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: <A href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6100">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-25-6100</a>
    [CrossRef] [PubMed]
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    [CrossRef]
  11. Y. Jiang, Ring Laser Gyroscopes. (Tsinghua University Press, Beijing, 1985), Chap.3.
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    [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]

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)

Willis E. Lamb, "Theory of an optical Maser,�?? Phys. Rev. 134, A1429-A1440 (1964).
[CrossRef]

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]

Other (1)

Y. Jiang, Ring 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

Fig. 2.
Fig. 2.

Computer calculations of intensity variations versus external cavity length

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.

Fig. 4.
Fig. 4.

Experimental waveforms of intensity variations versus external cavity length

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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