Abstract

We propose and demonstrate experimentally the transfer of one spatial degree of freedom of a laser beam onto another one. Using a multi-plane light conversion device (MPLC) and a modal analysis, we designed a passive setup with immediate response which couples a displacement and tilt in the transverse plane to a longitudinal shift of the focus point of a beam. With this design, we demonstrated a shift of the focal point of the output beam by 4 zR along the propagation axis.

© 2017 Optical Society of America

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References

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  1. D. Reddy and P. Saggau, “Development of a random access multiphoton microscope for fast three-dimensional functional recording of neuronal activity,”, Proc. SPIE 6443, 64430U (2007).
    [Crossref]
  2. G. Sancataldo, L. Scipioni, T. Ravasenga, L. Lanzanò, A. Diaspro, A. Barberis, and M. Duocastella, “Three-dimensional multiple-particle tracking with nanometric precision over tunable axial range,” Optica 4, 367–373 (2017).
    [Crossref]
  3. G. Druart, J. Taboury, N. Guérineau, R. Haïdar, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368 (2008).
    [Crossref] [PubMed]
  4. V. X. D. Yang, Y. Mao, B. A. Standish, N. R. Munce, S. Chiu, D. Burnes, B. C. Wilson, I. A. Vitkin, P. A. Himmer, and D. L. Dickensheets, “Doppler optical coherence tomography with a micro-electro-mechanical membrane mirror for high-speed dynamic focus tracking,” Opt. Lett. 31, 1262–1264 (2006).
    [Crossref] [PubMed]
  5. T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
    [Crossref]
  6. A. Kaplan, N. Friedman, and N. Davidson, “Acousto-optic lens with very fast focus scanning,” Opt. Lett. 26, 1078–1080 (2001).
    [Crossref]
  7. H.-C. Lin and Y.-H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97(6), 063505 (2010).
    [Crossref]
  8. S. Sato, A. Sugiyama, and R. Sato, “Variable-Focus Liquid-Crystal Fresnel Lens,” Japanese J. Appl. Phys. 24(8A), L626 (1985).
    [Crossref]
  9. G. Zhu, J. van Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express 13, 2153–2159 (2005).
    [Crossref] [PubMed]
  10. M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express 14, 12243–12254 (2006).
    [Crossref] [PubMed]
  11. R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
    [Crossref]
  12. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13, 1468–1476 (2005).
    [Crossref] [PubMed]
  13. B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E. 3, 159–163 (2000).
    [Crossref]
  14. M. Duocastella and C. B. Arnold, “Enhanced depth of field laser processing using an ultra-high-speed axial scanner,” Appl. Phys. Lett. 102(6), 061113 (2013).
    [Crossref]
  15. A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33, 2146–2148 (2008).
    [Crossref] [PubMed]
  16. M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22, 19293–19301 (2014).
    [Crossref] [PubMed]
  17. G. R. B. E. Römer, P. Bechtold, and P. J. Harshman, “Electro-optic and Acousto-optic Laser Beam Scanners,” Phy. Procedia 56, 29–39 (2014).
    [Crossref]
  18. L. Garcia, O. Pinel, P. Jian, N. Barré, L. Jaffrès, J.-F. Morizur, and G. Labroille, “Fast adaptive laser shaping based on multiple laser incoherent combining,” Proc. SPIE 10097, 1009705 (2017).
    [Crossref]
  19. J.-F. Morizur, L. Nicholls, P. Jian, S. Armstrong, N. Treps, B. Hage, M. Hsu, W. Bowen, J. Janousek, and H.-A. Bachor, “Programmable unitary spatial mode manipulation,” J. Opt. Soc. Am. A 27, 2524–2531 (2010).
    [Crossref]
  20. G. Labroille, B. Denolle, P. Jian, P. Genevaux, N. Treps, and J.-F. Morizur, “Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion,” Opt. Express 22, 15599–15607 (2014).
    [Crossref] [PubMed]
  21. D. Z. Anderson, “Alignment of resonant optical cavities,” Appl. Opt. 23, 2944–2949 (1984).
    [Crossref] [PubMed]
  22. M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, “Optimal optical measurement of small displacements,” J. Opt. B. Quantum Semiclassical Opt. 12(6), 495 (2004).
    [Crossref]
  23. V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum displacement of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537–1539 (2006).
    [Crossref] [PubMed]
  24. M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
    [Crossref] [PubMed]
  25. A. E. Siegman, Lasers, (University Science Books, 1986), Chap. 16.
  26. V. Delaubert, “Quantum imaging with a small number of transverse modes,” Australian National University and Université Pierre et Marie Curie, Ph.D thesis, January2007.

2017 (2)

G. Sancataldo, L. Scipioni, T. Ravasenga, L. Lanzanò, A. Diaspro, A. Barberis, and M. Duocastella, “Three-dimensional multiple-particle tracking with nanometric precision over tunable axial range,” Optica 4, 367–373 (2017).
[Crossref]

L. Garcia, O. Pinel, P. Jian, N. Barré, L. Jaffrès, J.-F. Morizur, and G. Labroille, “Fast adaptive laser shaping based on multiple laser incoherent combining,” Proc. SPIE 10097, 1009705 (2017).
[Crossref]

2014 (3)

2013 (1)

M. Duocastella and C. B. Arnold, “Enhanced depth of field laser processing using an ultra-high-speed axial scanner,” Appl. Phys. Lett. 102(6), 061113 (2013).
[Crossref]

2010 (2)

H.-C. Lin and Y.-H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97(6), 063505 (2010).
[Crossref]

J.-F. Morizur, L. Nicholls, P. Jian, S. Armstrong, N. Treps, B. Hage, M. Hsu, W. Bowen, J. Janousek, and H.-A. Bachor, “Programmable unitary spatial mode manipulation,” J. Opt. Soc. Am. A 27, 2524–2531 (2010).
[Crossref]

2009 (1)

R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
[Crossref]

2008 (2)

2007 (2)

D. Reddy and P. Saggau, “Development of a random access multiphoton microscope for fast three-dimensional functional recording of neuronal activity,”, Proc. SPIE 6443, 64430U (2007).
[Crossref]

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

2006 (3)

2005 (2)

2004 (1)

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, “Optimal optical measurement of small displacements,” J. Opt. B. Quantum Semiclassical Opt. 12(6), 495 (2004).
[Crossref]

2001 (1)

2000 (1)

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E. 3, 159–163 (2000).
[Crossref]

1992 (1)

T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
[Crossref]

1985 (1)

S. Sato, A. Sugiyama, and R. Sato, “Variable-Focus Liquid-Crystal Fresnel Lens,” Japanese J. Appl. Phys. 24(8A), L626 (1985).
[Crossref]

1984 (1)

Anderson, D. Z.

Armstrong, S.

Arnold, C. B.

M. Duocastella and C. B. Arnold, “Enhanced depth of field laser processing using an ultra-high-speed axial scanner,” Appl. Phys. Lett. 102(6), 061113 (2013).
[Crossref]

A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33, 2146–2148 (2008).
[Crossref] [PubMed]

Bachor, H.-A.

Barberis, A.

Barré, N.

L. Garcia, O. Pinel, P. Jian, N. Barré, L. Jaffrès, J.-F. Morizur, and G. Labroille, “Fast adaptive laser shaping based on multiple laser incoherent combining,” Proc. SPIE 10097, 1009705 (2017).
[Crossref]

Bechtold, P.

G. R. B. E. Römer, P. Bechtold, and P. J. Harshman, “Electro-optic and Acousto-optic Laser Beam Scanners,” Phy. Procedia 56, 29–39 (2014).
[Crossref]

Berge, B.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E. 3, 159–163 (2000).
[Crossref]

Bi, K.

R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
[Crossref]

Bowen, W.

Bowen, W. P.

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, “Optimal optical measurement of small displacements,” J. Opt. B. Quantum Semiclassical Opt. 12(6), 495 (2004).
[Crossref]

Buchhave, P.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Burnes, D.

Chiu, S.

Davidson, N.

Delaubert, V.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum displacement of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537–1539 (2006).
[Crossref] [PubMed]

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, “Optimal optical measurement of small displacements,” J. Opt. B. Quantum Semiclassical Opt. 12(6), 495 (2004).
[Crossref]

V. Delaubert, “Quantum imaging with a small number of transverse modes,” Australian National University and Université Pierre et Marie Curie, Ph.D thesis, January2007.

Denolle, B.

Diaspro, A.

Dickensheets, D. L.

Druart, G.

Du, R.

R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
[Crossref]

Duocastella, M.

Durst, M.

Durst, M. E.

Fabre, C.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Friedman, N.

Funato, H.

T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
[Crossref]

Garcia, L.

L. Garcia, O. Pinel, P. Jian, N. Barré, L. Jaffrès, J.-F. Morizur, and G. Labroille, “Fast adaptive laser shaping based on multiple laser incoherent combining,” Proc. SPIE 10097, 1009705 (2017).
[Crossref]

Genevaux, P.

Guérineau, N.

Hage, B.

Haïdar, R.

Harb, C. C.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum displacement of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537–1539 (2006).
[Crossref] [PubMed]

Harshman, P. J.

G. R. B. E. Römer, P. Bechtold, and P. J. Harshman, “Electro-optic and Acousto-optic Laser Beam Scanners,” Phy. Procedia 56, 29–39 (2014).
[Crossref]

Himmer, P. A.

Hsu, M.

Hsu, M. T. L.

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, “Optimal optical measurement of small displacements,” J. Opt. B. Quantum Semiclassical Opt. 12(6), 495 (2004).
[Crossref]

Jaffrès, L.

L. Garcia, O. Pinel, P. Jian, N. Barré, L. Jaffrès, J.-F. Morizur, and G. Labroille, “Fast adaptive laser shaping based on multiple laser incoherent combining,” Proc. SPIE 10097, 1009705 (2017).
[Crossref]

Janousek, J.

J.-F. Morizur, L. Nicholls, P. Jian, S. Armstrong, N. Treps, B. Hage, M. Hsu, W. Bowen, J. Janousek, and H.-A. Bachor, “Programmable unitary spatial mode manipulation,” J. Opt. Soc. Am. A 27, 2524–2531 (2010).
[Crossref]

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Jian, P.

Kaplan, A.

Kattnig, A.

Labroille, G.

L. Garcia, O. Pinel, P. Jian, N. Barré, L. Jaffrès, J.-F. Morizur, and G. Labroille, “Fast adaptive laser shaping based on multiple laser incoherent combining,” Proc. SPIE 10097, 1009705 (2017).
[Crossref]

G. Labroille, B. Denolle, P. Jian, P. Genevaux, N. Treps, and J.-F. Morizur, “Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion,” Opt. Express 22, 15599–15607 (2014).
[Crossref] [PubMed]

Lam, P. K.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum displacement of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537–1539 (2006).
[Crossref] [PubMed]

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, “Optimal optical measurement of small displacements,” J. Opt. B. Quantum Semiclassical Opt. 12(6), 495 (2004).
[Crossref]

Lanzanò, L.

Lassen, M.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Li, D.

R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
[Crossref]

Lin, H.-C.

H.-C. Lin and Y.-H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97(6), 063505 (2010).
[Crossref]

Lin, Y.-H.

H.-C. Lin and Y.-H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97(6), 063505 (2010).
[Crossref]

Luo, Q.

R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
[Crossref]

Mao, Y.

McLeod, E.

Mermillod-Blondin, A.

Morizur, J.-F.

Munce, N. R.

Nicholls, L.

Oron, D.

Peseux, J.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E. 3, 159–163 (2000).
[Crossref]

Pinel, O.

L. Garcia, O. Pinel, P. Jian, N. Barré, L. Jaffrès, J.-F. Morizur, and G. Labroille, “Fast adaptive laser shaping based on multiple laser incoherent combining,” Proc. SPIE 10097, 1009705 (2017).
[Crossref]

Primot, J.

Ravasenga, T.

Reddy, D.

D. Reddy and P. Saggau, “Development of a random access multiphoton microscope for fast three-dimensional functional recording of neuronal activity,”, Proc. SPIE 6443, 64430U (2007).
[Crossref]

Römer, G. R. B. E.

G. R. B. E. Römer, P. Bechtold, and P. J. Harshman, “Electro-optic and Acousto-optic Laser Beam Scanners,” Phy. Procedia 56, 29–39 (2014).
[Crossref]

Saggau, P.

D. Reddy and P. Saggau, “Development of a random access multiphoton microscope for fast three-dimensional functional recording of neuronal activity,”, Proc. SPIE 6443, 64430U (2007).
[Crossref]

Sancataldo, G.

Sato, R.

S. Sato, A. Sugiyama, and R. Sato, “Variable-Focus Liquid-Crystal Fresnel Lens,” Japanese J. Appl. Phys. 24(8A), L626 (1985).
[Crossref]

Sato, S.

S. Sato, A. Sugiyama, and R. Sato, “Variable-Focus Liquid-Crystal Fresnel Lens,” Japanese J. Appl. Phys. 24(8A), L626 (1985).
[Crossref]

Sauer, H.

Scipioni, L.

Shibaguchi, T.

T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers, (University Science Books, 1986), Chap. 16.

Silberberg, Y.

Standish, B. A.

Sugiyama, A.

S. Sato, A. Sugiyama, and R. Sato, “Variable-Focus Liquid-Crystal Fresnel Lens,” Japanese J. Appl. Phys. 24(8A), L626 (1985).
[Crossref]

Taboury, J.

Tal, E.

Treps, N.

van Howe, J.

Vicidomini, G.

Vitkin, I. A.

Wagner, K.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Wilson, B. C.

Xu, C.

Xue, S.

R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
[Crossref]

Yang, V. X. D.

Zeng, S.

R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
[Crossref]

Zhu, G.

Zipfel, W.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

H.-C. Lin and Y.-H. Lin, “A fast response and large electrically tunable-focusing imaging system based on switching of two modes of a liquid crystal lens,” Appl. Phys. Lett. 97(6), 063505 (2010).
[Crossref]

M. Duocastella and C. B. Arnold, “Enhanced depth of field laser processing using an ultra-high-speed axial scanner,” Appl. Phys. Lett. 102(6), 061113 (2013).
[Crossref]

Eur. Phys. J. E. (1)

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E. 3, 159–163 (2000).
[Crossref]

J. Mod. Opt. (1)

R. Du, K. Bi, S. Zeng, D. Li, S. Xue, and Q. Luo, “Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors,” J. Mod. Opt. 56, 81–84 (2009).
[Crossref]

J. Opt. B. Quantum Semiclassical Opt. (1)

M. T. L. Hsu, V. Delaubert, P. K. Lam, and W. P. Bowen, “Optimal optical measurement of small displacements,” J. Opt. B. Quantum Semiclassical Opt. 12(6), 495 (2004).
[Crossref]

J. Opt. Soc. Am. A (1)

Japanese J. Appl. Phys. (2)

T. Shibaguchi and H. Funato, “Lead-lanthanum zirconate-titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes,” Japanese J. Appl. Phys. 31, 3196–3200 (1992).
[Crossref]

S. Sato, A. Sugiyama, and R. Sato, “Variable-Focus Liquid-Crystal Fresnel Lens,” Japanese J. Appl. Phys. 24(8A), L626 (1985).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Optica (1)

Phy. Procedia (1)

G. R. B. E. Römer, P. Bechtold, and P. J. Harshman, “Electro-optic and Acousto-optic Laser Beam Scanners,” Phy. Procedia 56, 29–39 (2014).
[Crossref]

Phys. Rev. Lett. (1)

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, “Tools for Multimode Quantum Information: Modulation, Detection, and Spatial Quantum Correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Proc. SPIE (2)

L. Garcia, O. Pinel, P. Jian, N. Barré, L. Jaffrès, J.-F. Morizur, and G. Labroille, “Fast adaptive laser shaping based on multiple laser incoherent combining,” Proc. SPIE 10097, 1009705 (2017).
[Crossref]

D. Reddy and P. Saggau, “Development of a random access multiphoton microscope for fast three-dimensional functional recording of neuronal activity,”, Proc. SPIE 6443, 64430U (2007).
[Crossref]

Other (2)

A. E. Siegman, Lasers, (University Science Books, 1986), Chap. 16.

V. Delaubert, “Quantum imaging with a small number of transverse modes,” Australian National University and Université Pierre et Marie Curie, Ph.D thesis, January2007.

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Figures (6)
Fig. 1
Fig. 1 The MPLC system couples the displacement (δd0) and tilt (δt0) of a beam to the scanning of its focal point (δz0).

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Fig. 2
Fig. 2 Target modes before orthonormalization (output mode basis).

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Fig. 3
Fig. 3 Intensity profiles of i) Input mode basis, ii) Output mode basis. The MPLC matches mode (i, n) with mode (ii, n) with n ∈ [[0, 4]].

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Fig. 4
Fig. 4 Left: Calculated trajectory in normalized displacement. δd0 represents the lateral displacement imposed on the beam and w0 is the waist of the beam, δt0 represents the tilt imposed on the beam. This trajectory needs to be impressed on the input beam for the focus point of the beam at the output of the MPLC to see its focus point vary between 0 zR and 4 zR, zR being the Rayleigh length of the beam. Right: Overlap between the desired output (perfectly defocused Gaussian beam) and the reference beam ie. a Gaussian beam focused at 0 zR (yellow color or (a)), the beam which would be produced by an ideal unitary operation (red color or (b)) and the beam which can be produced by the actual MPLC we calculated (brown color or (c)).

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Fig. 5
Fig. 5 Experimental setup built to implement the defocus of a beam with an MPLC device. The output beam of a single mode fiber, collimated by an output coupler (OC), is mode-matched to the correct waist size with lens f1. We select the correct polarization with a polarizing beam splitter (PBS) in order for the beam to be compatible with the spatial light modulator (SLM). Two reflections on the SLM allow to impress on the beam two successive angles α1, α2. The focus point of the beam is imaged with a 4-f telescope and launched into the MPLC. At the output of the MPLC, lens f2 performs a 2-f imaging of the defocused beam. The beam transverse profile is monitored by a beam profiler.

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Fig. 6
Fig. 6 Left: Photograph of the MPLC device used in the experimental setup. The MPLC consists of a plane mirror facing a planar phase plate on which 10 successive phase profiles are written to implement the desired transformation. Right: Experimental demonstration of defocusing over 4 zR range using the displacement and tilt of a beam combined with an MPLC. The waist size evolution in the y direction along the propagation direction of the output beam is shown for 6 different focusing positions. The dotted black line represents the theoretical waist size.

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Tables (1)

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Table 1 Overlap between theoretical modes and simulated modes at the output of the MPLC

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Equations (7)

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E 0 | p 0 + δ p 0 ≃ ℰ 0 ( u 0 | p 0 + δ p 0 × ∂ u 0 ∂ p | p 0 ) = E 0 | p 0 + δ p 0 p C × E 1 | p 0
E 0 ( ρ , z ) | z 0 + δ z 0 = ℰ 0 [ LG 00 ( ρ , z ) | z 0 + i δ z 0 z R ( α + LG 00 ( ρ , z ) | z 0 + LG 01 ( ρ , z ) | z 0 ) ] exp ( − i k ( z − z 0 ) )
E 0 ( ρ , z ) | d 0 + δ d 0 = ℰ 0 [ HG 00 ( ρ , z ) | d 0 + δ d 0 w 0 × HG 01 ( ρ , z ) | d 0 ] exp ( − i k z ) .
E 0 ( ρ , z ) | t 0 + δ t 0 = ℰ 0 [ HG 00 ( ρ , z ) | t 0 + i δ t 0 w 0 2 × HG 01 ( ρ , z ) | t 0 ] exp ( − i k z ) .
E out obj | δ z 0 ( k ) ≃ E out | δ z 0 ( k ) = ∑ i = 0 4 f i ( δ z 0 ( k ) ) × v i
E in ( δ z 0 ( k ) ) = ∑ i = 0 4 f i ( δ z 0 ( k ) ) × u i
F ( δ d 0 ( k ) , δ t 0 ( k ) ) = | 〈 E in ( δ d 0 ( k ) , δ t 0 ( k ) ) | ∑ i = 0 4 f i ( δ z 0 ( k ) ) × u i 〉 | 2

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