 (2006).
    [CrossRef]
  18. S. K. Kim, G. Stewart, W. Johnstone, and B. Culshaw, “Mode-hop-free single-longitudinal-mode erbium-doped fiber laser frequency scanned with a fiber ring resonator,” Appl. Opt. 38, 5154–5157 (1999).
    [CrossRef]
  19. P. T. Marty, J. Morel, and T. Feurer, “All-fiber frequency-stabilized erbium doped ring laser,” Opt. Express 18, 26821–26827 (2010).
    [CrossRef]

2012 (1)

M. X. Ma, H. Y. Yang, P. Xu, Z. L. Hu, and Y. M. Hu, “Investigation on characteristics of mode hopping in ultra-narrow linewidth erbium-doped fiber ring laser under pump modulation,” Acta Optica Sinica 32, 0314002 (2012). (in Chinese)
[CrossRef]

2010 (1)

2008 (1)

X. X. Yang, L. Zhan, Q. S. Shen, and Y. X. Xia, “High-power single-longitudinal-mode fiber laser with a ring Fabry-Perot resonator and a saturable absorber,” IEEE Photon. Technol. Lett. 20, 879–881 (2008).
[CrossRef]

2006 (2)

2005 (2)

A. Polynkin, P. Ploynkin, M. Mansuripur, and N. Peyghambarian, “Single-frequency fiber ring laser with 1 W output power at 1.5 μm,” Opt. Express 13, 3179–3184 (2005).
[CrossRef]

X. F. Chen, J. P. Yao, F. Zeng, and Z. C. Deng, “Single-longitudinal-mode fiber ring laser employing an equivalent phase-shifted fiber Bragg grating,” IEEE Photon. Technol. Lett. 17, 1390–1392 (2005).
[CrossRef]

2004 (1)

D.-L. Cheng, T.-C. Yen, E.-C. Liu, and K.-L. Chuang, “Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback,” IEEE Photon. Technol. Lett. 16, 1435–1437 (2004).
[CrossRef]

2003 (1)

D. J. DeShazer, J. García-Ojalvo, and R. Roy, “Bursting dynamics of a fiber laser with an injected signal,” Phys. Rev. E 67, 036602 (2003).
[CrossRef]

1999 (1)

1996 (2)

R. J. Forster and N. Langford, “Longitudinal mode control of a narrow-linewidth fiber laser by use of the intrinsic birefringence of the fiber laser,” Opt. Lett. 21, 1679–1681 (1996).
[CrossRef]

J. L. Zhang, C.-Y. Yue, G. W. Schinn, W. R. L. Clements, and J. W. Y. Lit, “Stable single-mode compound-ring erbium-doped fiber laser,” J. Lightwave Technol. 14, 104–109 (1996).
[CrossRef]

1995 (1)

1993 (1)

T. A. Heumier and J. L. Carlsten, “Detecting mode hopping in semiconductor lasers by monitoring intensity noise,” IEEE J. Quantum Electron. 29, 2756–2761 (1993).
[CrossRef]

1990 (1)

L. Bager, “All-electronic suppression of mode hopping noise in diode lasers,” IEEE Photon. Technol. Lett. 2, 899–901 (1990).
[CrossRef]

1989 (1)

M. Ohtsu, K.-Y. Liou, E. C. Burrows, C. A. Burrus, and G. Eisenstein, “A simple interferometric method for monitoring mode hopping in tunable external-cavity semiconductor lasers,” J. Lightwave Technol. 7, 68–76 (1989).
[CrossRef]

1988 (1)

I. McMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode, standing-wave, CW dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef]

1982 (1)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18, 1647–1653 (1982).
[CrossRef]

Bager, L.

L. Bager, “All-electronic suppression of mode hopping noise in diode lasers,” IEEE Photon. Technol. Lett. 2, 899–901 (1990).
[CrossRef]

Beck, M.

I. McMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode, standing-wave, CW dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef]

Burrows, E. C.

M. Ohtsu, K.-Y. Liou, E. C. Burrows, C. A. Burrus, and G. Eisenstein, “A simple interferometric method for monitoring mode hopping in tunable external-cavity semiconductor lasers,” J. Lightwave Technol. 7, 68–76 (1989).
[CrossRef]

Burrus, C. A.

M. Ohtsu, K.-Y. Liou, E. C. Burrows, C. A. Burrus, and G. Eisenstein, “A simple interferometric method for monitoring mode hopping in tunable external-cavity semiconductor lasers,” J. Lightwave Technol. 7, 68–76 (1989).
[CrossRef]

Carlsten, J. L.

T. A. Heumier and J. L. Carlsten, “Detecting mode hopping in semiconductor lasers by monitoring intensity noise,” IEEE J. Quantum Electron. 29, 2756–2761 (1993).
[CrossRef]

Chen, X. F.

X. F. Chen, J. P. Yao, F. Zeng, and Z. C. Deng, “Single-longitudinal-mode fiber ring laser employing an equivalent phase-shifted fiber Bragg grating,” IEEE Photon. Technol. Lett. 17, 1390–1392 (2005).
[CrossRef]

Cheng, D.-L.

D.-L. Cheng, T.-C. Yen, E.-C. Liu, and K.-L. Chuang, “Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback,” IEEE Photon. Technol. Lett. 16, 1435–1437 (2004).
[CrossRef]

Cheng, Y.

Chuang, K.-L.

D.-L. Cheng, T.-C. Yen, E.-C. Liu, and K.-L. Chuang, “Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback,” IEEE Photon. Technol. Lett. 16, 1435–1437 (2004).
[CrossRef]

Clements, W. R. L.

J. L. Zhang, C.-Y. Yue, G. W. Schinn, W. R. L. Clements, and J. W. Y. Lit, “Stable single-mode compound-ring erbium-doped fiber laser,” J. Lightwave Technol. 14, 104–109 (1996).
[CrossRef]

Culshaw, B.

Dandridge, A.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18, 1647–1653 (1982).
[CrossRef]

Deng, Z. C.

X. F. Chen, J. P. Yao, F. Zeng, and Z. C. Deng, “Single-longitudinal-mode fiber ring laser employing an equivalent phase-shifted fiber Bragg grating,” IEEE Photon. Technol. Lett. 17, 1390–1392 (2005).
[CrossRef]

DeShazer, D. J.

D. J. DeShazer, J. García-Ojalvo, and R. Roy, “Bursting dynamics of a fiber laser with an injected signal,” Phys. Rev. E 67, 036602 (2003).
[CrossRef]

Eisenstein, G.

M. Ohtsu, K.-Y. Liou, E. C. Burrows, C. A. Burrus, and G. Eisenstein, “A simple interferometric method for monitoring mode hopping in tunable external-cavity semiconductor lasers,” J. Lightwave Technol. 7, 68–76 (1989).
[CrossRef]

Feurer, T.

Forster, R. J.

García-Ojalvo, J.

D. J. DeShazer, J. García-Ojalvo, and R. Roy, “Bursting dynamics of a fiber laser with an injected signal,” Phys. Rev. E 67, 036602 (2003).
[CrossRef]

Giallorenzi, T. G.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18, 1647–1653 (1982).
[CrossRef]

Heumier, T. A.

T. A. Heumier and J. L. Carlsten, “Detecting mode hopping in semiconductor lasers by monitoring intensity noise,” IEEE J. Quantum Electron. 29, 2756–2761 (1993).
[CrossRef]

Hu, Y. M.

M. X. Ma, H. Y. Yang, P. Xu, Z. L. Hu, and Y. M. Hu, “Investigation on characteristics of mode hopping in ultra-narrow linewidth erbium-doped fiber ring laser under pump modulation,” Acta Optica Sinica 32, 0314002 (2012). (in Chinese)
[CrossRef]

Hu, Z. L.

M. X. Ma, H. Y. Yang, P. Xu, Z. L. Hu, and Y. M. Hu, “Investigation on characteristics of mode hopping in ultra-narrow linewidth erbium-doped fiber ring laser under pump modulation,” Acta Optica Sinica 32, 0314002 (2012). (in Chinese)
[CrossRef]

Hui, R. Q.

R. Q. Hui and M. O’Sullivan, Fiber Optic Measurement Techniques (Elsevier, 2009).

Johnstone, W.

Kang, M. S.

Kim, B. Y.

Kim, S. K.

Kringlebotn, J. T.

Laming, R. I.

Langford, N.

Lee, M. S.

Liou, K.-Y.

M. Ohtsu, K.-Y. Liou, E. C. Burrows, C. A. Burrus, and G. Eisenstein, “A simple interferometric method for monitoring mode hopping in tunable external-cavity semiconductor lasers,” J. Lightwave Technol. 7, 68–76 (1989).
[CrossRef]

Lit, J. W. Y.

J. L. Zhang, C.-Y. Yue, G. W. Schinn, W. R. L. Clements, and J. W. Y. Lit, “Stable single-mode compound-ring erbium-doped fiber laser,” J. Lightwave Technol. 14, 104–109 (1996).
[CrossRef]

Liu, E.-C.

D.-L. Cheng, T.-C. Yen, E.-C. Liu, and K.-L. Chuang, “Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback,” IEEE Photon. Technol. Lett. 16, 1435–1437 (2004).
[CrossRef]

Loh, W. H.

Ma, M. X.

M. X. Ma, H. Y. Yang, P. Xu, Z. L. Hu, and Y. M. Hu, “Investigation on characteristics of mode hopping in ultra-narrow linewidth erbium-doped fiber ring laser under pump modulation,” Acta Optica Sinica 32, 0314002 (2012). (in Chinese)
[CrossRef]

Mansuripur, M.

Marty, P. T.

McMackin, I.

I. McMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode, standing-wave, CW dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef]

Meng, Z.

Morel, J.

O’Sullivan, M.

R. Q. Hui and M. O’Sullivan, Fiber Optic Measurement Techniques (Elsevier, 2009).

Ohtsu, M.

M. Ohtsu, K.-Y. Liou, E. C. Burrows, C. A. Burrus, and G. Eisenstein, “A simple interferometric method for monitoring mode hopping in tunable external-cavity semiconductor lasers,” J. Lightwave Technol. 7, 68–76 (1989).
[CrossRef]

Payne, D. N.

Peyghambarian, N.

Ploynkin, P.

Polynkin, A.

Radzewicz, C.

I. McMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode, standing-wave, CW dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef]

Raymer, M. G.

I. McMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode, standing-wave, CW dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef]

Roy, R.

D. J. DeShazer, J. García-Ojalvo, and R. Roy, “Bursting dynamics of a fiber laser with an injected signal,” Phys. Rev. E 67, 036602 (2003).
[CrossRef]

Schinn, G. W.

J. L. Zhang, C.-Y. Yue, G. W. Schinn, W. R. L. Clements, and J. W. Y. Lit, “Stable single-mode compound-ring erbium-doped fiber laser,” J. Lightwave Technol. 14, 104–109 (1996).
[CrossRef]

Shen, Q. S.

X. X. Yang, L. Zhan, Q. S. Shen, and Y. X. Xia, “High-power single-longitudinal-mode fiber laser with a ring Fabry-Perot resonator and a saturable absorber,” IEEE Photon. Technol. Lett. 20, 879–881 (2008).
[CrossRef]

Stewart, G.

Tveten, A. B.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18, 1647–1653 (1982).
[CrossRef]

Whitenett, G.

Xia, Y. X.

X. X. Yang, L. Zhan, Q. S. Shen, and Y. X. Xia, “High-power single-longitudinal-mode fiber laser with a ring Fabry-Perot resonator and a saturable absorber,” IEEE Photon. Technol. Lett. 20, 879–881 (2008).
[CrossRef]

Xu, P.

M. X. Ma, H. Y. Yang, P. Xu, Z. L. Hu, and Y. M. Hu, “Investigation on characteristics of mode hopping in ultra-narrow linewidth erbium-doped fiber ring laser under pump modulation,” Acta Optica Sinica 32, 0314002 (2012). (in Chinese)
[CrossRef]

Yang, H. Y.

M. X. Ma, H. Y. Yang, P. Xu, Z. L. Hu, and Y. M. Hu, “Investigation on characteristics of mode hopping in ultra-narrow linewidth erbium-doped fiber ring laser under pump modulation,” Acta Optica Sinica 32, 0314002 (2012). (in Chinese)
[CrossRef]

Yang, X. X.

X. X. Yang, L. Zhan, Q. S. Shen, and Y. X. Xia, “High-power single-longitudinal-mode fiber laser with a ring Fabry-Perot resonator and a saturable absorber,” IEEE Photon. Technol. Lett. 20, 879–881 (2008).
[CrossRef]

Yao, J. P.

X. F. Chen, J. P. Yao, F. Zeng, and Z. C. Deng, “Single-longitudinal-mode fiber ring laser employing an equivalent phase-shifted fiber Bragg grating,” IEEE Photon. Technol. Lett. 17, 1390–1392 (2005).
[CrossRef]

Yen, T.-C.

D.-L. Cheng, T.-C. Yen, E.-C. Liu, and K.-L. Chuang, “Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback,” IEEE Photon. Technol. Lett. 16, 1435–1437 (2004).
[CrossRef]

Yong, J. C.

Yue, C.-Y.

J. L. Zhang, C.-Y. Yue, G. W. Schinn, W. R. L. Clements, and J. W. Y. Lit, “Stable single-mode compound-ring erbium-doped fiber laser,” J. Lightwave Technol. 14, 104–109 (1996).
[CrossRef]

Zeng, F.

X. F. Chen, J. P. Yao, F. Zeng, and Z. C. Deng, “Single-longitudinal-mode fiber ring laser employing an equivalent phase-shifted fiber Bragg grating,” IEEE Photon. Technol. Lett. 17, 1390–1392 (2005).
[CrossRef]

Zhan, L.

X. X. Yang, L. Zhan, Q. S. Shen, and Y. X. Xia, “High-power single-longitudinal-mode fiber laser with a ring Fabry-Perot resonator and a saturable absorber,” IEEE Photon. Technol. Lett. 20, 879–881 (2008).
[CrossRef]

Zhang, J. L.

J. L. Zhang, C.-Y. Yue, G. W. Schinn, W. R. L. Clements, and J. W. Y. Lit, “Stable single-mode compound-ring erbium-doped fiber laser,” J. Lightwave Technol. 14, 104–109 (1996).
[CrossRef]

Acta Optica Sinica (1)

M. X. Ma, H. Y. Yang, P. Xu, Z. L. Hu, and Y. M. Hu, “Investigation on characteristics of mode hopping in ultra-narrow linewidth erbium-doped fiber ring laser under pump modulation,” Acta Optica Sinica 32, 0314002 (2012). (in Chinese)
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

T. A. Heumier and J. L. Carlsten, “Detecting mode hopping in semiconductor lasers by monitoring intensity noise,” IEEE J. Quantum Electron. 29, 2756–2761 (1993).
[CrossRef]

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18, 1647–1653 (1982).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

X. F. Chen, J. P. Yao, F. Zeng, and Z. C. Deng, “Single-longitudinal-mode fiber ring laser employing an equivalent phase-shifted fiber Bragg grating,” IEEE Photon. Technol. Lett. 17, 1390–1392 (2005).
[CrossRef]

X. X. Yang, L. Zhan, Q. S. Shen, and Y. X. Xia, “High-power single-longitudinal-mode fiber laser with a ring Fabry-Perot resonator and a saturable absorber,” IEEE Photon. Technol. Lett. 20, 879–881 (2008).
[CrossRef]

L. Bager, “All-electronic suppression of mode hopping noise in diode lasers,” IEEE Photon. Technol. Lett. 2, 899–901 (1990).
[CrossRef]

D.-L. Cheng, T.-C. Yen, E.-C. Liu, and K.-L. Chuang, “Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback,” IEEE Photon. Technol. Lett. 16, 1435–1437 (2004).
[CrossRef]

J. Lightwave Technol. (4)

J. L. Zhang, C.-Y. Yue, G. W. Schinn, W. R. L. Clements, and J. W. Y. Lit, “Stable single-mode compound-ring erbium-doped fiber laser,” J. Lightwave Technol. 14, 104–109 (1996).
[CrossRef]

M. Ohtsu, K.-Y. Liou, E. C. Burrows, C. A. Burrus, and G. Eisenstein, “A simple interferometric method for monitoring mode hopping in tunable external-cavity semiconductor lasers,” J. Lightwave Technol. 7, 68–76 (1989).
[CrossRef]

M. S. Kang, M. S. Lee, J. C. Yong, and B. Y. Kim, “Characterization of wavelength-tunable single-frequency fiber laser employing acousto-optic tunable filter,” J. Lightwave Technol. 24, 1812–1823 (2006).
[CrossRef]

Z. Meng, G. Stewart, and G. Whitenett, “Stable single-mode operation of a narrow-linewidth, linearly polarized, erbium-fiber ring laser using a saturable absorber,” J. Lightwave Technol. 24, 2179–2183 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

I. McMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode, standing-wave, CW dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef]

Phys. Rev. E (1)

D. J. DeShazer, J. García-Ojalvo, and R. Roy, “Bursting dynamics of a fiber laser with an injected signal,” Phys. Rev. E 67, 036602 (2003).
[CrossRef]

Other (1)

R. Q. Hui and M. O’Sullivan, Fiber Optic Measurement Techniques (Elsevier, 2009).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Experimental set-up for detecting mode hopping based on an unbalanced MI. (b) Schematic of the cavity configuration of the EDFRL. PD, photodetector; FRM, Faraday rotation mirror; A/D, analog to digital converter (sampling rate per channel is 100 kHz); PZT, piezoelectric ceramic transducer; ω0=12.5kHz.

Fig. 2.
Fig. 2.

Mode-hop-induced discrete phase change versus frequency jump.

Fig. 3.
Fig. 3.

Output signal when mode hopping occurs. (a) Output of the F–P scanner. (b) Time series of sinφ(t) and cosφ(t).

Fig. 4.
Fig. 4.

Transient coherence collapse during mode hopping. (a) Interference waveform. (b) Fluctuation of the fringe visibility.

Fig. 5.
Fig. 5.

Another occasional mode hop. (a), (b) Time series of sinφ(t) and cosφ(t), respectively. (c) Interference waveform.

Fig. 6.
Fig. 6.

Consecutive mode hops introduced via cavity length modulation. (a) The driving signal imposed on the PZT. (b) Time series of sinφ(t) and cosφ(t). (c) Time series of the phase working point.

Fig. 7.
Fig. 7.

Induced mode hopping accompanied with frequency drift. (a) Partial enlargement for Fig. 6(c). (b) Schematic of mode hopping accompanied with frequency drift.

Equations (6)

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

I=A+Bcos[Ccosω0t+φ(t)],
I=A+B{[J0(C)+2k=1(1)kJ2k(C)cos2kω0t]cosφ(t)[2k=0(1)kJ2k+1(C)cos(2k+1)ω0t]sinφ(t)}.
BJ1(C)sinφ(t),
BJ2(C)cosφ(t),
Δφ(t)=4πnlcΔν,
Δν=ν2ν1=(q2q1)cnL,ν1,2=q1,2cnL,

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