Abstract

This paper describes the first demonstration of ultraviolet (266nm) vortex generation using the combination of a frequency-doubled nanosecond green laser, a spiral phase plate, and a periodically bonded β-BaB2O4 device. For a laser pumping energy of 9.1 mJ, an ultraviolet vortex energy of 1.24 mJ was obtained, corresponding to a conversion efficiency of 13.7%.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. K. Hara, S. Matsumoto, T. Onda, W. Nagashima, I. Shoji, “Efficient ultraviolet second-harmonic generation from a walk-off-compensating β-BaB2O4 device with a new structure fabricated by room-temperature bonding,” Appl. Phys. Express 5(5), 052201 (2012).
    [CrossRef]
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    [CrossRef]
  27. A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1-6), 372–380 (1998).
    [CrossRef]
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    [CrossRef]

2014 (1)

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

2013 (4)

S. M. Li, L. J. Kong, Z. C. Ren, Y. Li, C. Tu, H. T. Wang, “Managing orbital angular momentum in second-harmonic generation,” Phys. Rev. A 88(3), 035801 (2013).
[CrossRef]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[CrossRef]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[CrossRef] [PubMed]

2012 (2)

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

K. Hara, S. Matsumoto, T. Onda, W. Nagashima, I. Shoji, “Efficient ultraviolet second-harmonic generation from a walk-off-compensating β-BaB2O4 device with a new structure fabricated by room-temperature bonding,” Appl. Phys. Express 5(5), 052201 (2012).
[CrossRef]

2011 (3)

2010 (1)

2009 (2)

2008 (1)

2007 (1)

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

2005 (1)

C. Chen, Z. Lin, Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80(1), 1–25 (2005).
[CrossRef]

2004 (1)

M. Padgett, J. Courtial, L. Allen, “Light’s orbital angular momentum,” Phys. Today 57(5), 35–40 (2004).
[CrossRef]

2003 (1)

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

2002 (1)

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

2001 (1)

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

1998 (1)

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1-6), 372–380 (1998).
[CrossRef]

1996 (1)

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

1993 (1)

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

1992 (3)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, 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]

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: Tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

T. Suga, Y. Takahashi, H. Takagi, B. Gibbesch, G. Elssner, “Structure of Al-Al and Al-Si3N4 interfaces bonded at room temperature by means of the surface activation method,” Acta Metall. Mater. 40, S133–S137 (1992).
[CrossRef]

1989 (1)

Adachi, S.

Allen, L.

M. Padgett, J. Courtial, L. Allen, “Light’s orbital angular momentum,” Phys. Today 57(5), 35–40 (2004).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, 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, 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]

Aoki, N.

Arita, Y.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, 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]

Berzanskis, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1-6), 372–380 (1998).
[CrossRef]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: Tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Chen, C.

C. Chen, Z. Lin, Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80(1), 1–25 (2005).
[CrossRef]

C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, S. Lin, “New nonlinear-optical crystal: LiB3O5,” J. Opt. Soc. Am. B 6(4), 616–621 (1989).
[CrossRef]

Chen, M.

Chujo, K.

Courtial, J.

M. Padgett, J. Courtial, L. Allen, “Light’s orbital angular momentum,” Phys. Today 57(5), 35–40 (2004).
[CrossRef]

Curtis, J. E.

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

David, C.

Dholakia, K.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[CrossRef] [PubMed]

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

Ekinci, Y.

Elssner, G.

T. Suga, Y. Takahashi, H. Takagi, B. Gibbesch, G. Elssner, “Structure of Al-Al and Al-Si3N4 interfaces bonded at room temperature by means of the surface activation method,” Acta Metall. Mater. 40, S133–S137 (1992).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: Tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Gibbesch, B.

T. Suga, Y. Takahashi, H. Takagi, B. Gibbesch, G. Elssner, “Structure of Al-Al and Al-Si3N4 interfaces bonded at room temperature by means of the surface activation method,” Acta Metall. Mater. 40, S133–S137 (1992).
[CrossRef]

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, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[CrossRef]

Guzenko, V. A.

Hara, K.

K. Hara, S. Matsumoto, T. Onda, W. Nagashima, I. Shoji, “Efficient ultraviolet second-harmonic generation from a walk-off-compensating β-BaB2O4 device with a new structure fabricated by room-temperature bonding,” Appl. Phys. Express 5(5), 052201 (2012).
[CrossRef]

Harke, B.

Hell, S. W.

Hirose, T.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Indebetouw, G.

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

Jiang, A.

Juman, G.

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

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: Tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Keller, J.

Kong, L. J.

S. M. Li, L. J. Kong, Z. C. Ren, Y. Li, C. Tu, H. T. Wang, “Managing orbital angular momentum in second-harmonic generation,” Phys. Rev. A 88(3), 035801 (2013).
[CrossRef]

Koss, B. A.

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

Koyama, M.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Langner, A.

Li, R.

Li, S. M.

S. M. Li, L. J. Kong, Z. C. Ren, Y. Li, C. Tu, H. T. Wang, “Managing orbital angular momentum in second-harmonic generation,” Phys. Rev. A 88(3), 035801 (2013).
[CrossRef]

Li, Y.

S. M. Li, L. J. Kong, Z. C. Ren, Y. Li, C. Tu, H. T. Wang, “Managing orbital angular momentum in second-harmonic generation,” Phys. Rev. A 88(3), 035801 (2013).
[CrossRef]

Lin, S.

Lin, Z.

C. Chen, Z. Lin, Z. Wang, “The development of new borate-based UV nonlinear optical crystals,” Appl. Phys. B 80(1), 1–25 (2005).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: Tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Matijosius, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1-6), 372–380 (1998).
[CrossRef]

Matsumoto, S.

K. Hara, S. Matsumoto, T. Onda, W. Nagashima, I. Shoji, “Efficient ultraviolet second-harmonic generation from a walk-off-compensating β-BaB2O4 device with a new structure fabricated by room-temperature bonding,” Appl. Phys. Express 5(5), 052201 (2012).
[CrossRef]

Mazilu, M.

Miyamoto, K.

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

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[CrossRef]

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

M. Koyama, T. Hirose, M. Okida, K. Miyamoto, T. Omatsu, “Power scaling of a picosecond vortex laser based on a stressed Yb-doped fiber amplifier,” Opt. Express 19(2), 994–999 (2011).
[CrossRef] [PubMed]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-17967 .
[CrossRef] [PubMed]

Molina-Terriza, G.

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

Morita, R.

Nagashima, W.

K. Hara, S. Matsumoto, T. Onda, W. Nagashima, I. Shoji, “Efficient ultraviolet second-harmonic generation from a walk-off-compensating β-BaB2O4 device with a new structure fabricated by room-temperature bonding,” Appl. Phys. Express 5(5), 052201 (2012).
[CrossRef]

Nakamura, K.

Oka, K.

Okida, M.

Omatsu, T.

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

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[CrossRef]

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

M. Koyama, T. Hirose, M. Okida, K. Miyamoto, T. Omatsu, “Power scaling of a picosecond vortex laser based on a stressed Yb-doped fiber amplifier,” Opt. Express 19(2), 994–999 (2011).
[CrossRef] [PubMed]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-17967 .
[CrossRef] [PubMed]

Onda, T.

K. Hara, S. Matsumoto, T. Onda, W. Nagashima, I. Shoji, “Efficient ultraviolet second-harmonic generation from a walk-off-compensating β-BaB2O4 device with a new structure fabricated by room-temperature bonding,” Appl. Phys. Express 5(5), 052201 (2012).
[CrossRef]

Padgett, M.

M. Padgett, J. Courtial, L. Allen, “Light’s orbital angular momentum,” Phys. Today 57(5), 35–40 (2004).
[CrossRef]

Padgett, M. J.

A. M. Yao, M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon 3(2), 161–204 (2011).
[CrossRef]

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

Päivänranta, B.

Piskarskas, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1-6), 372–380 (1998).
[CrossRef]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Ren, Z. C.

S. M. Li, L. J. Kong, Z. C. Ren, Y. Li, C. Tu, H. T. Wang, “Managing orbital angular momentum in second-harmonic generation,” Phys. Rev. A 88(3), 035801 (2013).
[CrossRef]

Schönle, A.

Shimatake, K.

Shoji, I.

K. Hara, S. Matsumoto, T. Onda, W. Nagashima, I. Shoji, “Efficient ultraviolet second-harmonic generation from a walk-off-compensating β-BaB2O4 device with a new structure fabricated by room-temperature bonding,” Appl. Phys. Express 5(5), 052201 (2012).
[CrossRef]

Simpson, N. B.

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

Smilgevicius, V.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1-6), 372–380 (1998).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, 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. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1-6), 372–380 (1998).
[CrossRef]

Suga, T.

T. Suga, Y. Takahashi, H. Takagi, B. Gibbesch, G. Elssner, “Structure of Al-Al and Al-Si3N4 interfaces bonded at room temperature by means of the surface activation method,” Acta Metall. Mater. 40, S133–S137 (1992).
[CrossRef]

Takagi, H.

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K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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Nat. Phys. (1)

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

Nature (2)

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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Phys. Rev. Lett. (1)

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, T. Omatsu, “Transfer of Light Helicity to Nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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M. Watabe, G. Juman, K. Miyamoto, T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci Rep 4, 4281 (2014).
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Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
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Figures (5)

Fig. 1
Fig. 1

Simulated spatial profile for the frequency-doubled UV vortex output from (a) a 0.5-mm-long bulk BBO crystal, (b) a 2-mm-long bulk BBO crystal, and (c) 2-mm-long periodically bonded BBO device, shown schematically in (d).

Fig. 2
Fig. 2

Experimental setup used to produce UV vortices.

Fig. 3
Fig. 3

Experimental vortex outputs. (a), (b) Near- and far-field intensity profiles for a green vortex, and (c) self-interference fringes in the near field. (d), (e) Near- and far-field intensity profiles for the UV output from a 2-mm-long bulk BBO crystal, and (f) self-interference fringes. (g), (h) Near- and far-field intensity profiles for the UV output from a 2-mm-long periodically bonded BBO device, and (i) self-interference fringes in the near field.

Fig. 4
Fig. 4

Line-intensity profiles (along a broken line shown in Figs. 3(f) and 3(i)) of the UV outputs obtained by using (a) the bulk BBO crystal, and the periodically bonded BBO device.

Fig. 5
Fig. 5

(a) UV vortex output energy as a function of the green vortex energy. (b) UV vortex conversion efficiency as a function of the green vortex energy.

Equations (3)

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E 2 ω bulk ( x , y ) = 0 L ( E ω ( x , y + ρ z ) ) 2 d z = 0 L [ ( x + i ( y + ρ z ) ) exp ( x 2 + ( y + ρ z ) 2 ω 0 2 ) ] 2 d z ,
I 2 ω bulk ( x , y ) | E 2 ω bulk ( x , y ) | 2 .
I 2ω device (x,y)= | n=0 N1 nΛ (n+1)Λ [ ( x+i( y+ρz ) )exp( x 2 + ( y+ρz ) 2 ω 0 2 ) ] 2 dz | 2 ,

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