Abstract

The self-mixing interference in birefringent dual frequency laser is systematically studied for the first time. The output intensities of two orthogonal modes are both modulated by external cavity length, and their phase relationship is experimentally and theoretically demonstrated. When frequency difference is greater than line width of homogeneous broadening gain curve, the phase relationship is determined by phase difference of two modes. If the frequency difference is smaller than the line width, modes competion will play an important role. Our results can advance the research of self-mixing interferometer of orthogonally polarized dual frequency laser.

© 2004 Optical Society of America

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References

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  1. T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. 55, 1711–1714 (1985).
    [Crossref] [PubMed]
  2. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543–1545 (2003).
    [Crossref] [PubMed]
  3. H. Osmundsen and N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. QE. 19, 465–469 (1983).
    [Crossref]
  4. N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Intrum. Meas. 46, 847–850 (1997).
    [Crossref]
  5. P. A. Roos, M. Stephens, and C. Wiemen, “Laser Vibrometer based on optical feedback induced frequency modulation of a single mode laser diode,” Appl. Opt. 35, 6754–6761 (1996).
    [Crossref] [PubMed]
  6. S. S. Hara, A. Yoshida, and M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1471–179 (1986).
  7. W. M. Wang, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference inside a single mode diode laser for optical sensing applications,” IEEE J. Lightwave Tech. 12, 1577–1587 (1994).
    [Crossref]
  8. W. M. Wang, W. J. O. Boyle, and K. T. V. Grattan, “Self-mixing interference in a diode laser: Experimental observations and Theoretical Analysis,” Appl. Opt. 32, 1551–1558 (1993).
    [Crossref] [PubMed]
  9. P. J. D. Groot, G. M. Gallatin, and S. H. Macomber, “Ranging and velocimetry signal generation in a backscatter-modulated laser diode,” Appl. Opt. 27, 4475–4479 (1988).
    [Crossref] [PubMed]
  10. S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. 33, 335–339 (2001).
    [Crossref]
  11. S. Yang and S. Zhang, “The frequency split phenomenon in a HeNe laser with a rotation quartz crystal plate in its cavity,” Opt. Commun. 68, 55–57 (1988).
    [Crossref]
  12. S. Zhang, K. Li, and G. Jin, “Birefringent tuning double frequency He-Ne laser,” Appl. Opt. 29, 1265–1267 (1990).
    [Crossref] [PubMed]
  13. S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. 90, 279–282 (1992).
    [Crossref]
  14. Y. Xiao, S. Zhang, and Y. Li, “Tuning characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency laser,” Chin. Phys. Lett. 20, 230–233 (2003).
    [Crossref]
  15. G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. 20, 1163–1169 (1984).
    [Crossref]
  16. R.W. Tkach and A.R. Chraplyvy, “Regimes of feedback effects in 1.5-µm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
    [Crossref]
  17. A. Olsson and C.L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. QE. 17, 1320–1323 (1981).
    [Crossref]
  18. P.J. Brannon, “Laser feedback: its effect on laser frequency,” Appl. Opt. 15, 1119–1120 (1976).
    [Crossref] [PubMed]

2003 (2)

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543–1545 (2003).
[Crossref] [PubMed]

Y. Xiao, S. Zhang, and Y. Li, “Tuning characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency laser,” Chin. Phys. Lett. 20, 230–233 (2003).
[Crossref]

2001 (1)

S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. 33, 335–339 (2001).
[Crossref]

1997 (1)

N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Intrum. Meas. 46, 847–850 (1997).
[Crossref]

1996 (1)

1994 (1)

W. M. Wang, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference inside a single mode diode laser for optical sensing applications,” IEEE J. Lightwave Tech. 12, 1577–1587 (1994).
[Crossref]

1993 (1)

1992 (1)

S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. 90, 279–282 (1992).
[Crossref]

1990 (1)

1988 (2)

P. J. D. Groot, G. M. Gallatin, and S. H. Macomber, “Ranging and velocimetry signal generation in a backscatter-modulated laser diode,” Appl. Opt. 27, 4475–4479 (1988).
[Crossref] [PubMed]

S. Yang and S. Zhang, “The frequency split phenomenon in a HeNe laser with a rotation quartz crystal plate in its cavity,” Opt. Commun. 68, 55–57 (1988).
[Crossref]

1986 (2)

S. S. Hara, A. Yoshida, and M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1471–179 (1986).

R.W. Tkach and A.R. Chraplyvy, “Regimes of feedback effects in 1.5-µm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[Crossref]

1985 (1)

T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. 55, 1711–1714 (1985).
[Crossref] [PubMed]

1984 (1)

G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. 20, 1163–1169 (1984).
[Crossref]

1983 (1)

H. Osmundsen and N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. QE. 19, 465–469 (1983).
[Crossref]

1981 (1)

A. Olsson and C.L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. QE. 17, 1320–1323 (1981).
[Crossref]

1976 (1)

Acket, G. A.

G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. 20, 1163–1169 (1984).
[Crossref]

Blondel, M.

Boef, A. D.

G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. 20, 1163–1169 (1984).
[Crossref]

Bosch, T.

N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Intrum. Meas. 46, 847–850 (1997).
[Crossref]

Boyle, W. J. O.

Brannon, P.J.

Chraplyvy, A.R.

R.W. Tkach and A.R. Chraplyvy, “Regimes of feedback effects in 1.5-µm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[Crossref]

Gade, N.

H. Osmundsen and N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. QE. 19, 465–469 (1983).
[Crossref]

Gallatin, G. M.

Gao, S.

S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. 33, 335–339 (2001).
[Crossref]

Grattan, K. T. V.

W. M. Wang, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference inside a single mode diode laser for optical sensing applications,” IEEE J. Lightwave Tech. 12, 1577–1587 (1994).
[Crossref]

W. M. Wang, W. J. O. Boyle, and K. T. V. Grattan, “Self-mixing interference in a diode laser: Experimental observations and Theoretical Analysis,” Appl. Opt. 32, 1551–1558 (1993).
[Crossref] [PubMed]

Groot, P. J. D.

Guo, J.

S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. 33, 335–339 (2001).
[Crossref]

Hara, S. S.

S. S. Hara, A. Yoshida, and M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1471–179 (1986).

Jin, G.

S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. 90, 279–282 (1992).
[Crossref]

S. Zhang, K. Li, and G. Jin, “Birefringent tuning double frequency He-Ne laser,” Appl. Opt. 29, 1265–1267 (1990).
[Crossref] [PubMed]

Lenstra, D.

G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. 20, 1163–1169 (1984).
[Crossref]

Lescure, M.

N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Intrum. Meas. 46, 847–850 (1997).
[Crossref]

Li, K.

S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. 90, 279–282 (1992).
[Crossref]

S. Zhang, K. Li, and G. Jin, “Birefringent tuning double frequency He-Ne laser,” Appl. Opt. 29, 1265–1267 (1990).
[Crossref] [PubMed]

Li, Y.

Y. Xiao, S. Zhang, and Y. Li, “Tuning characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency laser,” Chin. Phys. Lett. 20, 230–233 (2003).
[Crossref]

Lin, D.

S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. 33, 335–339 (2001).
[Crossref]

Macomber, S. H.

Megret, P.

Mukai, T.

T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. 55, 1711–1714 (1985).
[Crossref] [PubMed]

Olsson, A.

A. Olsson and C.L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. QE. 17, 1320–1323 (1981).
[Crossref]

Osmundsen, H.

H. Osmundsen and N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. QE. 19, 465–469 (1983).
[Crossref]

Otsuka, K.

T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. 55, 1711–1714 (1985).
[Crossref] [PubMed]

Palmer, A. W.

W. M. Wang, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference inside a single mode diode laser for optical sensing applications,” IEEE J. Lightwave Tech. 12, 1577–1587 (1994).
[Crossref]

Panajotov, K.

Roos, P. A.

Sciamanna, M.

Servagent, N.

N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Intrum. Meas. 46, 847–850 (1997).
[Crossref]

Stephens, M.

Sumi, M.

S. S. Hara, A. Yoshida, and M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1471–179 (1986).

Tang, C.L.

A. Olsson and C.L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. QE. 17, 1320–1323 (1981).
[Crossref]

Thienpont, H.

Tkach, R.W.

R.W. Tkach and A.R. Chraplyvy, “Regimes of feedback effects in 1.5-µm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[Crossref]

Verbeek, B. H.

G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. 20, 1163–1169 (1984).
[Crossref]

Veretennicoff, I.

Wang, W. M.

W. M. Wang, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference inside a single mode diode laser for optical sensing applications,” IEEE J. Lightwave Tech. 12, 1577–1587 (1994).
[Crossref]

W. M. Wang, W. J. O. Boyle, and K. T. V. Grattan, “Self-mixing interference in a diode laser: Experimental observations and Theoretical Analysis,” Appl. Opt. 32, 1551–1558 (1993).
[Crossref] [PubMed]

Wiemen, C.

Wu, M.

S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. 90, 279–282 (1992).
[Crossref]

Xiao, Y.

Y. Xiao, S. Zhang, and Y. Li, “Tuning characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency laser,” Chin. Phys. Lett. 20, 230–233 (2003).
[Crossref]

Yang, S.

S. Yang and S. Zhang, “The frequency split phenomenon in a HeNe laser with a rotation quartz crystal plate in its cavity,” Opt. Commun. 68, 55–57 (1988).
[Crossref]

Yin, C.

S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. 33, 335–339 (2001).
[Crossref]

Yoshida, A.

S. S. Hara, A. Yoshida, and M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. 25, 1471–179 (1986).

Zhang, S.

Y. Xiao, S. Zhang, and Y. Li, “Tuning characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency laser,” Chin. Phys. Lett. 20, 230–233 (2003).
[Crossref]

S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. 90, 279–282 (1992).
[Crossref]

S. Zhang, K. Li, and G. Jin, “Birefringent tuning double frequency He-Ne laser,” Appl. Opt. 29, 1265–1267 (1990).
[Crossref] [PubMed]

S. Yang and S. Zhang, “The frequency split phenomenon in a HeNe laser with a rotation quartz crystal plate in its cavity,” Opt. Commun. 68, 55–57 (1988).
[Crossref]

Appl. Opt. (6)

Chin. Phys. Lett. (1)

Y. Xiao, S. Zhang, and Y. Li, “Tuning characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency laser,” Chin. Phys. Lett. 20, 230–233 (2003).
[Crossref]

IEEE J. Lightwave Tech. (1)

W. M. Wang, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference inside a single mode diode laser for optical sensing applications,” IEEE J. Lightwave Tech. 12, 1577–1587 (1994).
[Crossref]

IEEE J. QE. (3)

H. Osmundsen and N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. QE. 19, 465–469 (1983).
[Crossref]

G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. 20, 1163–1169 (1984).
[Crossref]

A. Olsson and C.L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. QE. 17, 1320–1323 (1981).
[Crossref]

IEEE Trans. Intrum. Meas. (1)

N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Intrum. Meas. 46, 847–850 (1997).
[Crossref]

J. Lightwave Technol. (1)

R.W. Tkach and A.R. Chraplyvy, “Regimes of feedback effects in 1.5-µm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[Crossref]

Opt. Commun. (2)

S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. 90, 279–282 (1992).
[Crossref]

S. Yang and S. Zhang, “The frequency split phenomenon in a HeNe laser with a rotation quartz crystal plate in its cavity,” Opt. Commun. 68, 55–57 (1988).
[Crossref]

Opt. Laser Tech. (1)

S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. 33, 335–339 (2001).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. 55, 1711–1714 (1985).
[Crossref] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup. M1, M2, ME: mirrors; QC: uniaxial quartz crystal; W: glass window anti-reflective coated; PZT: piezoelectric transducer; PBS: Wollaston prism; D1, D2: photodetectors; OS: oscilloscope; SP: spectrometer; AD: avalanche photodiode; P: polarizer; BS: beam splitter; SI: scanning interferometer.

Fig. 2.
Fig. 2.

Oscilloscope waveforms of the intensity modulation curves of two orthogonally polarized lights with different frequency differences: (a)Δν=70MHz, (b)Δν=150MHz, (c) Δν=275MHz, (d)Δν=550MHz, (e)Δν=730MHz, (f)Δν=1100MHz. l=67.5mm

Fig. 3.
Fig. 3.

Oscilloscope waveforms of the intensity modulation curves of two orthogonal polarized lights with different frequency differences: (a) Δν=70MHz, (b) Δν=150MHz, (c) Δν=275MHz, (d)Δν=550MHz, (e)Δν=730MHz, (f)Δν=1100MHz. l=135mm

Fig. 4.
Fig. 4.

Oscilloscope waveforms of the intensity modulation curves of two orthogonal polarized lights with different frequency differences: (a) Δν=70MHz, (b) Δν=150MHz, (c) Δν=275MHz, (d)Δν=550MHz, (e)Δν=730MHz, (f)Δν=1100MHz. l=270mm

Equations (7)

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

r 1 r eff o exp [ ( g o α o ) L ] exp ( i ω o τ c ) = 1 ,
r 1 r eff e exp [ ( g e α e ) L ] exp ( i ω e τ c ) = 1
I o = I o 0 + ε o η o cos ( ω o τ )
I e = I e 0 + ε e η e cos ( ω e τ ) ,
I o = I o 0 + ε o η o cos ( 4 π c ν o l ) ,
I e = I e 0 + ε e η e cos ( 4 π c ν e l )
δ = 4 π Δ ν l c = 2 π l L Δ ν Λ ,

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