Abstract

We developed an octave-band tunable optical vortex laser based on a 532 nm optical vortex pumped optical parametric oscillator with a simple linear-cavity configuration by employing cascaded non-critical phase-matching LiB3O5 crystals. The optical vortex output was tunable from 735 to 1903 nm. For a pump energy of 9 mJ, an optical vortex pulse energy of 0.24–2.36 mJ was obtained, corresponding to an optical-optical efficiency of 0.3-26%.

© 2016 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [Crossref] [PubMed]
  2. S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
    [Crossref]
  3. M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
    [Crossref]
  4. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
    [Crossref]
  5. K. T. Gahagan and G. A. Swartzlander., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996).
    [Crossref] [PubMed]
  6. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
    [Crossref]
  7. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [Crossref] [PubMed]
  8. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
    [Crossref] [PubMed]
  9. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
    [Crossref] [PubMed]
  10. K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
    [Crossref] [PubMed]
  11. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
    [Crossref]
  12. T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, and S. J. B. Yoo, “Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices,” Opt. Express 20(9), 9396–9402 (2012).
    [Crossref] [PubMed]
  13. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
  14. I. B. Djordjevic, “Heterogeneous transparent optical networking based on coded OAM modulation,” IEEE Photonics J. 3(3), 531–537 (2011).
    [Crossref]
  15. K. Shigematsu, Y. Toda, K. Yamane, and R. Morita, “Orbital angular momentum spectral dynamics of GaN excitons excited by optical vortices,” Jpn. J. Appl. Phys. 52(8), 08JL08 (2013).
    [Crossref]
  16. G. F. Quinteiro and T. Kuhn, “Light-hole transitions in quantum dots: realizing full control by highly focused optical-vortex beams,” Phys. Rev. B 90(11), 115401 (2014).
    [Crossref]
  17. S. Bretschneider, C. Eggeling, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy by optical shelving,” Phys. Rev. Lett. 98(21), 218103 (2007).
    [Crossref] [PubMed]
  18. I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
    [Crossref] [PubMed]
  19. B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16(6), 4154–4162 (2008).
    [Crossref] [PubMed]
  20. M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
    [Crossref]
  21. F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
    [Crossref] [PubMed]
  22. M. C. Gower, “Industrial applications of laser micromachining,” Opt. Express 7(2), 56–67 (2000).
    [Crossref] [PubMed]
  23. T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
    [Crossref] [PubMed]
  24. C. Hnatovsky, V. G. Shvedov, N. Shostka, A. V. Rode, and W. Krolikowski, “Polarization-dependent ablation of silicon using tightly focused femtosecond laser vortex pulses,” Opt. Lett. 37(2), 226–228 (2012).
    [Crossref] [PubMed]
  25. J. J. J. Nivas, H. Shutong, K. K. Anoop, A. Rubano, R. Fittipaldi, A. Vecchione, D. Paparo, L. Marrucci, R. Bruzzese, and S. Amoruso, “Laser ablation of silicon induced by a femtosecond optical vortex beam,” Opt. Lett. 40(20), 4611–4614 (2015).
    [Crossref] [PubMed]
  26. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
    [Crossref] [PubMed]
  27. D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
    [Crossref]
  28. M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 4281 (2014).
    [Crossref] [PubMed]
  29. F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
    [Crossref]
  30. M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
    [Crossref]
  31. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56(5), 4193–4196 (1997).
    [Crossref]
  32. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
    [Crossref] [PubMed]
  33. Y. F. Chen, K. W. Su, T. H. Lu, and K. F. Huang, “Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation,” Phys. Rev. Lett. 96(3), 033905 (2006).
    [Crossref] [PubMed]
  34. A. Beržanskis, A. Matijošius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
    [Crossref]
  35. Y. Li, Z. Y. Zhou, D. S. Ding, and B. S. Shi, “Sum frequency generation with two orbital angular momentum carrying laser beams,” J. Opt. Soc. Am. B 32(3), 407–411 (2015).
    [Crossref]
  36. A. Bahabad and A. Arie, “Generation of optical vortex beams by nonlinear wave mixing,” Opt. Express 15(26), 17619–17624 (2007).
    [Crossref] [PubMed]
  37. T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
    [Crossref] [PubMed]
  38. M. Zhi, K. Wang, X. Hua, H. Schuessler, J. Strohaber, and A. V. Sokolov, “Generation of femtosecond optical vortices by molecular modulation in a Raman-active crystal,” Opt. Express 21(23), 27750–27758 (2013).
    [Crossref] [PubMed]
  39. A. J. Lee, T. Omatsu, and H. M. Pask, “Direct generation of a first-Stokes vortex laser beam from a self-Raman laser,” Opt. Express 21(10), 12401–12409 (2013).
    [Crossref] [PubMed]
  40. T. Yusufu, Y. Tokizane, M. Yamada, K. Miyamoto, and T. Omatsu, “Tunable 2-μm optical vortex parametric oscillator,” Opt. Express 20(21), 23666–23675 (2012).
    [Crossref] [PubMed]
  41. A. Abulikemu, T. Yusufu, R. Mamuti, K. Miyamoto, and T. Omatsu, “Widely-tunable vortex output from a singly resonant optical parametric oscillator,” Opt. Express 23(14), 18338–18344 (2015).
    [Crossref] [PubMed]
  42. K. Furuki, M.-T. Horikawa, A. Ogawa, K. Miyamoto, and T. Omatsu, “Tunable mid-infrared (6.3-12 μm)optical vortex pulse generation,” Opt. Express 22(21), 26351–26357 (2014).
    [Crossref] [PubMed]

2016 (3)

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
[Crossref] [PubMed]

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
[Crossref]

2015 (5)

J. J. J. Nivas, H. Shutong, K. K. Anoop, A. Rubano, R. Fittipaldi, A. Vecchione, D. Paparo, L. Marrucci, R. Bruzzese, and S. Amoruso, “Laser ablation of silicon induced by a femtosecond optical vortex beam,” Opt. Lett. 40(20), 4611–4614 (2015).
[Crossref] [PubMed]

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Y. Li, Z. Y. Zhou, D. S. Ding, and B. S. Shi, “Sum frequency generation with two orbital angular momentum carrying laser beams,” J. Opt. Soc. Am. B 32(3), 407–411 (2015).
[Crossref]

A. Abulikemu, T. Yusufu, R. Mamuti, K. Miyamoto, and T. Omatsu, “Widely-tunable vortex output from a singly resonant optical parametric oscillator,” Opt. Express 23(14), 18338–18344 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (4)

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

K. Shigematsu, Y. Toda, K. Yamane, and R. Morita, “Orbital angular momentum spectral dynamics of GaN excitons excited by optical vortices,” Jpn. J. Appl. Phys. 52(8), 08JL08 (2013).
[Crossref]

M. Zhi, K. Wang, X. Hua, H. Schuessler, J. Strohaber, and A. V. Sokolov, “Generation of femtosecond optical vortices by molecular modulation in a Raman-active crystal,” Opt. Express 21(23), 27750–27758 (2013).
[Crossref] [PubMed]

A. J. Lee, T. Omatsu, and H. M. Pask, “Direct generation of a first-Stokes vortex laser beam from a self-Raman laser,” Opt. Express 21(10), 12401–12409 (2013).
[Crossref] [PubMed]

2012 (5)

2011 (1)

I. B. Djordjevic, “Heterogeneous transparent optical networking based on coded OAM modulation,” IEEE Photonics J. 3(3), 531–537 (2011).
[Crossref]

2010 (1)

2009 (1)

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

2008 (2)

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16(6), 4154–4162 (2008).
[Crossref] [PubMed]

2007 (3)

S. Bretschneider, C. Eggeling, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy by optical shelving,” Phys. Rev. Lett. 98(21), 218103 (2007).
[Crossref] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

A. Bahabad and A. Arie, “Generation of optical vortex beams by nonlinear wave mixing,” Opt. Express 15(26), 17619–17624 (2007).
[Crossref] [PubMed]

2006 (1)

Y. F. Chen, K. W. Su, T. H. Lu, and K. F. Huang, “Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation,” Phys. Rev. Lett. 96(3), 033905 (2006).
[Crossref] [PubMed]

2005 (1)

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
[Crossref] [PubMed]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

2002 (2)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

2000 (2)

M. C. Gower, “Industrial applications of laser micromachining,” Opt. Express 7(2), 56–67 (2000).
[Crossref] [PubMed]

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[Crossref] [PubMed]

1998 (1)

A. Beržanskis, A. Matijošius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

1997 (1)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56(5), 4193–4196 (1997).
[Crossref]

1996 (2)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref] [PubMed]

K. T. Gahagan and G. A. Swartzlander., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996).
[Crossref] [PubMed]

1993 (1)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Abulikemu, A.

Ahmed, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Alexander, T. J.

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[Crossref] [PubMed]

Allen, L.

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56(5), 4193–4196 (1997).
[Crossref]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Amoruso, S.

Anoop, K. K.

Aoki, N.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
[Crossref] [PubMed]

Arie, A.

Arnold, C. B.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

Ashrafi, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Ashrafi, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Bahabad, A.

Bao, C.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Barada, D.

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

Barnett, S. M.

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Beržanskis, A.

A. Beržanskis, A. Matijošius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

Boyd, R. W.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Bretschneider, S.

S. Bretschneider, C. Eggeling, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy by optical shelving,” Phys. Rev. Lett. 98(21), 218103 (2007).
[Crossref] [PubMed]

Broekmans, O. D.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Bruzzese, R.

Buryak, A. V.

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[Crossref] [PubMed]

Cai, X.

Cao, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Chen, Y. F.

Y. F. Chen, K. W. Su, T. H. Lu, and K. F. Huang, “Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation,” Phys. Rev. Lett. 96(3), 033905 (2006).
[Crossref] [PubMed]

Chujo, K.

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56(5), 4193–4196 (1997).
[Crossref]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

De Martini, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56(5), 4193–4196 (1997).
[Crossref]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref] [PubMed]

Ding, D. S.

Djordjevic, I. B.

I. B. Djordjevic, “Heterogeneous transparent optical networking based on coded OAM modulation,” IEEE Photonics J. 3(3), 531–537 (2011).
[Crossref]

Djordjevic, S. S.

Dowling, J. P.

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
[Crossref] [PubMed]

Duocastella, M.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

Eggeling, C.

S. Bretschneider, C. Eggeling, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy by optical shelving,” Phys. Rev. Lett. 98(21), 218103 (2007).
[Crossref] [PubMed]

Farge, G.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Fittipaldi, R.

Fontaine, N. K.

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Furuki, K.

Gahagan, K. T.

Geisler, D. J.

Gower, M. C.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Harke, B.

Hell, S. W.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16(6), 4154–4162 (2008).
[Crossref] [PubMed]

S. Bretschneider, C. Eggeling, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy by optical shelving,” Phys. Rev. Lett. 98(21), 218103 (2007).
[Crossref] [PubMed]

Heller, I.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Hidai, H.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
[Crossref] [PubMed]

F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
[Crossref]

Hnatovsky, C.

Horikawa, M.-T.

Hua, X.

Huang, H.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Huang, K. F.

Y. F. Chen, K. W. Su, T. H. Lu, and K. F. Huang, “Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation,” Phys. Rev. Lett. 96(3), 033905 (2006).
[Crossref] [PubMed]

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

Juman, G.

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 4281 (2014).
[Crossref] [PubMed]

Kapale, K. T.

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
[Crossref] [PubMed]

Karimi, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Kawata, S.

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

Keller, J.

Kivshar, Y. S.

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[Crossref] [PubMed]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Krolikowski, W.

Kuhn, T.

G. F. Quinteiro and T. Kuhn, “Light-hole transitions in quantum dots: realizing full control by highly focused optical-vortex beams,” Phys. Rev. B 90(11), 115401 (2014).
[Crossref]

Lavery, M. P. J.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Lee, A. J.

Li, L.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Li, Y.

Lu, T. H.

Y. F. Chen, K. W. Su, T. H. Lu, and K. F. Huang, “Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation,” Phys. Rev. Lett. 96(3), 033905 (2006).
[Crossref] [PubMed]

Mamuti, R.

Marrucci, L.

J. J. J. Nivas, H. Shutong, K. K. Anoop, A. Rubano, R. Fittipaldi, A. Vecchione, D. Paparo, L. Marrucci, R. Bruzzese, and S. Amoruso, “Laser ablation of silicon induced by a femtosecond optical vortex beam,” Opt. Lett. 40(20), 4611–4614 (2015).
[Crossref] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Matijošius, A.

A. Beržanskis, A. Matijošius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

Menges, C.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Miatto, F. M.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Miyamoto, K.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
[Crossref] [PubMed]

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
[Crossref]

A. Abulikemu, T. Yusufu, R. Mamuti, K. Miyamoto, and T. Omatsu, “Widely-tunable vortex output from a singly resonant optical parametric oscillator,” Opt. Express 23(14), 18338–18344 (2015).
[Crossref] [PubMed]

K. Furuki, M.-T. Horikawa, A. Ogawa, K. Miyamoto, and T. Omatsu, “Tunable mid-infrared (6.3-12 μm)optical vortex pulse generation,” Opt. Express 22(21), 26351–26357 (2014).
[Crossref] [PubMed]

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 4281 (2014).
[Crossref] [PubMed]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

T. Yusufu, Y. Tokizane, M. Yamada, K. Miyamoto, and T. Omatsu, “Tunable 2-μm optical vortex parametric oscillator,” Opt. Express 20(21), 23666–23675 (2012).
[Crossref] [PubMed]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
[Crossref] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Molisch, A. F.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Morita, R.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
[Crossref] [PubMed]

F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
[Crossref]

K. Shigematsu, Y. Toda, K. Yamane, and R. Morita, “Orbital angular momentum spectral dynamics of GaN excitons excited by optical vortices,” Jpn. J. Appl. Phys. 52(8), 08JL08 (2013).
[Crossref]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
[Crossref] [PubMed]

Nagali, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Nakamura, K.

Nivas, J. J. J.

Ogawa, A.

Ohno, S.

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

Okida, M.

Omatsu, T.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
[Crossref] [PubMed]

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
[Crossref]

A. Abulikemu, T. Yusufu, R. Mamuti, K. Miyamoto, and T. Omatsu, “Widely-tunable vortex output from a singly resonant optical parametric oscillator,” Opt. Express 23(14), 18338–18344 (2015).
[Crossref] [PubMed]

K. Furuki, M.-T. Horikawa, A. Ogawa, K. Miyamoto, and T. Omatsu, “Tunable mid-infrared (6.3-12 μm)optical vortex pulse generation,” Opt. Express 22(21), 26351–26357 (2014).
[Crossref] [PubMed]

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 4281 (2014).
[Crossref] [PubMed]

A. J. Lee, T. Omatsu, and H. M. Pask, “Direct generation of a first-Stokes vortex laser beam from a self-Raman laser,” Opt. Express 21(10), 12401–12409 (2013).
[Crossref] [PubMed]

T. Yusufu, Y. Tokizane, M. Yamada, K. Miyamoto, and T. Omatsu, “Tunable 2-μm optical vortex parametric oscillator,” Opt. Express 20(21), 23666–23675 (2012).
[Crossref] [PubMed]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
[Crossref] [PubMed]

Padgett, M. J.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

M. P. J. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56(5), 4193–4196 (1997).
[Crossref]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref] [PubMed]

Paparo, D.

Pask, H. M.

Peterman, E. J. G.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Piccirillo, B.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Piskarskas, A.

A. Beržanskis, A. Matijošius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

Quinteiro, G. F.

G. F. Quinteiro and T. Kuhn, “Light-hole transitions in quantum dots: realizing full control by highly focused optical-vortex beams,” Phys. Rev. B 90(11), 115401 (2014).
[Crossref]

Ramachandran, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Ren, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Rode, A. V.

Rubano, A.

Sammut, R. A.

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[Crossref] [PubMed]

Santamato, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Schönle, A.

Schuessler, H.

Sciarrino, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Scott, R. P.

Shi, B. S.

Shigematsu, K.

K. Shigematsu, Y. Toda, K. Yamane, and R. Morita, “Orbital angular momentum spectral dynamics of GaN excitons excited by optical vortices,” Jpn. J. Appl. Phys. 52(8), 08JL08 (2013).
[Crossref]

Shostka, N.

Shutong, H.

Shvedov, V. G.

Simpson, N. B.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref] [PubMed]

Sitters, G.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Smilgevicius, V.

A. Beržanskis, A. Matijošius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

Sokolov, A. V.

Speirits, F. C.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Stabinis, A.

A. Beržanskis, A. Matijošius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

Strohaber, J.

Su, K. W.

Y. F. Chen, K. W. Su, T. H. Lu, and K. F. Huang, “Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation,” Phys. Rev. Lett. 96(3), 033905 (2006).
[Crossref] [PubMed]

Su, T.

Swartzlander, G. A.

Takahashi, F.

F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
[Crossref]

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
[Crossref] [PubMed]

Takizawa, S.

F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
[Crossref]

Toda, Y.

K. Shigematsu, Y. Toda, K. Yamane, and R. Morita, “Orbital angular momentum spectral dynamics of GaN excitons excited by optical vortices,” Jpn. J. Appl. Phys. 52(8), 08JL08 (2013).
[Crossref]

Tokizane, Y.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Toyoda, K.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Tur, M.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Ullal, C. K.

Vecchione, A.

Wang, J.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Wang, K.

Watabe, M.

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 4281 (2014).
[Crossref] [PubMed]

Wende, W.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Westphal, V.

Willner, A. E.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Wuite, G. J. L.

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Xie, G.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Yamada, M.

Yamane, K.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
[Crossref] [PubMed]

K. Shigematsu, Y. Toda, K. Yamane, and R. Morita, “Orbital angular momentum spectral dynamics of GaN excitons excited by optical vortices,” Jpn. J. Appl. Phys. 52(8), 08JL08 (2013).
[Crossref]

Yan, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Yoo, S. J. B.

Yoshida, I.

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

Yusufu, T.

Zeilinger, A.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Zhao, Z.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Zhi, M.

Zhou, Z. Y.

Adv. Opt. Photonics (1)

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Appl. Phys. Lett. (1)

D. Barada, G. Juman, I. Yoshida, K. Miyamoto, S. Kawata, S. Ohno, and T. Omatsu, “Constructive spin-orbital angular momentum coupling can twist materials to create spiral structures in optical vortex illumination,” Appl. Phys. Lett. 108(5), 051108 (2016).
[Crossref]

IEEE Photonics J. (1)

I. B. Djordjevic, “Heterogeneous transparent optical networking based on coded OAM modulation,” IEEE Photonics J. 3(3), 531–537 (2011).
[Crossref]

J. Mod. Opt. (1)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

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

Jpn. J. Appl. Phys. (1)

K. Shigematsu, Y. Toda, K. Yamane, and R. Morita, “Orbital angular momentum spectral dynamics of GaN excitons excited by optical vortices,” Jpn. J. Appl. Phys. 52(8), 08JL08 (2013).
[Crossref]

Laser Photonics Rev. (2)

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

Nano Lett. (1)

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Nat. Methods (1)

I. Heller, G. Sitters, O. D. Broekmans, G. Farge, C. Menges, W. Wende, S. W. Hell, E. J. G. Peterman, and G. J. L. Wuite, “STED nanoscopy combined with optical tweezers reveals protein dynamics on densely covered DNA,” Nat. Methods 10(9), 910–916 (2013).
[Crossref] [PubMed]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

New J. Phys. (1)

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Opt. Commun. (2)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

A. Beržanskis, A. Matijošius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

Opt. Express (10)

A. Bahabad and A. Arie, “Generation of optical vortex beams by nonlinear wave mixing,” Opt. Express 15(26), 17619–17624 (2007).
[Crossref] [PubMed]

M. Zhi, K. Wang, X. Hua, H. Schuessler, J. Strohaber, and A. V. Sokolov, “Generation of femtosecond optical vortices by molecular modulation in a Raman-active crystal,” Opt. Express 21(23), 27750–27758 (2013).
[Crossref] [PubMed]

A. J. Lee, T. Omatsu, and H. M. Pask, “Direct generation of a first-Stokes vortex laser beam from a self-Raman laser,” Opt. Express 21(10), 12401–12409 (2013).
[Crossref] [PubMed]

T. Yusufu, Y. Tokizane, M. Yamada, K. Miyamoto, and T. Omatsu, “Tunable 2-μm optical vortex parametric oscillator,” Opt. Express 20(21), 23666–23675 (2012).
[Crossref] [PubMed]

A. Abulikemu, T. Yusufu, R. Mamuti, K. Miyamoto, and T. Omatsu, “Widely-tunable vortex output from a singly resonant optical parametric oscillator,” Opt. Express 23(14), 18338–18344 (2015).
[Crossref] [PubMed]

K. Furuki, M.-T. Horikawa, A. Ogawa, K. Miyamoto, and T. Omatsu, “Tunable mid-infrared (6.3-12 μm)optical vortex pulse generation,” Opt. Express 22(21), 26351–26357 (2014).
[Crossref] [PubMed]

T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, and S. J. B. Yoo, “Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices,” Opt. Express 20(9), 9396–9402 (2012).
[Crossref] [PubMed]

B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16(6), 4154–4162 (2008).
[Crossref] [PubMed]

M. C. Gower, “Industrial applications of laser micromachining,” Opt. Express 7(2), 56–67 (2000).
[Crossref] [PubMed]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010).
[Crossref] [PubMed]

Opt. Lett. (3)

Optica (1)

Phys. Rev. A (3)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56(5), 4193–4196 (1997).
[Crossref]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Phys. Rev. B (1)

G. F. Quinteiro and T. Kuhn, “Light-hole transitions in quantum dots: realizing full control by highly focused optical-vortex beams,” Phys. Rev. B 90(11), 115401 (2014).
[Crossref]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, “Optical vortex solitons in parametric wave mixing,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(2), 2042–2049 (2000).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

S. Bretschneider, C. Eggeling, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy by optical shelving,” Phys. Rev. Lett. 98(21), 218103 (2007).
[Crossref] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
[Crossref] [PubMed]

Y. F. Chen, K. W. Su, T. H. Lu, and K. F. Huang, “Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation,” Phys. Rev. Lett. 96(3), 033905 (2006).
[Crossref] [PubMed]

Phys. Status Solidi., A Appl. Mater. Sci. (1)

F. Takahashi, S. Takizawa, H. Hidai, K. Miyamoto, R. Morita, and T. Omatsu, “Optical vortex pulse illumination to create chiral mono crystalline silicon nanostructures,” Phys. Status Solidi., A Appl. Mater. Sci. 213(4), 1063–1068 (2016).
[Crossref]

Sci. Rep. (2)

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 4281 (2014).
[Crossref] [PubMed]

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 21738 (2016).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup of the 532 nm first-order optical vortex pumped LBO OPO with a simple linear cavity configuration. (b) Self-referenced interferometry employing a transmission grating.

Fig. 2
Fig. 2

(a,c,e) Transverse beam profile and (b,d,f) self-referenced fringes of the pump, signal (900 nm), and idler (1300 nm) outputs, respectively, for a compact cavity configuration (~215 mm). (g) The temporal evolution of the pump, signal and idler outputs.

Fig. 3
Fig. 3

(a,c) Transverse beam profile and (b,d) self-referenced fringes of the signal (900 nm) and idler (1300 nm) beams, respectively, for a compact cavity configuration (~215 mm). (e,g) Transverse beam profile and (f,h) wavefronts of the signal and idler beams, respectively, for a cavity length of 315 mm. (i,k) Transverse beam profile and (j,l) self-referenced fringes of the signal and idler beams, respectively, for an extended cavity configuration (~435 mm).

Fig. 4
Fig. 4

(a,b) Transverse beam profile of the signal (960 nm) and idler (1190nm) outputs for a compact cavity configuration (~215 mm). (c,d) Transverse beam profile of the signal (960 nm) and idler (1190nm) outputs for a cavity length of 315 mm. (e,f) Transverse beam profile of the signal and idler beams, respectively, for an extended cavity configuration (~435 mm).

Fig. 5
Fig. 5

Estimated Fresnel number of the LBO OPO as a function of effective cavity length. Insets show the transverse beam profile of signal (900 nm) and idler (1300 nm) beams. The compact (extended) cavity forces the signal (idler) beam into the vortex mode.

Fig. 6
Fig. 6

Power scaling of the signal and idler from the NCPM-LBO optical cavity with (a) compact and (b) extended cavity configurations.

Fig. 7
Fig. 7

Experimentally measured tunability of the vortex signal and idler.

Fig. 8
Fig. 8

Estimated coupling loss of the cavity as a function of the lasing wavelength.

Fig. 9
Fig. 9

Spatial form of the (a) signal (a) and (b) idler beams in the region of 990–1110 nm, where a double resonance occurs in the cavity. The double resonance occurs at 1020 nm and 1110 nm.

Equations (1)

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F= a 2 Lλ

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