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Polarization flipping and hysteresis phenomenon in laser with optical feedback

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Abstract

We realize polarization control in He-Ne laser by optical feedback. Polarization flipping occurs when the length of the anisotropy feedback cavity is modulated. The relationship between polarization flipping and phase retardation of birefringence component placed in feedback cavity is built. The hysteresis effect of polarization flipping is observed. We build a system to measure the size of hysteresis loop based on Laser Feedback Interferometer (LFI). The variation of hysteresis loop with phase retardation is measured. The width of hysteresis loop decreases when phase retardation increases.

©2013 Optical Society of America

1. Introduction

Laser feedback phenomenon first was observed by King and Steward in 1963 [1]. Since then, a great amount of work has been done experimentally [2] and theoretically [3]. Some phenomena have been used in the fields of velocity [46], displacement [79], absolute distance [1012] and vibration measurement [13]. Recently, the polarization flipping induced by optical feedback has attracted considerable interest [14]. Floch and associates [15,16] observed the polarization flipping and hysteresis effect by changing the anisotropy values of laser intracavity. Stephan and associates [17,18] experimentally and theoretically studied the polarization flipping induced by optical feedback from a polarizer external cavity. However, in Floch and Stephan’s experiments, the size of hysteresis loop could not be modulated. Fei and associates [19] observed the polarization flipping and hysteresis phenomenon induced by optical feedback from a birefringence external cavity. Although they could modify the size of hysteresis loop, the error from nonlinearity and hysteresis effect of piezoelectric transducer (PZT) is introduced into the system.

In the prior works listed above, the position of polarization flipping could not be controlled and thus as the effect of polarization flipping could not be used as optical measurements. In this paper, we present a completely new technique for polarization control based on anisotropy optical feedback. In this new technique, a birefringence material placed in feedback cavity forms an anisotropy optical cavity. When the length of feedback cavity is modulated, the polarization flipping with hysteresis happens. The position of polarization flipping determined by the magnitude of phase retardation of birefringence material varies with the phase retardation of birefringence material. The relationship between flipping point and phase retardation could be used to determine the magnitude of phase retardation of birefringence material placed in feedback cavity. The width of hysteresis loop also is measured by Laser feedback interferometer (LFI) and it decreases when the phase retardation of birefringence component in feedback cavity increases.

2. Experimental setup

The experiment setup is shown in Fig. 1 . A half-intracavity, single-mode, linearly polarized He-Ne laser is used as light source. The working wavelength is 632.8 nm. The ratio of gaseous pressure in the laser is He:Ne = 9:1 and Ne20:Ne22 = 1:1. The laser cavity is made up of mirrors M1, M2 with reflectivity of 99.8 and 98.8%, respectively. The cavity length is 150 mm.

 figure: Fig. 1

Fig. 1 Experimental setup of polarization flipping with hysteresis. D1, D2, photo detector; M1, M2, high reflectors; S, birefringence sample; ME, feedback mirror; PZT, piezoelectric transducer; P, polarizer; DA, digital–to–analog signal conversion; AD, analog–to–digital signal conversion; AMP, voltage amplification.

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The external cavity is made up of M2 and feedback mirror ME, with the sample S with birefringence between them. The external cavity length is 100 mm. ME has reflectivity of 10% and is used to reflect laser beams back into the laser. A piezoelectric transducer (PZT) is used to tune, push and pull ME.

P is a polarizer used to separate the beam of different polarization from the laser. When the polarization state of the laser is the same direction as that of the polarizer polarization, the beam can reach and be detected by detector D2. Otherwise, the output voltage of D2 maintains its minimum. Thus, the output voltage flipping of detector D2 shows polarization flipping of the laser. D1 is used to detect the laser intensity.

3. Experimental results and analyses

When the length of feedback cavity is scanned by PZT, the effective gain of o light and e light [20] are modulated and the modulation curve is similar to cosine function. In some external cavity length, the o light effective gain is higher than 0 and at other external cavity length, e light effective gain is higher than 0. However, the o light effective gain and e light effective gain cannot higher than 0 at the same external cavity with our experiment parameters. According to Lamb’s semi-classical theory, the laser mode flips at the condition of effective gain is higher than 0. Therefore, the polarization state flip and laser intensity transfer occur when the length of anisotropy external cavity is tuned by PZT. The experimental results for polarization flipping and intensity transfer are shown in Fig. 2 .

 figure: Fig. 2

Fig. 2 Waveforms of polarization flipping and intensity transfer.

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In Fig. 2, the top curves are for laser intensity outputting from D1. These are different from that of conventional laser feedback. Firstly, there are dips at B and F point while the conventional laser feedback curves are similar to cosine form [1]. Secondly, the polarization flips vertically 90 o at positions of B or F in Fig. 2. The distance between points A to D or E to H is one period of λ/2. The position of polarization flipping point, B or F, varies in according to the phase retardation magnitude of birefringence sample S.

The middle curve in Fig. 2 is the output of D2. At the beginning, the polarization direction of polarizer P is orthogonal to laser polarization state and PZT is not scanned. So the minimum voltage is observed on oscilloscope 2. When PZT is scanning, the voltage on oscilloscope 2 is similar to square wave, as Fig. 2. Each edge means that one polarization flipping happens.

The lowest curve in Fig. 2 is the voltage applied to PZT. Its maximum is 100 V which makes PZT a displacement of 0.5 µm.

The relationship between polarization flipping point and phase retardation magnitude is analyzed as Fig. 3 .

 figure: Fig. 3

Fig. 3 Analysis for phase retardation between polarization flipping point and phase retardation.

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In the feedback cavity, laser passes through the birefringence sample S twice, so, the retardation of o light and e light in Fig. 3 is 2δ, where δ is phase retardation of birefringence sample S. According to Fig. 3, the relationship between flipping point and phase retardation can be expressed as

δ=(lBClAD+lFGlEH)×90o=(VBCVAD+VFGVEH)×90o
where C is the same intensity point of B point. G is that of F. lBC is the feedback cavity variation between C point and B point. lAD, lFG and lEH are the same as lBC. VBC is the PZT voltage between C point and B point. VAD, VFG and VEH are the same as VBC.

According to the relationship between the polarization flipping point and phase retardation, as shown in Eq. (1), the phase retardation of birefringence material can be measured by this system. The results are shown in Table 1 . The birefringence material is quartz wave plates and the measurement temperature is 22°C. The results show that the measurement precise of phase retardation is higher than 0.5°.

Tables Icon

Table 1. Measurement results of phase retardation of wave plates

However, the nonlinearity and hysteresis of PZT, as shown in Fig. 4 , will introduce error into the measurement system in Fig. 1. In Fig. 1, the rising and falling curves of displacement-voltage does not coincide, that is the PZT hysteresis. The relationship between displacement and voltage is nonlinearity in voltage rising or falling edge, that is the PZT nonlinear.

 figure: Fig. 4

Fig. 4 PZT nonlinearity and hysteresis.

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In order to eliminate the error induced by PZT nonlinearity and hysteresis, a set of displacement measurement system is introduced into our experimental system, as shown in Fig. 5 .

 figure: Fig. 5

Fig. 5 Experimental setup of polarization flipping and hysteresis loop with displacement measurement. ML, microchip laser; BS, beam splitter; PD: photodiode; LK, lock-in amplifier; other labels in text.

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The displacement measurement system is a quasi-common-path Nd:YAG laser feedback interferometer (QLFI) based on the principle of frequency shifting and heterodyne phase-measuring methods, as shown in Fig. 5. The laser-diode-pumped 1064 nm Nd:YAG microchip laser output is single longitudinal mode, and its relaxation oscillation frequency ωR is about 200 kHz. Two acousto-optic modulators (AOMs) are used in series to shift the frequency of the feedback light. AOM1 is driven by an rf signal generator (RF1) at 70.0 MHz, and AOM2 by RF2 at (70.0 MHz + Ω), with Ω an adjustable value. When the laser beam, labeled B1 (frequency ω), impinges on AOM1 at the Bragg incidence angle, the −1 order diffracted beam is generated, labeled B2 (frequency ω-70.0 MHz). The distance between the two AOMs is kept short enough to ensure that both B1 and B2 pass the aperture of AOM2. After AOM2, the + 1-order diffracted beam is generated, labeled B3 (frequency ω + Ω). A reference mirror Mr is placed near the target ME. B1 is used as reference light and B3 is used as measurement light. The measurement light is focused on target and then reflected back along the same path as B3 as measurement feedback light (MFL). Reference light is reflected by Mr along an optic path which is parallel to the measurement feedback light as reference feedback light (RFL). MFL and RFL is quasi-common-path. The phase retardations of reference feedback light and measurement feedback light are measured by the synchronous detection simultaneously and their difference offers the phase variation caused only by the target displacement. With this scheme, the phase detection error caused by dead path is largely inhabited.

The length variation of feedback cavity, or the displacement of feedback mirror ME is related to the feedback light phase variation by

ΔL=c2nωΔP
where ΔL is the displacement of feedback mirror ME, ΔP is the feedback light phase variation, c is the light velocity in vacuum, and n is the refractive index of the air.

In our experiment, the laser output intensity and PZT displacement are detected simultaneously when the triangular-wave voltage applied to PZT. The laser output intensity and PZT displacement are listed in Fig. 6 . The points b and f are PZT displacement when the polarization flipping occur at the points B and F in Fig. 5. The displacement difference between b and f is the hysteresis magnitude of polarization flipping, as shown in Table 2 .

 figure: Fig. 6

Fig. 6 Polarization flipping hysteresis in different phase retardation of (a) δ = 16.42°, (b) δ = 27.89°, (c) δ = 44.87°, (d) δ = 69.48°, (e) δ = 78.95°, (f) δ = 83.81°.

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Tables Icon

Table 2. Hysteresis magnitude of polarization flipping

By adjusting the phase retardation of birefringence component in the feedback cavity, we can change the width of hysteresis loop, as shown in Fig. 6 and Table 2. The width decreases when the phase retardation of birefringence component increases.

4. Conclusion

In our work, the polarization flipping with hysteresis induced by birefringence feedback is observed. When the length of feedback cavity is changed, the polarization states flips with hysteresis between two eigenstates. The position of polarization flipping is determined by phase retardation of birefringence component. The relationship between polarization flipping and phase retardation is built. We could modify the size of hysteresis loop of polarization flipping by changing the phase retardation. The width of hysteresis loop decreases when the phase retardation increases.

Acknowledgments

This work is supported by the Key Program of the National Natural Science Foundation of China (NSFC) (No. 61036016) and Scientific and Technological Achievements Transformation and Industrialization Project by the Beijing Municipal Education Commission.

References and links

1. P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 180–182 (1963).

2. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003). [CrossRef]   [PubMed]  

3. W. Xiong, P. Glanznig, P. Paddon, and A. D. May, “Stability of polarized modes in a quasi-isotropic laser: experimental confirmation,” J. Opt. Soc. Am. B 4, 1276–1280 (1987).

4. P. J. Brannon, “Laser feedback: its effect on laser frequency,” Appl. Opt. 15(5), 1119–1120 (1976). [CrossRef]   [PubMed]  

5. E. T. Shimizu, “Directional discrimination in the self-mixing type laser Doppler velocimeter,” Appl. Opt. 26(21), 4541–4544 (1987). [CrossRef]   [PubMed]  

6. S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas. 38(2), 574–577 (1989). [CrossRef]  

7. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995). [CrossRef]  

8. S. Donati, L. Falzoni, and S. Merlo, “A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45(6), 942–947 (1996). [CrossRef]  

9. S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997). [CrossRef]  

10. F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37(28), 6684–6689 (1998). [CrossRef]   [PubMed]  

11. S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 18(4), 582–595 (1982). [CrossRef]  

12. T. Suzuki, T. Muto, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38(3), 543–548 (1999). [CrossRef]  

13. P. A. Roos, M. Stephens, and C. E. Wieman, “Laser Vibrometer based on optical-feedback-induced frequency modulation of a single-mode laser diode,” Appl. Opt. 35(34), 6754–6761 (1996). [CrossRef]   [PubMed]  

14. L. G. Fei and S. L. Zhang, “Self-mixing interference effects of orthogonally polarized dual frequency laser,” Opt. Express 12(25), 6100–6105 (2004). [CrossRef]   [PubMed]  

15. A. Le Floch, G. Ropars, J. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984). [CrossRef]  

16. G. Ropars, A. Le Floch, and R. Le Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A 46(1), 623–640 (1992). [CrossRef]   [PubMed]  

17. G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55(7), 703–706 (1985). [CrossRef]   [PubMed]  

18. W. Xiong, P. Glanznig, P. Paddon, A. D. May, M. Bourouis, S. Laniepce, and G. Stéphan, “Stability of polarized modes in a quasi-isotropic laser: Experimental confirmation,” J. Opt. Soc. Am. B 8(6), 1236–1243 (1991). [CrossRef]  

19. L. G. Fei, S. L. Zhang, Y. Li, and J. Zhu, “Polarization control in a He-Ne laser using birefringence feedback,” Opt. Express 13(8), 3117–3122 (2005). [CrossRef]   [PubMed]  

20. W. X. Chen, S. L. Zhang, and X. W. Long, “Locking phenomenon of polarization flipping in He-Ne laser with a phase anisotropy feedback cavity,” Appl. Opt. 51(7), 888–893 (2012). [CrossRef]   [PubMed]  

References

  • View by:

  1. P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 180–182 (1963).
  2. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
    [Crossref] [PubMed]
  3. W. Xiong, P. Glanznig, P. Paddon, and A. D. May, “Stability of polarized modes in a quasi-isotropic laser: experimental confirmation,” J. Opt. Soc. Am. B 4, 1276–1280 (1987).
  4. P. J. Brannon, “Laser feedback: its effect on laser frequency,” Appl. Opt. 15(5), 1119–1120 (1976).
    [Crossref] [PubMed]
  5. E. T. Shimizu, “Directional discrimination in the self-mixing type laser Doppler velocimeter,” Appl. Opt. 26(21), 4541–4544 (1987).
    [Crossref] [PubMed]
  6. S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas. 38(2), 574–577 (1989).
    [Crossref]
  7. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
    [Crossref]
  8. S. Donati, L. Falzoni, and S. Merlo, “A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45(6), 942–947 (1996).
    [Crossref]
  9. S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
    [Crossref]
  10. F. Gouaux, N. Servagent, and T. Bosch, “Absolute distance measurement with an optical feedback interferometer,” Appl. Opt. 37(28), 6684–6689 (1998).
    [Crossref] [PubMed]
  11. S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 18(4), 582–595 (1982).
    [Crossref]
  12. T. Suzuki, T. Muto, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38(3), 543–548 (1999).
    [Crossref]
  13. P. A. Roos, M. Stephens, and C. E. Wieman, “Laser Vibrometer based on optical-feedback-induced frequency modulation of a single-mode laser diode,” Appl. Opt. 35(34), 6754–6761 (1996).
    [Crossref] [PubMed]
  14. L. G. Fei and S. L. Zhang, “Self-mixing interference effects of orthogonally polarized dual frequency laser,” Opt. Express 12(25), 6100–6105 (2004).
    [Crossref] [PubMed]
  15. A. Le Floch, G. Ropars, J. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
    [Crossref]
  16. G. Ropars, A. Le Floch, and R. Le Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A 46(1), 623–640 (1992).
    [Crossref] [PubMed]
  17. G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55(7), 703–706 (1985).
    [Crossref] [PubMed]
  18. W. Xiong, P. Glanznig, P. Paddon, A. D. May, M. Bourouis, S. Laniepce, and G. Stéphan, “Stability of polarized modes in a quasi-isotropic laser: Experimental confirmation,” J. Opt. Soc. Am. B 8(6), 1236–1243 (1991).
    [Crossref]
  19. L. G. Fei, S. L. Zhang, Y. Li, and J. Zhu, “Polarization control in a He-Ne laser using birefringence feedback,” Opt. Express 13(8), 3117–3122 (2005).
    [Crossref] [PubMed]
  20. W. X. Chen, S. L. Zhang, and X. W. Long, “Locking phenomenon of polarization flipping in He-Ne laser with a phase anisotropy feedback cavity,” Appl. Opt. 51(7), 888–893 (2012).
    [Crossref] [PubMed]

2012 (1)

2005 (1)

2004 (1)

2003 (1)

1999 (1)

T. Suzuki, T. Muto, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38(3), 543–548 (1999).
[Crossref]

1998 (1)

1997 (1)

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[Crossref]

1996 (2)

S. Donati, L. Falzoni, and S. Merlo, “A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45(6), 942–947 (1996).
[Crossref]

P. A. Roos, M. Stephens, and C. E. Wieman, “Laser Vibrometer based on optical-feedback-induced frequency modulation of a single-mode laser diode,” Appl. Opt. 35(34), 6754–6761 (1996).
[Crossref] [PubMed]

1995 (1)

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

1992 (1)

G. Ropars, A. Le Floch, and R. Le Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A 46(1), 623–640 (1992).
[Crossref] [PubMed]

1991 (1)

1989 (1)

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas. 38(2), 574–577 (1989).
[Crossref]

1987 (2)

1985 (1)

G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55(7), 703–706 (1985).
[Crossref] [PubMed]

1984 (1)

A. Le Floch, G. Ropars, J. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

1982 (1)

S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 18(4), 582–595 (1982).
[Crossref]

1976 (1)

1963 (1)

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 180–182 (1963).

Blondel, M.

Bosch, T.

Bourouis, M.

Brannon, P. J.

Chen, W. X.

Donati, S.

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[Crossref]

S. Donati, L. Falzoni, and S. Merlo, “A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45(6), 942–947 (1996).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Falzoni, L.

S. Donati, L. Falzoni, and S. Merlo, “A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45(6), 942–947 (1996).
[Crossref]

Fei, L. G.

Giuliani, G.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Glanznig, P.

Gouaux, F.

Hugon, D.

G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical feedback,” Phys. Rev. Lett. 55(7), 703–706 (1985).
[Crossref] [PubMed]

Ikeda, H.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas. 38(2), 574–577 (1989).
[Crossref]

Ito, M.

S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 18(4), 582–595 (1982).
[Crossref]

Kimura, T.

S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 18(4), 582–595 (1982).
[Crossref]

King, P. G. R.

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 180–182 (1963).

Kobayashi, S.

S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, “Direct frequency modulation in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 18(4), 582–595 (1982).
[Crossref]

Laniepce, S.

Le Floch, A.

G. Ropars, A. Le Floch, and R. Le Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A 46(1), 623–640 (1992).
[Crossref] [PubMed]

A. Le Floch, G. Ropars, J. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

Le Naour, R.

G. Ropars, A. Le Floch, and R. Le Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A 46(1), 623–640 (1992).
[Crossref] [PubMed]

A. Le Floch, G. Ropars, J. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

Lenormand, J.

A. Le Floch, G. Ropars, J. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

Li, Y.

Long, X. W.

Maruyama, T.

T. Suzuki, T. Muto, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38(3), 543–548 (1999).
[Crossref]

May, A. D.

Mégret, P.

Merlo, S.

S. Merlo and S. Donati, “Reconstruction of displacement waveforms with a single-channel laser-diode feedback interferometer,” IEEE J. Quantum Electron. 33(4), 527–531 (1997).
[Crossref]

S. Donati, L. Falzoni, and S. Merlo, “A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements,” IEEE Trans. Instrum. Meas. 45(6), 942–947 (1996).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron. 31(1), 113–119 (1995).
[Crossref]

Muto, T.

T. Suzuki, T. Muto, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38(3), 543–548 (1999).
[Crossref]

Naito, H.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas. 38(2), 574–577 (1989).
[Crossref]

Paddon, P.

Panajotov, K.

Roos, P. A.

Ropars, G.

G. Ropars, A. Le Floch, and R. Le Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A 46(1), 623–640 (1992).
[Crossref] [PubMed]

A. Le Floch, G. Ropars, J. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

Sasaki, O.

T. Suzuki, T. Muto, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38(3), 543–548 (1999).
[Crossref]

Sciamanna, M.

Servagent, N.

Shimizu, E. T.

Shinohara, S.

S. Shinohara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi, “Compact and versatile self-mixing type semiconductor laser Doppler velocimeters with direction discrimination circuit,” IEEE Trans. Instrum. Meas. 38(2), 574–577 (1989).
[Crossref]

Stephan, G.

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[Crossref]

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[Crossref]

J. Opt. Soc. Am. B (2)

New Sci. (1)

P. G. R. King and G. J. Steward, “Metrology with an optical maser,” New Sci. 17, 180–182 (1963).

Opt. Eng. (1)

T. Suzuki, T. Muto, O. Sasaki, and T. Maruyama, “Self-mixing type of phase-locked laser diode interferometer,” Opt. Eng. 38(3), 543–548 (1999).
[Crossref]

Opt. Express (2)

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Experimental setup of polarization flipping with hysteresis. D1, D2, photo detector; M1, M2, high reflectors; S, birefringence sample; ME, feedback mirror; PZT, piezoelectric transducer; P, polarizer; DA, digital–to–analog signal conversion; AD, analog–to–digital signal conversion; AMP, voltage amplification.
Fig. 2
Fig. 2 Waveforms of polarization flipping and intensity transfer.
Fig. 3
Fig. 3 Analysis for phase retardation between polarization flipping point and phase retardation.
Fig. 4
Fig. 4 PZT nonlinearity and hysteresis.
Fig. 5
Fig. 5 Experimental setup of polarization flipping and hysteresis loop with displacement measurement. ML, microchip laser; BS, beam splitter; PD: photodiode; LK, lock-in amplifier; other labels in text.
Fig. 6
Fig. 6 Polarization flipping hysteresis in different phase retardation of (a) δ = 16.42°, (b) δ = 27.89°, (c) δ = 44.87°, (d) δ = 69.48°, (e) δ = 78.95°, (f) δ = 83.81°.

Tables (2)

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Table 1 Measurement results of phase retardation of wave plates

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Table 2 Hysteresis magnitude of polarization flipping

Equations (2)

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δ=( l BC l AD + l FG l EH )× 90 o =( V BC V AD + V FG V EH )× 90 o
ΔL= c 2nω ΔP

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