Abstract

The feedback phenomenon of orthogonally polarized dual frequency laser has not been explained theoretically. This paper gives a model based on Lamb’s semi-classical gas-laser theory for the first time. The intensity reflectivity of the feedback mirror, the polarization characteristics of the dual frequency laser and external cavity length are considered besides the parameters studied before. The intensities of o-light and e-light are tuned by feedback mirror. The intensity alternation, leaning of curves and height difference of the two equal–intensity points etc. are discovered in the region of moderate optical feedback level. The experiments are done and the results are in good agreement with the theoretical model.

©2005 Optical Society of America

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References

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  1. Th. H. Peek, P.T. Bolwjin, and C. Th. J. Alkemade, “ Axial mode number of gas lasers from moving-mirror experiments,” Am. J. Phys. 35, 820–831 (1967).
    [Crossref]
  2. Y. Ding, S. Zhang, and Y. Li, “Displacement sensors based on feedback effect of orthogonally polarized lights of frequency-split HeNe lasers,” Opt. Eng. 42, 2225–2228 (2003).
    [Crossref]
  3. J. Kao, M. Kikuchi, I. Yamaguchi, and S. Ozono, “Optical feedback displacement sensor using a laser diode and its performance improvement,” Meas. Sci, Technol. 6, 45–52 (1995).
    [Crossref]
  4. A. Bearden, MP. O’Neill, LC. Osborne, and TL. Wong, “Imaging and vibrational analysis with laser-feedback interferometry,” Opt. Lett. 18, 238–240 (1993).
    [Crossref] [PubMed]
  5. T. L. Wong, S.L. Sabato, and A. Brarden, “PHOEBE, a prototype scanning laser-feedback microscope for imaging biological cells in aqueous media,” J. Microscopy. 177, 162–170 (1995).
    [Crossref]
  6. W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle, “Self-mixing interference inside a single-mode diode-laser for optical sensing applications,” J. Lightwave Technol. 12, 1577–1587(1994).
    [Crossref]
  7. T. Suzuki, S. Hirabayashi, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38, 543–548 (1999).
    [Crossref]
  8. G. Liu, S. Zhang, and J. Zhu, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He-Ne laser,” Opt. Commun. 221, 387–393 (2003).
    [Crossref]
  9. L. Fei and S. Zhang, “Self-mixing interference effects of orthogonally polarized dual frequency laser,” Opt. Express 12, 6100–6105 (2004). URL: http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6100
    [Crossref] [PubMed]
  10. Willis E. Lamb, “Theory of an optical Maser,” Phys. Rev. 134, A1429–A1440 (1964).
    [Crossref]
  11. Y. JiangRing Laser Gyroscopes. (Tsinghua University Press, Beijing,1985), Chap.3.
  12. L. Li, S. Zhang, and S. Li, “The new phenomena of orthogonally polarized lights in laser feedback,” Opt. Commun. 200, 303–307 (2001).
    [Crossref]
  13. W. M. Doyle and M. B. White, “Effects of atomic degeneracy and cavity anisotropy on the behavior of a gas laser,” Phys. Rev. 147, 359–367(1966).
    [Crossref]

2004 (1)

2003 (2)

Y. Ding, S. Zhang, and Y. Li, “Displacement sensors based on feedback effect of orthogonally polarized lights of frequency-split HeNe lasers,” Opt. Eng. 42, 2225–2228 (2003).
[Crossref]

G. Liu, S. Zhang, and J. Zhu, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He-Ne laser,” Opt. Commun. 221, 387–393 (2003).
[Crossref]

2001 (1)

L. Li, S. Zhang, and S. Li, “The new phenomena of orthogonally polarized lights in laser feedback,” Opt. Commun. 200, 303–307 (2001).
[Crossref]

1999 (1)

T. Suzuki, S. Hirabayashi, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38, 543–548 (1999).
[Crossref]

1995 (2)

J. Kao, M. Kikuchi, I. Yamaguchi, and S. Ozono, “Optical feedback displacement sensor using a laser diode and its performance improvement,” Meas. Sci, Technol. 6, 45–52 (1995).
[Crossref]

T. L. Wong, S.L. Sabato, and A. Brarden, “PHOEBE, a prototype scanning laser-feedback microscope for imaging biological cells in aqueous media,” J. Microscopy. 177, 162–170 (1995).
[Crossref]

1994 (1)

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

1993 (1)

1967 (1)

Th. H. Peek, P.T. Bolwjin, and C. Th. J. Alkemade, “ Axial mode number of gas lasers from moving-mirror experiments,” Am. J. Phys. 35, 820–831 (1967).
[Crossref]

1966 (1)

W. M. Doyle and M. B. White, “Effects of atomic degeneracy and cavity anisotropy on the behavior of a gas laser,” Phys. Rev. 147, 359–367(1966).
[Crossref]

1964 (1)

Willis E. Lamb, “Theory of an optical Maser,” Phys. Rev. 134, A1429–A1440 (1964).
[Crossref]

Alkemade, C. Th. J.

Th. H. Peek, P.T. Bolwjin, and C. Th. J. Alkemade, “ Axial mode number of gas lasers from moving-mirror experiments,” Am. J. Phys. 35, 820–831 (1967).
[Crossref]

Bearden, A.

Bolwjin, P.T.

Th. H. Peek, P.T. Bolwjin, and C. Th. J. Alkemade, “ Axial mode number of gas lasers from moving-mirror experiments,” Am. J. Phys. 35, 820–831 (1967).
[Crossref]

Boyle, W. J. O.

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

Brarden, A.

T. L. Wong, S.L. Sabato, and A. Brarden, “PHOEBE, a prototype scanning laser-feedback microscope for imaging biological cells in aqueous media,” J. Microscopy. 177, 162–170 (1995).
[Crossref]

Ding, Y.

Y. Ding, S. Zhang, and Y. Li, “Displacement sensors based on feedback effect of orthogonally polarized lights of frequency-split HeNe lasers,” Opt. Eng. 42, 2225–2228 (2003).
[Crossref]

Doyle, W. M.

W. M. Doyle and M. B. White, “Effects of atomic degeneracy and cavity anisotropy on the behavior of a gas laser,” Phys. Rev. 147, 359–367(1966).
[Crossref]

Fei, L.

Grattan, K. T. V.

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

Hirabayashi, S.

T. Suzuki, S. Hirabayashi, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38, 543–548 (1999).
[Crossref]

Jiang, Y.

Y. JiangRing Laser Gyroscopes. (Tsinghua University Press, Beijing,1985), Chap.3.

Kao, J.

J. Kao, M. Kikuchi, I. Yamaguchi, and S. Ozono, “Optical feedback displacement sensor using a laser diode and its performance improvement,” Meas. Sci, Technol. 6, 45–52 (1995).
[Crossref]

Kikuchi, M.

J. Kao, M. Kikuchi, I. Yamaguchi, and S. Ozono, “Optical feedback displacement sensor using a laser diode and its performance improvement,” Meas. Sci, Technol. 6, 45–52 (1995).
[Crossref]

Lamb, Willis E.

Willis E. Lamb, “Theory of an optical Maser,” Phys. Rev. 134, A1429–A1440 (1964).
[Crossref]

Li, L.

L. Li, S. Zhang, and S. Li, “The new phenomena of orthogonally polarized lights in laser feedback,” Opt. Commun. 200, 303–307 (2001).
[Crossref]

Li, S.

L. Li, S. Zhang, and S. Li, “The new phenomena of orthogonally polarized lights in laser feedback,” Opt. Commun. 200, 303–307 (2001).
[Crossref]

Li, Y.

Y. Ding, S. Zhang, and Y. Li, “Displacement sensors based on feedback effect of orthogonally polarized lights of frequency-split HeNe lasers,” Opt. Eng. 42, 2225–2228 (2003).
[Crossref]

Liu, G.

G. Liu, S. Zhang, and J. Zhu, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He-Ne laser,” Opt. Commun. 221, 387–393 (2003).
[Crossref]

Maruyama, T.

T. Suzuki, S. Hirabayashi, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38, 543–548 (1999).
[Crossref]

O’Neill, MP.

Osborne, LC.

Ozono, S.

J. Kao, M. Kikuchi, I. Yamaguchi, and S. Ozono, “Optical feedback displacement sensor using a laser diode and its performance improvement,” Meas. Sci, Technol. 6, 45–52 (1995).
[Crossref]

Palmer, A. W.

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

Peek, Th. H.

Th. H. Peek, P.T. Bolwjin, and C. Th. J. Alkemade, “ Axial mode number of gas lasers from moving-mirror experiments,” Am. J. Phys. 35, 820–831 (1967).
[Crossref]

Sabato, S.L.

T. L. Wong, S.L. Sabato, and A. Brarden, “PHOEBE, a prototype scanning laser-feedback microscope for imaging biological cells in aqueous media,” J. Microscopy. 177, 162–170 (1995).
[Crossref]

Sasaki, O.

T. Suzuki, S. Hirabayashi, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38, 543–548 (1999).
[Crossref]

Suzuki, T.

T. Suzuki, S. Hirabayashi, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38, 543–548 (1999).
[Crossref]

Wang, W. M.

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

White, M. B.

W. M. Doyle and M. B. White, “Effects of atomic degeneracy and cavity anisotropy on the behavior of a gas laser,” Phys. Rev. 147, 359–367(1966).
[Crossref]

Wong, T. L.

T. L. Wong, S.L. Sabato, and A. Brarden, “PHOEBE, a prototype scanning laser-feedback microscope for imaging biological cells in aqueous media,” J. Microscopy. 177, 162–170 (1995).
[Crossref]

Wong, TL.

Yamaguchi, I.

J. Kao, M. Kikuchi, I. Yamaguchi, and S. Ozono, “Optical feedback displacement sensor using a laser diode and its performance improvement,” Meas. Sci, Technol. 6, 45–52 (1995).
[Crossref]

Zhang, S.

L. Fei and S. Zhang, “Self-mixing interference effects of orthogonally polarized dual frequency laser,” Opt. Express 12, 6100–6105 (2004). URL: http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6100
[Crossref] [PubMed]

Y. Ding, S. Zhang, and Y. Li, “Displacement sensors based on feedback effect of orthogonally polarized lights of frequency-split HeNe lasers,” Opt. Eng. 42, 2225–2228 (2003).
[Crossref]

G. Liu, S. Zhang, and J. Zhu, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He-Ne laser,” Opt. Commun. 221, 387–393 (2003).
[Crossref]

L. Li, S. Zhang, and S. Li, “The new phenomena of orthogonally polarized lights in laser feedback,” Opt. Commun. 200, 303–307 (2001).
[Crossref]

Zhu, J.

G. Liu, S. Zhang, and J. Zhu, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He-Ne laser,” Opt. Commun. 221, 387–393 (2003).
[Crossref]

Am. J. Phys. (1)

Th. H. Peek, P.T. Bolwjin, and C. Th. J. Alkemade, “ Axial mode number of gas lasers from moving-mirror experiments,” Am. J. Phys. 35, 820–831 (1967).
[Crossref]

J. Lightwave Technol. (1)

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

J. Microscopy. (1)

T. L. Wong, S.L. Sabato, and A. Brarden, “PHOEBE, a prototype scanning laser-feedback microscope for imaging biological cells in aqueous media,” J. Microscopy. 177, 162–170 (1995).
[Crossref]

Meas. Sci, Technol. (1)

J. Kao, M. Kikuchi, I. Yamaguchi, and S. Ozono, “Optical feedback displacement sensor using a laser diode and its performance improvement,” Meas. Sci, Technol. 6, 45–52 (1995).
[Crossref]

Opt. Commun. (2)

G. Liu, S. Zhang, and J. Zhu, “Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He-Ne laser,” Opt. Commun. 221, 387–393 (2003).
[Crossref]

L. Li, S. Zhang, and S. Li, “The new phenomena of orthogonally polarized lights in laser feedback,” Opt. Commun. 200, 303–307 (2001).
[Crossref]

Opt. Eng. (2)

T. Suzuki, S. Hirabayashi, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38, 543–548 (1999).
[Crossref]

Y. Ding, S. Zhang, and Y. Li, “Displacement sensors based on feedback effect of orthogonally polarized lights of frequency-split HeNe lasers,” Opt. Eng. 42, 2225–2228 (2003).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. (2)

W. M. Doyle and M. B. White, “Effects of atomic degeneracy and cavity anisotropy on the behavior of a gas laser,” Phys. Rev. 147, 359–367(1966).
[Crossref]

Willis E. Lamb, “Theory of an optical Maser,” Phys. Rev. 134, A1429–A1440 (1964).
[Crossref]

Other (1)

Y. JiangRing Laser Gyroscopes. (Tsinghua University Press, Beijing,1985), Chap.3.

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Figures (4)

Fig. 1.
Fig. 1. Schematic of (a) feedback effect in a He-Ne laser, (b) an equivalent system

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Fig. 2.
Fig. 2. Computer calculations of intensity variations versus external cavity length

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Fig. 3.
Fig. 3. Experimental setup. M1, M2, M3: mirrors; T: discharge tube; W: glass window coated with anti-reflective layer; Q: uniaxial quartz crystal; PZT: piezoelectric transducer; PBS: Wollaston prism; D1, D2: photoelectric detectors; C: signal processing circuit; F-P: Fabry-Perot scanning interferometer; OS: oscilloscope.

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Fig. 4.
Fig. 4. Experimental waveforms of intensity variations versus external cavity length

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Equations (15)

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I o = 1 D ( α 1 β 2 − α 2 θ 12 )
I e = 1 D ( α 2 β 1 − α 1 θ 21 ) ,
D = β 1 β 2 − θ 12 θ 21
α 1 / 2 = α 1 / 2 ′ − ν 1 / 2 2 Q 12 ,
Q 0 = ( 4 πL λ ) ( 1 − R 1 + 1 − R 2 ) ,
R f 1 / 2 = R 2 + ( 1 − R 2 ) { 1 − ( 1 − R 3 ) [ 1 + R 2 R 3 + 2 ( R 2 R 3 ) 1 2 cos δ 1 / 2 ] } ,
Q 1 / 2 = 4 πL λ 1 / 2 1 − R 1 + 1 − R f 1 / 2 ,
I o = M 1 + c 8 DL ( 1 − R 2 ) ( 1 − R 3 ) ( 1 + R 2 R 3 ) N 1 + 2 R 2 R 3 ( θ 12 cos δ 2 − β 2 cos δ 1 ) ( 1 + R 2 R 3 ) 3 + 2 ( 1 + R 2 R 3 ) ( cos δ 2 + cos δ 1 ) + 4 R 2 R 3 cos δ 1 cos δ 2 ,
I e = M 2 + c 8 DL ( 1 − R 2 ) ( 1 − R 3 ) ( 1 + R 2 R 3 ) N 2 + 2 R 2 R 3 ( θ 21 cos δ 1 − β 1 cos δ 2 ) ( 1 + R 2 R 3 ) 3 + 2 ( 1 + R 2 R 3 ) ( cos δ 2 + cos δ 1 ) + 4 R 2 R 3 cos δ 1 cos δ 2
N 1 = θ 12 − β 2
N 2 = θ 21 − β 1 ,
M 1 = I o 0 + α 1 ′ β 2 − α 2 ′ θ 12 D + c 8 L ( 1 − R 1 ) N 1
M 2 = I e 0 + α 2 ′ β 1 − α 1 ′ θ 21 D + c 8 L ( 1 − R 1 ) N 2 ,
δ 1 = δ 2 + 4 π l c Δ ν ,
Δ ν = ν 1 − ν 2 ,

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