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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 23683–23688
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In-line rotation sensor based on VCSEL behavior under polarization-rotating optical feedback

Shogo Ura, Shinichiro Shoda, Kenzo Nishio, and Yasuhiro Awatsuji  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 23683-23688 (2011)
http://dx.doi.org/10.1364/OE.19.023683


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Abstract

Lasing behavior of a single-transverse-mode vertical-cavity surface-emitting laser (VCSEL) was observed while the polarization direction of an optical feedback was rotated. Optical powers of two polarization modes of a VCSEL showed sinusoidal dependences on the polarization-rotation angle. The power variation was seen when an optical feedback ratio was larger than –20 dB, though the variation depth dropped suddenly as the feedback ratio became smaller than –25 dB. An in-line type rotation sensor utilizing this behavior is proposed. The sensor system was constructed and the detection principle was demonstrated.

© 2011 OSA

1. Introduction

Vertical-cavity surface-emitting lasers (VCSELs) provide various advantages such as their compactness, low-power consumption, circular output beam, capability of monolithic integration of a two-dimensional array, low-cost production resulting from wafer-level testing, and easy handling without end-face cleaving, in comparison with edge-emitting diode lasers. The lasing behavior of a VCSEL, however, is sensitive to an optical feedback, indicating that sufficient suppression or control of the feedback is required for practical applications with stable operation. On the other hand, a static and/or dynamic change of VCSEL oscillation due to an optical feedback can be utilized for optical switching, sensing, and manipulation. In fact, there are a variety of reports on applications to optical pickup heads [1

1. J. A. Hudgings, S. F. Lim, G. S. Li, W. Yuen, K. Y. Lau, and C. J. Chang-Hasnain, “Compact, integrated optical disk readout head using a novel bistable vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 11(2), 245–247 (1999). [CrossRef]

,2

2. S.-Y. Ye, S. Mitsugi, Y.-J. Kim, and K. Goto, “Numerical simulation of readout using optical feedback in the integrated vertical cavity surface emitting laser microprobe head,” Jpn. J. Appl. Phys. 41(Part 1, No. 3B), 1636–1637 (2002). [CrossRef]

], optical probing [3

3. D. Heinis, C. Gorecki, C. Bringer, V. Bardinal, T. Camps, J.-B. Doucet, P. Dubreuil, and C. Fontaine, “Miniaturized scanning near-field microscope sensor based on optical feedback inside a single-mode oxide-confined vertical-cavity surface-emitting laser,” Jpn. J. Appl. Phys. 42(Part 2, No. 12A), L1469–L1471 (2003). [CrossRef]

,4

4. J. Hashizume, S. Shinada, F. Koyama, and K. Iga, “Reflection induced voltage change of surface emitting laser for optical probing,” Opt. Rev. 9(5), 186–188 (2002). [CrossRef]

], displacement sensing [5

5. D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009). [CrossRef]

], a laser Doppler velocimeter [6

6. J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1006–1012 (2004). [CrossRef]

], a liquid crystal modulator [7

7. C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Enhancement of a liquid-crystal modulator using an external-cavity VCSEL,” IEEE Photon. Technol. Lett. 11(8), 940–942 (1999). [CrossRef]

], and coherent population trapping [8

8. N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett. 92(22), 221113 (2008). [CrossRef]

].

This time we investigated and found that the optical power of a polarization mode of a VCSEL varied sinusoidally when an optical-feedback polarization was rotated. This behavior may be predicted from previously reported papers [9

9. S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993). [CrossRef]

15

15. S. Xiang, W. Pan, L. Yan, B. Luo, N. Jiang, and L. Yang, “Polarization properties of vertical-cavity surface-emitting lasers subject to feedback with variably rotated polarization angle,” Appl. Opt. 48(27), 5176–5183 (2009). [CrossRef] [PubMed]

], but there have been few reports on the direct measurement of the sinusoidal dependence. The power variation was observed even when the optical feedback ratio was as low as –20 dB.

As an application of this behavior, we propose here a micro-optic in-line rotation sensor. There are several types of rotation sensors depending on applications. Optical sensing can provide noncontact measurement as magnetic sensing, resulting in long-life sensing. Another great advantage of an optical sensor in comparison with electric or magnetic ones is an easy application to large electro-magnetic-noise circumstance. In fact, an optical rotary encoder is widely used, where a disk with multiple transparent or reflection slits is attached to a rotation spindle [16

16. K. van der Pool, “High resolution optical encoders” (1995). http://www.opticalencoder.com/copi-high-resolution-optical-encoders-tutorial-article.html.

,17

17. Products guide, “Delta rotary optical encoder” (2011). http://www.delta.com.tw/product/em/motion/motion_encoder/download/catalogue/ROE_catalouge_en.pdf.

]. A beam from a light source or an optical fiber is injected, and a transmitted or reflected beam from the disk is detected by a photodiode or collected by an optical fiber. Its angular resolution is determined by the number of the slits from several tens to thousands per revolution. Miniaturization of the head size is mainly limited by the disk diameter to a few centimeters. Another typical example is a fiber-optic gyroscope utilizing the Sagnac effect [18

18. J. L. Davis and S. Ezekiel, “Closed-loop, low-noise fiber-optic rotation sensor,” Opt. Lett. 6(10), 505–507 (1981). [CrossRef] [PubMed]

,19

19. H. J. Arditty and H. C. Leèfovre, “Sagnac effect in fiber gyroscopes,” Opt. Lett. 6(8), 401–403 (1981). [CrossRef] [PubMed]

]. It serves as a high-resolution angular sensor but is not good at high-speed rotation sensing. The sensor head includes a fiber coil where the diameter is typically several centimeters. In this paper, an in-line rotation sensor based on the VCSEL behavior under polarization rotating optical feedback is proposed. The proposed configuration can provide significant size reduction of a sensing head down to the optical fiber diameter.

2. VCSEL behavior under polarization-rotating optical feedback

At first, VCSEL behavior was characterized under polarization-rotating optical feedback. A single-transverse-mode VCSEL (Model: AS-0001, wavelength: 850 nm) provided by Fuji Xerox Co., Ltd. was used in this study. Two polarization modes were degenerated to the single transverse mode. The polarization directions were orthogonal with each other. Dependences of the oscillation powers of the two modes upon an operating current were measured in the absence of an optical feedback and are summarized in Fig. 1
Fig. 1 Measured dependences of the oscillation powers of x-polarization (circles) and y-polarization (triangles) modes of a VCSEL upon an operating current without an optical feedback.
. An oscillation mode of higher power indicated by circles was named as the x-polarization mode, and the other mode indicated by triangles was identified as the y-polarization mode. No polarization switching occurred when an optical feedback was absent.

Figure 2
Fig. 2 Experimental setup for measuring oscillation powers of the x- and y-polarization modes under optical feedback with polarization rotation.
illustrates an experimental setup for measuring output power variations under polarization-rotating optical feedback. A VCSEL was driven by an operating current of 1.0 mA. The output power was 0.59 mW. An output wave diverging from the VCSEL was focused by an objective lens (OBL) onto a mirror coated on a quarter-wave plate (QWP) through a polarization-independent beam splitter (PIBS). The reflected wave from the mirror was returned and focused onto the VCSEL through the QWP and PIBS again. The polarization of the optical feedback to the VCSEL was rotated by the rotation of the QWP. The output wave from the VCSEL was reflected by the PIBS to be detected by a photodiode through a polarizer so that the optical powers of the x- and y-polarization modes were measured.

Obtained optical power dependences of the polarization modes upon a feedback polarization angle θ are shown in Fig. 3
Fig. 3 Measured optical powers of the x-polarization (circles) and y-polarization (triangles) modes of the VCSEL against polarization-rotation angle of the optical feedback. Dashed curves show theoretical prediction.
. A feedback ratio, which is a ratio of the returned power against the VCSEL output power, was –8.9 dB. Circles and triangles indicate x- and y-polarization modes, respectively. A polarization state of the VCSEL at θ = 0° was the same as the one without optical feedback, namely the x-polarization mode. The power of the x-polarization mode decreased as θ increased to 90°, since an optical feedback component for x-polarization decreased. In the meantime, the power of the y-polarization mode increased. The powers of the two modes were nearly the same at θ = 90°, where the feedback components for both polarizations were also the same. As θ increased from 90° to 180°, the optical feedback components and the polarization of VCSEL returned to the initial state.

If an oscillation-power ratio between the x- and y-polarization modes is assumed to be proportional to a power ratio between x and y components of the feedback light, the oscillation powers of Px for x polarization and Py for y polarization depend on θ sinusoidally and can be expressed by
Px=P02(1+cos2θ),
(1)
Py=P02sin2θ,
(2)
where P0 indicates Px at θ = 0. These dependences are shown by dashed curves in Fig. 3.

The optical power variations of the x- and y-polarization modes in Fig. 3 were 109 μW and 150 μW, respectively. We measured the dependence of the variation upon the optical feedback ratio. Obtained results are summarized in Fig. 4
Fig. 4 Measured optical power variations of the x-polarization (squares) and y-polarization (rhombi) modes of the VCSEL against optical feedback ratio.
. Squares and rhombi indicate x- and y-polarization modes, respectively. Large power variation higher than 80 μW was obtained for the optical feedback ratio higher than –20 dB, while the variation dropped suddenly when the feedback ratio became lower than –25 dB.

3. Basic configuration of proposed in-line rotation sensor

The obtained polarization behavior of a VCSEL under optical feedback suggests that VCSELs can be used signal amplifiers with some limiting performance in a polarization rotation sensing. We propose here a new scheme of a rotation sensing system. A schematic diagram of a basic configuration of the proposed scheme using a VCSEL with optical feedback is depicted in Fig. 5
Fig. 5 Proposed concept of rotation sensing system using a VCSEL with optical feedback.
.

A reflective half-wave plate (RHWP) such as a mirror with QWP is fixed on a rotation-measured object such as a motor spindle. A polarization-maintaining fiber (PMF) may be used to introduce a sensing optical beam to RHWP, resulting in small sensing-head space as well as being electromagnetic-noise free. By introducing optical feedback to a VCSEL and counting the periods of the power variation of x- or y-polarization mode of a VCSEL, you can determine the rotation speed.

4. Experimental demonstration of operation principle

The operation principle of the proposed sensing system was confirmed experimentally. An experimental setup was illustrated in Fig. 6
Fig. 6 Experimental setup for measuring feedback optical power and VCSEL power.
. The output wave from the VCSEL was once collimated by an objective lens (OL1), split by a PIBS into two beams. One beam reflected by the PIBS was detected by a photodiode (PD1) with a polarizer. The other beam transmitted through the PIBS was focused by another objective lens (OL2) to an end of a PMF, launched from the other end of the PMF, reflected by a RHWP attached to a motor-spindle head, coupled again to the PMF, and returned to the PIBS. A half power of the returned beam was reflected by the PIBS and detected by another photodiode (PD2) with another polarizer. The other half transmitted through PIBS and was focused by OL1 to the emission point of the VCSEL.

The VCSEL was driven by an operating current of 1.0 mA. Output signals of PD1 and PD2 were monitored by an oscilloscope simultaneously. Obtained signals are shown in Fig. 7
Fig. 7 Obtained output signals from PD1 (lower side) and PD2 (upper side).
. Four periods of variations correspond to one revolution of the spindle. The rotation speed of the spindle was measured to be 3000 rpm. A signal level of PD1 was 50 times higher than that of PD2. This shows that the proposed sensing configuration had an advantage of much higher signal-to-noise ratio owing to VCSEL amplification function in comparison with a configuration where the polarization of the returned light was directly measured. We also observed higher stability in the PD1 signal than the PD2 signal. This higher stability comes from the fact that the VCSEL output power is constant even when the returned power fluctuates due to vibration, dust, mirror contamination, etc.

5. Conclusions

A new rotation sensing system using VCSEL behavior under optical feedback was proposed and demonstrated. A wave launched from a VCSEL is reflected and polarization-rotated by a reflective half-wave plate attached on a rotating object such as a motor spindle, and is returned to the VCSEL. Since the powers of two orthogonal polarization modes of the VCSEL depend on a feedback polarization rotation, the rotation can be detected by monitoring one of the mode powers. A prototype system was constructed, and the sensing principle was demonstrated. It was confirmed that the returned optical power was amplified and reconstructed by the VCSEL, indicating a possibility of a rotation sensor with high stability and high signal-to-noise ratio. The limit of detectable rotation speed depends on the response time of the VCSEL as well as that of the photodiode. Normally they are ~GHz judging from the well-known modulation time of the VCSEL and the response time of the photodiode as far as the injected power is sufficient. Even if they become slow down to ~MHz due to the feedback power reduction, they are still much faster than the mechanical rotation speed. Another concern would be polarization switching or modulation. We did not observe any polarization switching in our experiments. The VCSEL showed stable two-mode operation like multimode operation observed in edge-emitting diode lasers. However, there remained the possibility of the occurrence of ultrafast polarization switching such as GHz frequency, because the response frequency of the utilized photodetection system was not so high. This kind of switching may limit the sensing speed. The sensing head consists of a polarization-maintaining fiber and a mirror on a quarter-wave plate. This tiny and simple configuration of a submillimeter diameter would make a revolution in the rotation sensing technology.

Acknowledgments

This research work was financially supported in part by Japan Science and Technology Agency in Research for Promoting Technological Seeds.

References and links

1.

J. A. Hudgings, S. F. Lim, G. S. Li, W. Yuen, K. Y. Lau, and C. J. Chang-Hasnain, “Compact, integrated optical disk readout head using a novel bistable vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 11(2), 245–247 (1999). [CrossRef]

2.

S.-Y. Ye, S. Mitsugi, Y.-J. Kim, and K. Goto, “Numerical simulation of readout using optical feedback in the integrated vertical cavity surface emitting laser microprobe head,” Jpn. J. Appl. Phys. 41(Part 1, No. 3B), 1636–1637 (2002). [CrossRef]

3.

D. Heinis, C. Gorecki, C. Bringer, V. Bardinal, T. Camps, J.-B. Doucet, P. Dubreuil, and C. Fontaine, “Miniaturized scanning near-field microscope sensor based on optical feedback inside a single-mode oxide-confined vertical-cavity surface-emitting laser,” Jpn. J. Appl. Phys. 42(Part 2, No. 12A), L1469–L1471 (2003). [CrossRef]

4.

J. Hashizume, S. Shinada, F. Koyama, and K. Iga, “Reflection induced voltage change of surface emitting laser for optical probing,” Opt. Rev. 9(5), 186–188 (2002). [CrossRef]

5.

D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett. 94(9), 091103 (2009). [CrossRef]

6.

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1006–1012 (2004). [CrossRef]

7.

C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Enhancement of a liquid-crystal modulator using an external-cavity VCSEL,” IEEE Photon. Technol. Lett. 11(8), 940–942 (1999). [CrossRef]

8.

N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett. 92(22), 221113 (2008). [CrossRef]

9.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993). [CrossRef]

10.

D. V. Kuksenkov and H. Temkin, “Polarization related properties of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 390–395 (1997). [CrossRef]

11.

F. Robert, P. Besnard, M. L. Chares, and G. M. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. 33(12), 2231–2239 (1997). [CrossRef]

12.

C. Masoller and N. B. Abraham, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74(8), 1078–1080 (1999). [CrossRef]

13.

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]

14.

Y. Hong, P. S. Spencer, and K. A. Shore, “Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback,” Opt. Lett. 29(18), 2151–2153 (2004). [CrossRef] [PubMed]

15.

S. Xiang, W. Pan, L. Yan, B. Luo, N. Jiang, and L. Yang, “Polarization properties of vertical-cavity surface-emitting lasers subject to feedback with variably rotated polarization angle,” Appl. Opt. 48(27), 5176–5183 (2009). [CrossRef] [PubMed]

16.

K. van der Pool, “High resolution optical encoders” (1995). http://www.opticalencoder.com/copi-high-resolution-optical-encoders-tutorial-article.html.

17.

Products guide, “Delta rotary optical encoder” (2011). http://www.delta.com.tw/product/em/motion/motion_encoder/download/catalogue/ROE_catalouge_en.pdf.

18.

J. L. Davis and S. Ezekiel, “Closed-loop, low-noise fiber-optic rotation sensor,” Opt. Lett. 6(10), 505–507 (1981). [CrossRef] [PubMed]

19.

H. J. Arditty and H. C. Leèfovre, “Sagnac effect in fiber gyroscopes,” Opt. Lett. 6(8), 401–403 (1981). [CrossRef] [PubMed]

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(230.3990) Optical devices : Micro-optical devices
(250.7260) Optoelectronics : Vertical cavity surface emitting lasers
(280.4788) Remote sensing and sensors : Optical sensing and sensors
(140.7260) Lasers and laser optics : Vertical cavity surface emitting lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: August 31, 2011
Revised Manuscript: October 27, 2011
Manuscript Accepted: October 27, 2011
Published: November 7, 2011

Virtual Issues
February 23, 2012 Spotlight on Optics

Citation
Shogo Ura, Shinichiro Shoda, Kenzo Nishio, and Yasuhiro Awatsuji, "In-line rotation sensor based on VCSEL behavior under polarization-rotating optical feedback," Opt. Express 19, 23683-23688 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23683


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References

  1. J. A. Hudgings, S. F. Lim, G. S. Li, W. Yuen, K. Y. Lau, and C. J. Chang-Hasnain, “Compact, integrated optical disk readout head using a novel bistable vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett.11(2), 245–247 (1999). [CrossRef]
  2. S.-Y. Ye, S. Mitsugi, Y.-J. Kim, and K. Goto, “Numerical simulation of readout using optical feedback in the integrated vertical cavity surface emitting laser microprobe head,” Jpn. J. Appl. Phys.41(Part 1, No. 3B), 1636–1637 (2002). [CrossRef]
  3. D. Heinis, C. Gorecki, C. Bringer, V. Bardinal, T. Camps, J.-B. Doucet, P. Dubreuil, and C. Fontaine, “Miniaturized scanning near-field microscope sensor based on optical feedback inside a single-mode oxide-confined vertical-cavity surface-emitting laser,” Jpn. J. Appl. Phys.42(Part 2, No. 12A), L1469–L1471 (2003). [CrossRef]
  4. J. Hashizume, S. Shinada, F. Koyama, and K. Iga, “Reflection induced voltage change of surface emitting laser for optical probing,” Opt. Rev.9(5), 186–188 (2002). [CrossRef]
  5. D. Larsson, A. Greve, J. M. Hvam, A. Boisen, and K. Yvind, “Self-mixing interferometry in vertical-cavity surface-emitting lasers for nanomechanical cantilever sensing,” Appl. Phys. Lett.94(9), 091103 (2009). [CrossRef]
  6. J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron.10(5), 1006–1012 (2004). [CrossRef]
  7. C. I. Wilkinson, J. Woodhead, J. E. F. Frost, J. S. Roberts, R. Wilson, and M. F. Lewis, “Enhancement of a liquid-crystal modulator using an external-cavity VCSEL,” IEEE Photon. Technol. Lett.11(8), 940–942 (1999). [CrossRef]
  8. N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett.92(22), 221113 (2008). [CrossRef]
  9. S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett.63(26), 3545–3547 (1993). [CrossRef]
  10. D. V. Kuksenkov and H. Temkin, “Polarization related properties of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron.3(2), 390–395 (1997). [CrossRef]
  11. F. Robert, P. Besnard, M. L. Chares, and G. M. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron.33(12), 2231–2239 (1997). [CrossRef]
  12. C. Masoller and N. B. Abraham, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett.74(8), 1078–1080 (1999). [CrossRef]
  13. 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]
  14. Y. Hong, P. S. Spencer, and K. A. Shore, “Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback,” Opt. Lett.29(18), 2151–2153 (2004). [CrossRef] [PubMed]
  15. S. Xiang, W. Pan, L. Yan, B. Luo, N. Jiang, and L. Yang, “Polarization properties of vertical-cavity surface-emitting lasers subject to feedback with variably rotated polarization angle,” Appl. Opt.48(27), 5176–5183 (2009). [CrossRef] [PubMed]
  16. K. van der Pool, “High resolution optical encoders” (1995). http://www.opticalencoder.com/copi-high-resolution-optical-encoders-tutorial-article.html .
  17. Products guide, “Delta rotary optical encoder” (2011). http://www.delta.com.tw/product/em/motion/motion_encoder/download/catalogue/ROE_catalouge_en.pdf .
  18. J. L. Davis and S. Ezekiel, “Closed-loop, low-noise fiber-optic rotation sensor,” Opt. Lett.6(10), 505–507 (1981). [CrossRef] [PubMed]
  19. H. J. Arditty and H. C. Leèfovre, “Sagnac effect in fiber gyroscopes,” Opt. Lett.6(8), 401–403 (1981). [CrossRef] [PubMed]

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