Abstract

Optical beam steering is a key element in many industrial and scientific applications like in material processing, information technologies, medical imaging and laser display. Even though galvanometer-based scanners offer flexibility, speed and accuracy at a relatively low cost, they still lack the necessary control over the polarization required for certain applications. We report on the development of a polarization steerable system assembled with a fiber polarization controller and a galvanometric scanner, both controlled by a digital signal processor board. The system implements control of the polarization decoupled from the pointing direction through a feed-forward control scheme. This enables to direct optical beams to a desired direction without affecting its initial polarization state. When considering the full working field of view, we are able to compensate polarization angle errors larger than 0.2 rad, in a temporal window of less than ∼ 20 ms. Given the unification of components to fully control any polarization state while steering an optical beam, the proposed system is potentially integrable and robust.

© 2012 OSA

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References

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  1. G. F. Marshall and G. E. Stutz, Handbook of Optical and Laser Scanning (CRC Press, 2004).
    [CrossRef]
  2. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  3. W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008).
    [CrossRef]
  4. P. Hariharan, Optical Interferometry, 2nd ed. (Academic Press, 2003).
  5. J. G. Rarity, “Quantum communications and beyond,” Philos. Trans. R. Soc. London, Ser. A 361, 1507–1518 (2003).
    [CrossRef]
  6. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
    [CrossRef]
  7. L. Bogaert, Y. Meuret, B. Van Giel, H. Murat, H. De Smet, and H. Thienpont, “Projection display for the generation of two orthogonal polarized images using liquid crystal on silicon,” Appl. Opt. 47, 1535–1542 (2008).
    [CrossRef] [PubMed]
  8. H. Cho, Optomechatronics: Fusion of Optical and Mechatronic Engineering (CRC Press, 2006).
  9. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  10. J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4, 82.1–82.21 (2002).
    [CrossRef]
  11. M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communications with Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
    [CrossRef]
  12. C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009).
    [CrossRef]
  13. C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14, 10050–10059 (2006).
    [CrossRef] [PubMed]
  14. C. Bonato, C. Pernechele, and P. Villoresi, “Influence of all-reflective optical systems in the transmission of polarization-encoded qubits,” J. Opt. Soc. Am. A 9, 899–906 (2007).
  15. G. Anzolin, A. Gardelein, M. Jofre, G. Molina-Terriza, and M. W. Mitchell, “Polarization change induced by a galvanometric optical scanner,” J. Opt. Soc. Am. A 27, 1946–1952 (2010).
    [CrossRef]
  16. K. Hirabayashi and C. Amano, “Feed-forward continuous and complete polarization control with a PLZT rotatable-variable waveplate and inline polarimeter,” J. Lightwave Technol. 21, 1920–1932 (2003).
    [CrossRef]
  17. P. Ge and M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
    [CrossRef]
  18. W. T. Ang, P. K. Khosla, and C. N. Riviere, “Feedforward Controller With Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory-Tracking Applications,” IEEE/ASME Trans. Mechatron. 12, 134–142 (2007).
    [CrossRef]
  19. U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
    [CrossRef]
  20. M. Johnson, “In-line fiber-optical polarization transformer,” Appl. Opt. 18, 1288–1289 (1979).
    [CrossRef] [PubMed]
  21. W. La and L. Qian, “Modeling Polarization in a Bidirectional Fiber System,” in Signal Processing in Photonics Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SPMC5.
  22. Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
    [CrossRef]
  23. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [CrossRef]
  24. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2010).

2010 (1)

2009 (2)

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009).
[CrossRef]

U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
[CrossRef]

2008 (2)

Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
[CrossRef]

L. Bogaert, Y. Meuret, B. Van Giel, H. Murat, H. De Smet, and H. Thienpont, “Projection display for the generation of two orthogonal polarized images using liquid crystal on silicon,” Appl. Opt. 47, 1535–1542 (2008).
[CrossRef] [PubMed]

2007 (3)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[CrossRef]

C. Bonato, C. Pernechele, and P. Villoresi, “Influence of all-reflective optical systems in the transmission of polarization-encoded qubits,” J. Opt. Soc. Am. A 9, 899–906 (2007).

W. T. Ang, P. K. Khosla, and C. N. Riviere, “Feedforward Controller With Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory-Tracking Applications,” IEEE/ASME Trans. Mechatron. 12, 134–142 (2007).
[CrossRef]

2006 (1)

2003 (3)

K. Hirabayashi and C. Amano, “Feed-forward continuous and complete polarization control with a PLZT rotatable-variable waveplate and inline polarimeter,” J. Lightwave Technol. 21, 1920–1932 (2003).
[CrossRef]

J. G. Rarity, “Quantum communications and beyond,” Philos. Trans. R. Soc. London, Ser. A 361, 1507–1518 (2003).
[CrossRef]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communications with Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[CrossRef]

2002 (2)

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4, 82.1–82.21 (2002).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

1995 (1)

P. Ge and M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
[CrossRef]

1979 (1)

Amano, C.

Ang, W. T.

U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
[CrossRef]

W. T. Ang, P. K. Khosla, and C. N. Riviere, “Feedforward Controller With Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory-Tracking Applications,” IEEE/ASME Trans. Mechatron. 12, 134–142 (2007).
[CrossRef]

Anzolin, G.

Aspelmeyer, M.

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14, 10050–10059 (2006).
[CrossRef] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communications with Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bogaert, L.

Bonato, C.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009).
[CrossRef]

C. Bonato, C. Pernechele, and P. Villoresi, “Influence of all-reflective optical systems in the transmission of polarization-encoded qubits,” J. Opt. Soc. Am. A 9, 899–906 (2007).

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14, 10050–10059 (2006).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Cho, H.

H. Cho, Optomechatronics: Fusion of Optical and Mechatronic Engineering (CRC Press, 2006).

Chuang, I.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2010).

De Smet, H.

Deppo, V. D.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009).
[CrossRef]

Drexler, W.

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008).
[CrossRef]

Fujimoto, J. G.

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008).
[CrossRef]

Gardelein, A.

Ge, P.

P. Ge and M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
[CrossRef]

Gisin, N.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Gorman, P. M.

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4, 82.1–82.21 (2002).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Interferometry, 2nd ed. (Academic Press, 2003).

Hirabayashi, K.

Jennewein, T.

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14, 10050–10059 (2006).
[CrossRef] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communications with Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[CrossRef]

Jofre, M.

Johnson, M.

Jouaneh, M.

P. Ge and M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
[CrossRef]

Khosla, P. K.

W. T. Ang, P. K. Khosla, and C. N. Riviere, “Feedforward Controller With Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory-Tracking Applications,” IEEE/ASME Trans. Mechatron. 12, 134–142 (2007).
[CrossRef]

Knight, P.

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4, 82.1–82.21 (2002).
[CrossRef]

La, W.

W. La and L. Qian, “Modeling Polarization in a Bidirectional Fiber System,” in Signal Processing in Photonics Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SPMC5.

Latt, W. T.

U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
[CrossRef]

Leeb, W. R.

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communications with Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[CrossRef]

Li, Z.-Y.

Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
[CrossRef]

Marshall, G. F.

G. F. Marshall and G. E. Stutz, Handbook of Optical and Laser Scanning (CRC Press, 2004).
[CrossRef]

Meuret, Y.

Mitchell, M. W.

Molina-Terriza, G.

Murat, H.

Naletto, G.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009).
[CrossRef]

Nielsen, M.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2010).

Pernechele, C.

C. Bonato, C. Pernechele, and P. Villoresi, “Influence of all-reflective optical systems in the transmission of polarization-encoded qubits,” J. Opt. Soc. Am. A 9, 899–906 (2007).

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14, 10050–10059 (2006).
[CrossRef] [PubMed]

Pfennigbauer, M.

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communications with Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[CrossRef]

Qian, L.

W. La and L. Qian, “Modeling Polarization in a Bidirectional Fiber System,” in Signal Processing in Photonics Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SPMC5.

Rarity, J. G.

J. G. Rarity, “Quantum communications and beyond,” Philos. Trans. R. Soc. London, Ser. A 361, 1507–1518 (2003).
[CrossRef]

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4, 82.1–82.21 (2002).
[CrossRef]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Riviere, C. N.

U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
[CrossRef]

W. T. Ang, P. K. Khosla, and C. N. Riviere, “Feedforward Controller With Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory-Tracking Applications,” IEEE/ASME Trans. Mechatron. 12, 134–142 (2007).
[CrossRef]

Shee, C. Y.

U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
[CrossRef]

Stutz, G. E.

G. F. Marshall and G. E. Stutz, Handbook of Optical and Laser Scanning (CRC Press, 2004).
[CrossRef]

Tan, U.-X.

U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
[CrossRef]

Tapster, P. R.

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4, 82.1–82.21 (2002).
[CrossRef]

Thew, R.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[CrossRef]

Thienpont, H.

Tian, C.-Y.

Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Tomaello, A.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009).
[CrossRef]

Van Giel, B.

Villoresi, P.

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009).
[CrossRef]

C. Bonato, C. Pernechele, and P. Villoresi, “Influence of all-reflective optical systems in the transmission of polarization-encoded qubits,” J. Opt. Soc. Am. A 9, 899–906 (2007).

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14, 10050–10059 (2006).
[CrossRef] [PubMed]

Wang, Y.-J.

Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
[CrossRef]

Widjaja, F.

U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Wu, C.-Q.

Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
[CrossRef]

Yang, S.-S.

Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
[CrossRef]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Zeilinger, A.

C. Bonato, M. Aspelmeyer, T. Jennewein, C. Pernechele, P. Villoresi, and A. Zeilinger, “Influence of satellite motion on polarization qubits in a Space-Earth quantum communication link,” Opt. Express 14, 10050–10059 (2006).
[CrossRef] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communications with Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[CrossRef]

Zhao, S.

Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
[CrossRef]

Appl. Opt. (2)

Chin. Phys. Lett. (1)

Z.-Y. Li, C.-Q. Wu, S.-S. Yang, C.-Y. Tian, S. Zhao, and Y.-J. Wang, “Generalized Principal-State-of-Polarization Analysis and Matrix Model for Piezoelectric Polarization Controllers,” Chin. Phys. Lett. 25, 1325–1328 (2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. R. Leeb, and A. Zeilinger, “Long-Distance Quantum Communications with Entangled Photons Using Satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[CrossRef]

IEEE/ASME Trans. Mechatron. (1)

W. T. Ang, P. K. Khosla, and C. N. Riviere, “Feedforward Controller With Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory-Tracking Applications,” IEEE/ASME Trans. Mechatron. 12, 134–142 (2007).
[CrossRef]

J. Lightwave Technol. (1)

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

G. Anzolin, A. Gardelein, M. Jofre, G. Molina-Terriza, and M. W. Mitchell, “Polarization change induced by a galvanometric optical scanner,” J. Opt. Soc. Am. A 27, 1946–1952 (2010).
[CrossRef]

C. Bonato, C. Pernechele, and P. Villoresi, “Influence of all-reflective optical systems in the transmission of polarization-encoded qubits,” J. Opt. Soc. Am. A 9, 899–906 (2007).

Nat. Photonics (1)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[CrossRef]

New J. Phys. (2)

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4, 82.1–82.21 (2002).
[CrossRef]

C. Bonato, A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, “Feasibility of satellite quantum key distribution,” New J. Phys. 11, 045017 (2009).
[CrossRef]

Opt. Express (1)

Philos. Trans. R. Soc. London, Ser. A (1)

J. G. Rarity, “Quantum communications and beyond,” Philos. Trans. R. Soc. London, Ser. A 361, 1507–1518 (2003).
[CrossRef]

Precis. Eng. (1)

P. Ge and M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
[CrossRef]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Sens. Actuators A (1)

U.-X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller,” Sens. Actuators A 150, 116–123 (2009).
[CrossRef]

Other (8)

W. La and L. Qian, “Modeling Polarization in a Bidirectional Fiber System,” in Signal Processing in Photonics Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SPMC5.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2010).

H. Cho, Optomechatronics: Fusion of Optical and Mechatronic Engineering (CRC Press, 2006).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

G. F. Marshall and G. E. Stutz, Handbook of Optical and Laser Scanning (CRC Press, 2004).
[CrossRef]

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008).
[CrossRef]

P. Hariharan, Optical Interferometry, 2nd ed. (Academic Press, 2003).

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Figures (9)

Fig. 1
Fig. 1

Optical system scheme. (LD) denotes the laser diode, (PC) polarization controller, (C) fiber-collimator, (CS) coordinate system, (DCM) dichroic mirror, (IO) imaging optics, (CCD) charge-coupled device camera, (DSP) digital signal processor, (GV) galvanometric scanner with (M1) mirror 1, (α) angle M1, (M2) mirror 2, (β) angle M2, (PL) polarimeter, (B1) beacon 1 and (B2) beacon 2.

Fig. 2
Fig. 2

Galvo scanner system model. (a) Scheme of the galvo scanner system, with the reference frame used in the calculations. An example of the optical path of a ray is indicated by the red line. (b) Physical model of the galvo mirrors substrate. The structure of the mirrors considers a quasi-real model of the galvo mirrors two-layer-compound made of a protective dielectric layer of quartz (SIO2), and the reflective substrate of silver (Ag).

Fig. 3
Fig. 3

Imaged beacons to retrieve the Tx-Rx relative angle rotation χ. (a) The angle is computed between the central vertical axis of the CCD image and the clockwise angle to the brighter beam spot. Notice that one of the beams is brighter than the other to easily identify both spots. Five pointing directions are considered with galvo mirrors’ angles and particular receiver orientation rotation, which are grouped in the triplet (α,β,χ): (0) zero pointing corresponds to (0°, 0°, 0°), (1) pointing 1 (3.56°, 12.19°, 336.47°), (2) pointing 2 (18.66°, 8.37°, 93.06°), (3) pointing 3 (7.99°, −0.13°, 4.01°) and (4) pointing 4 (−4.03°, 3.30°, 243°).

Fig. 4
Fig. 4

Stokes parameters measured while voltage-scanning actuator 1. The recorded Stokes parameters sequence follows a squared cosine function. It is repeated three and a half times to acquire several cycles through a specific PC actuator. The data is periodically sampled asynchronously. Each red circle corresponds to an identified voltage and Stokes parameters measurement pair. Black points that do not fit the pattern correspond to data samples at the return instant to 0V of the PC driving strategy. (top) S1, (middle) S2 and (bottom) S3 Stokes parameters. Similar measurement records are obtained for actuators 2 and 3 of the PC.

Fig. 5
Fig. 5

Processed Stokes parameters obtained by removing from the raw data the polarization transformation contribution of the galvo. To remove the galvo contribution, the inverse of the galvo Mueller matrix for zero pointing is applied. (top) S1, (middle) S2 and (bottom) S3 Stokes parameters. Similar measurement records are obtained for actuators 2 and 3 of the PC.

Fig. 6
Fig. 6

Polarization state measurement, from the PC data, on the Poincare sphere and associated actuator axis n̂k for each of the three PC actuators. For the current measurement the different (n̂3, n̂′2, n̂″1) are oriented in azimuth and elevation (θ, φ) as follows: (29.52°, 9.61°) actuator 1, (122.88°, −6.22°) actuator 2 and (45.15°, 43.35°) actuator 3. The first and the third actuators are similarly oriented along the same direction, while the second actuator is at 90° with respect to them.

Fig. 7
Fig. 7

Introduced relative phase retard with respect to the applied driving voltage for each PC actuator. Hysteresis has been strongly reduced by returning the drive voltage to zero before each measurement, and relatively slow driving speeds. The phase retard retrieved is relative to 0 V driving voltage. Blue circles (red squares) show the phase trajectory with increasing (decreasing) voltage.

Fig. 8
Fig. 8

Polarization controller inferred transfer function. Phase to voltage relation for each of the three PC actuators. The ascending and descending curves are each fit with 6th-order polynomials for real-time computation. With proper combination of the three PC phase retards, it is possible to generate any rotation matrix.

Fig. 9
Fig. 9

Error angle for different polarization states. The polarization states are measured with the receiving polarimeter. Different compensation configurations are presented, compensation of the Tx-Rx and galvo (blue-circle marker), galvo compensation (green-diamond marker), Tx-Rx orientation (cyan-square marker) and no compensation (red-cross marker). For each pointing direction and each compensation configuration, four different polarization states are used, taking as reference the zero pointing. Error angles are plotted in logarithmic scale, 10 · log10ε), for clearer visualization of error angles close to 0 rad. When the system performs the compensation, the error angle is below 0.2 rad.

Equations (15)

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S out = R ( χ ) G ( α , β ) PC ( ϕ 1 , ϕ 2 , ϕ 3 ) S in .
R ( χ ) = [ 1 0 0 0 0 cos ( χ ) sin ( χ ) 0 0 sin ( χ ) cos ( χ ) 0 0 0 0 1 ] .
PC ( ϕ 1 , ϕ 2 , ϕ 3 ) = A ( n ^ 3 , ϕ 3 + ϕ _ 3 ) A ( n ^ 2 , ϕ 2 + ϕ _ 2 ) A ( n ^ 1 , ϕ 1 + ϕ _ 1 ) .
A ( n ^ , ϕ ) I cos ϕ + n × sin ϕ + n ^ n ^ ( 1 cos ϕ )
n × [ 0 0 0 0 0 0 n z n y 0 n z 0 n x 0 n y n x 0 ] .
n ^ n ^ [ 1 0 0 0 0 n x 2 n x n y n x n z 0 n x n y n y 2 n y n z 0 n x n z n y n z n z 2 ] .
PC ( ϕ 1 , ϕ 2 , ϕ 3 ) = A ( n ^ 3 , ϕ 3 ) A ( n ^ 3 , ϕ _ 3 ) A ( n ^ 2 , ϕ 2 + ϕ _ 2 ) A ( n ^ 1 , ϕ 1 + ϕ _ 1 ) .
PC ( ϕ 1 , ϕ 2 , ϕ 3 ) = A ( n ^ 3 , ϕ _ 3 ) A ( n ^ 2 , ϕ 2 + ϕ _ 2 ) A 1 ( n ^ 3 , ϕ _ 3 ) A ( n ^ 3 , ϕ _ 3 ) A ( n ^ 1 , ϕ 1 + ϕ _ 1 ) .
PC ( ϕ 1 , ϕ 2 , ϕ 3 ) = A ( n ^ 1 , ϕ 1 + ϕ _ 1 ) A ( n ^ 2 , ϕ _ 2 ) A ( n ^ 3 , ϕ _ 3 )
PC ( ϕ 1 , ϕ 2 , ϕ 3 ) = A ( n ^ 3 , ϕ 3 ) A ( n ^ 2 , ϕ 2 ) A ( n ^ 1 , ϕ 1 ) A ( n ^ 1 , ϕ _ 1 ) A ( n ^ 2 , ϕ _ 2 ) A ( n ^ 3 , ϕ _ 3 ) .
PC ( ϕ 1 , ϕ 2 , ϕ 3 ) = A ( n ^ 3 , ϕ 3 ) A ( n ^ 2 , ϕ 2 ) A ( n ^ 1 , ϕ 1 ) M .
{ S out 1 = I M ( θ , φ , δ ) S in 1 S out 2 = I M ( θ , φ , δ ) S in 2 .
S out 1 = I M ( θ , φ , δ ) S in 1 .
PC ( ϕ 1 , ϕ 2 , ϕ 3 ) = G ( α , β ) 1 R 1 ( χ ) .
Δ ε = | 1 2 cos 1 ( cos [ 2 ( θ p x θ p z ) ] cos [ 2 ( φ p x φ p z ) ] ) | .

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