Abstract

Dark hollow beams (DHBs) have great potential in the applications of optical manipulation, and the generation of DHBs is still a challenging and rewarding issue. In this paper, we present a beam shaping system for generating DHBs. The proposed system is composed of a freeform lens array and a non-classical zoom system which has a constant focal length but various image locations. The DHBs with a well-controlled intensity profile generated by the proposed system is not sensitive to the change of the intensity distribution of the incident beam, which allows flexible choices of light sources. Moreover, the annular pattern produced by the DHB remains unchanged when the image plane is moved a long distance of 17mm, and the energy efficiency of the beam shaping system is greater than 90% when Fresnel loss is considered. The proposed beam shaping system endows the generated DHBs with new properties and may have great potential in the field of optical tweezers and atom guides.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  26. S. P. Kotova, A. M. Mayorova, and S. A. Samagin, “Ability of a four-channel liquid-crystal modulator to generate light fields with a complex intensity distribution,” J. Opt. Technol. 84(5), 323–330 (2017).
    [Crossref]
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2017 (1)

2015 (2)

M. Massari, G. Ruffato, M. Gintoli, F. Ricci, and F. Romanato, “Fabrication and characterization of high-quality spiral phase plates for optical applications,” Appl. Opt. 54(13), 4077–4083 (2015).
[Crossref]

G. Ruffato, M. Massari, M. Carli, and F. Romanato, “Spiral phase plates with radial discontinuities for the generation of multiring orbital angular momentum beams: fabrication, characterization, and application,” Opt. Eng. 54(11), 111307 (2015).
[Crossref]

2014 (2)

A. V. Korobtsov, S. P. Kotova, N. N. Losevsky, A. M. Mayorova, and S. A. Samagin, “A. M. Mayorova1 and S. A. Samagin, “Formation of contour optical traps using a four-channel liquid crystal focusing device,” Quantum Electron. 44(12), 1157–1164 (2014).
[Crossref]

R. Wu, P. Benítez, Y. Zhang, and J. C. Miñano, “Influence of the characteristics of a light source and target on the Monge-Ampére equation method in freeform optics design,” Opt. Lett. 39(3), 634–637 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

D. Huang, H. Timmers, A. Roberts, N. Shivaram, and A. S. Sandhu, “A low-cost spatial light modulator for use in undergraduate and graduate optics labs,” Am. J. Phys. 80(3), 211–215 (2012).
[Crossref]

2010 (2)

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[Crossref]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

2006 (1)

2004 (1)

L. Zhang, X. H. Lu, X. M. Chen, and S. L. He, “Generation of a Dark Hollow Beam inside a Cavity,” Chin. Phys. Lett. 21(2), 298–301 (2004).
[Crossref]

2002 (1)

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

2001 (2)

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow beam optical trap for cold atoms,” J. Opt. B Quantum Semiclassical Opt. 3(6), 353–357 (2001).
[Crossref]

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

2000 (2)

A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1–3), 139–143 (2000).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177(1–6), 297–301 (2000).
[Crossref]

1998 (3)

J. Yin, Y. Zhu, W. Jhe, and Z. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[Crossref]

H. Rubinsztein-Dunlop, T. A. Nieminen, M. E. J. Friese, and N. R. Heckenberg, “Optical Trapping of Absorbing Particles,” Adv. Quantum Chem. 30(08), 469–492 (1998).
[Crossref]

G. A. Swartzlander and K. T. Gahagan, “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15(2), 524–534 (1998).
[Crossref]

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

1996 (2)

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43(12), 2485–2491 (1996).
[Crossref]

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

1994 (1)

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[Crossref] [PubMed]

1993 (2)

X. Wang and M. G. Littman, “Laser cavity for generation of variable-radius rings of light,” Opt. Lett. 18(10), 767–768 (1993).
[Crossref] [PubMed]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

1992 (2)

1986 (1)

Allen, L.

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43(12), 2485–2491 (1996).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

Arlt, J.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177(1–6), 297–301 (2000).
[Crossref]

Ashkin, A.

Aubin, S.

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow beam optical trap for cold atoms,” J. Opt. B Quantum Semiclassical Opt. 3(6), 353–357 (2001).
[Crossref]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

Benítez, P.

Bjorkholm, J. E.

Bongs, K.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

Brasselet, E.

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[Crossref]

Burger, S.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

Carli, M.

G. Ruffato, M. Massari, M. Carli, and F. Romanato, “Spiral phase plates with radial discontinuities for the generation of multiring orbital angular momentum beams: fabrication, characterization, and application,” Opt. Eng. 54(11), 111307 (2015).
[Crossref]

Chai, L.

Chen, X. M.

L. Zhang, X. H. Lu, X. M. Chen, and S. L. He, “Generation of a Dark Hollow Beam inside a Cavity,” Chin. Phys. Lett. 21(2), 298–301 (2004).
[Crossref]

Choi, K.

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[Crossref] [PubMed]

Christe, S.

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow beam optical trap for cold atoms,” J. Opt. B Quantum Semiclassical Opt. 3(6), 353–357 (2001).
[Crossref]

Chu, S.

Chunkan, T.

Desyatnikov, A. S.

Dettmer, S.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

Dholakia, K.

Dienerowitz, M.

Dukel’skii, K. V.

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Dziedzic, J. M.

Ertmer, W.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

Fedotov, A. B.

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Fenichel, H.

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[Crossref] [PubMed]

Friese, M. E. J.

H. Rubinsztein-Dunlop, T. A. Nieminen, M. E. J. Friese, and N. R. Heckenberg, “Optical Trapping of Absorbing Particles,” Adv. Quantum Chem. 30(08), 469–492 (1998).
[Crossref]

Gahagan, K. T.

Gintoli, M.

He, S. L.

L. Zhang, X. H. Lu, X. M. Chen, and S. L. He, “Generation of a Dark Hollow Beam inside a Cavity,” Chin. Phys. Lett. 21(2), 298–301 (2004).
[Crossref]

Heckenberg, N. R.

H. Rubinsztein-Dunlop, T. A. Nieminen, M. E. J. Friese, and N. R. Heckenberg, “Optical Trapping of Absorbing Particles,” Adv. Quantum Chem. 30(08), 469–492 (1998).
[Crossref]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221 (1992).
[Crossref] [PubMed]

Hellweg, D.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

Hu, M. L.

Huang, D.

D. Huang, H. Timmers, A. Roberts, N. Shivaram, and A. S. Sandhu, “A low-cost spatial light modulator for use in undergraduate and graduate optics labs,” Am. J. Phys. 80(3), 211–215 (2012).
[Crossref]

Izdebskaya, Y. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

Jhe, W.

J. Yin, Y. Zhu, W. Jhe, and Z. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[Crossref]

Juodkazis, S.

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[Crossref]

Kivshar, Y. S.

Kondrat’ev, Yu. N.

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Korobtsov, A. V.

A. V. Korobtsov, S. P. Kotova, N. N. Losevsky, A. M. Mayorova, and S. A. Samagin, “A. M. Mayorova1 and S. A. Samagin, “Formation of contour optical traps using a four-channel liquid crystal focusing device,” Quantum Electron. 44(12), 1157–1164 (2014).
[Crossref]

Kotova, S. P.

S. P. Kotova, A. M. Mayorova, and S. A. Samagin, “Ability of a four-channel liquid-crystal modulator to generate light fields with a complex intensity distribution,” J. Opt. Technol. 84(5), 323–330 (2017).
[Crossref]

A. V. Korobtsov, S. P. Kotova, N. N. Losevsky, A. M. Mayorova, and S. A. Samagin, “A. M. Mayorova1 and S. A. Samagin, “Formation of contour optical traps using a four-channel liquid crystal focusing device,” Quantum Electron. 44(12), 1157–1164 (2014).
[Crossref]

Krauss, T. F.

Krolikowski, W.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

Kulin, S.

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow beam optical trap for cold atoms,” J. Opt. B Quantum Semiclassical Opt. 3(6), 353–357 (2001).
[Crossref]

Lee, H. S.

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[Crossref] [PubMed]

Li, H.

Li, Y. F.

Littman, M. G.

Liu, P.

Liu, X.

Losevsky, N. N.

A. V. Korobtsov, S. P. Kotova, N. N. Losevsky, A. M. Mayorova, and S. A. Samagin, “A. M. Mayorova1 and S. A. Samagin, “Formation of contour optical traps using a four-channel liquid crystal focusing device,” Quantum Electron. 44(12), 1157–1164 (2014).
[Crossref]

Lu, X. H.

L. Zhang, X. H. Lu, X. M. Chen, and S. L. He, “Generation of a Dark Hollow Beam inside a Cavity,” Chin. Phys. Lett. 21(2), 298–301 (2004).
[Crossref]

Malinauskas, M.

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[Crossref]

Massari, M.

G. Ruffato, M. Massari, M. Carli, and F. Romanato, “Spiral phase plates with radial discontinuities for the generation of multiring orbital angular momentum beams: fabrication, characterization, and application,” Opt. Eng. 54(11), 111307 (2015).
[Crossref]

M. Massari, G. Ruffato, M. Gintoli, F. Ricci, and F. Romanato, “Fabrication and characterization of high-quality spiral phase plates for optical applications,” Appl. Opt. 54(13), 4077–4083 (2015).
[Crossref]

Mayorova, A. M.

S. P. Kotova, A. M. Mayorova, and S. A. Samagin, “Ability of a four-channel liquid-crystal modulator to generate light fields with a complex intensity distribution,” J. Opt. Technol. 84(5), 323–330 (2017).
[Crossref]

A. V. Korobtsov, S. P. Kotova, N. N. Losevsky, A. M. Mayorova, and S. A. Samagin, “A. M. Mayorova1 and S. A. Samagin, “Formation of contour optical traps using a four-channel liquid crystal focusing device,” Quantum Electron. 44(12), 1157–1164 (2014).
[Crossref]

Mazilu, M.

McDuff, R.

Miñano, J. C.

Nieminen, T. A.

H. Rubinsztein-Dunlop, T. A. Nieminen, M. E. J. Friese, and N. R. Heckenberg, “Optical Trapping of Absorbing Particles,” Adv. Quantum Chem. 30(08), 469–492 (1998).
[Crossref]

O’Neil, A. T.

A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1–3), 139–143 (2000).
[Crossref]

Orozco, L. A.

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow beam optical trap for cold atoms,” J. Opt. B Quantum Semiclassical Opt. 3(6), 353–357 (2001).
[Crossref]

Padgett, M. J.

A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1–3), 139–143 (2000).
[Crossref]

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43(12), 2485–2491 (1996).
[Crossref]

Peker, B.

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow beam optical trap for cold atoms,” J. Opt. B Quantum Semiclassical Opt. 3(6), 353–357 (2001).
[Crossref]

Reece, P. J.

Ricci, F.

Roberts, A.

D. Huang, H. Timmers, A. Roberts, N. Shivaram, and A. S. Sandhu, “A low-cost spatial light modulator for use in undergraduate and graduate optics labs,” Am. J. Phys. 80(3), 211–215 (2012).
[Crossref]

Rode, A. V.

Rolston, S. L.

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow beam optical trap for cold atoms,” J. Opt. B Quantum Semiclassical Opt. 3(6), 353–357 (2001).
[Crossref]

Romanato, F.

G. Ruffato, M. Massari, M. Carli, and F. Romanato, “Spiral phase plates with radial discontinuities for the generation of multiring orbital angular momentum beams: fabrication, characterization, and application,” Opt. Eng. 54(11), 111307 (2015).
[Crossref]

M. Massari, G. Ruffato, M. Gintoli, F. Ricci, and F. Romanato, “Fabrication and characterization of high-quality spiral phase plates for optical applications,” Appl. Opt. 54(13), 4077–4083 (2015).
[Crossref]

Rubinsztein-Dunlop, H.

H. Rubinsztein-Dunlop, T. A. Nieminen, M. E. J. Friese, and N. R. Heckenberg, “Optical Trapping of Absorbing Particles,” Adv. Quantum Chem. 30(08), 469–492 (1998).
[Crossref]

Ruffato, G.

G. Ruffato, M. Massari, M. Carli, and F. Romanato, “Spiral phase plates with radial discontinuities for the generation of multiring orbital angular momentum beams: fabrication, characterization, and application,” Opt. Eng. 54(11), 111307 (2015).
[Crossref]

M. Massari, G. Ruffato, M. Gintoli, F. Ricci, and F. Romanato, “Fabrication and characterization of high-quality spiral phase plates for optical applications,” Appl. Opt. 54(13), 4077–4083 (2015).
[Crossref]

Samagin, S. A.

S. P. Kotova, A. M. Mayorova, and S. A. Samagin, “Ability of a four-channel liquid-crystal modulator to generate light fields with a complex intensity distribution,” J. Opt. Technol. 84(5), 323–330 (2017).
[Crossref]

A. V. Korobtsov, S. P. Kotova, N. N. Losevsky, A. M. Mayorova, and S. A. Samagin, “A. M. Mayorova1 and S. A. Samagin, “Formation of contour optical traps using a four-channel liquid crystal focusing device,” Quantum Electron. 44(12), 1157–1164 (2014).
[Crossref]

Sandhu, A. S.

D. Huang, H. Timmers, A. Roberts, N. Shivaram, and A. S. Sandhu, “A low-cost spatial light modulator for use in undergraduate and graduate optics labs,” Am. J. Phys. 80(3), 211–215 (2012).
[Crossref]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

Sengstock, K.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

Serebryannikov, E. E.

Shevandin, V. S.

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

Shivaram, N.

D. Huang, H. Timmers, A. Roberts, N. Shivaram, and A. S. Sandhu, “A low-cost spatial light modulator for use in undergraduate and graduate optics labs,” Am. J. Phys. 80(3), 211–215 (2012).
[Crossref]

Shvedov, V. G.

Simpson, N. B.

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43(12), 2485–2491 (1996).
[Crossref]

Smirnov, V. B.

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Smith, C. P.

Song, Y. J.

Stewart, B. W.

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[Crossref] [PubMed]

Swartzlander, G. A.

Tarasevitch, A. P.

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Timmers, H.

D. Huang, H. Timmers, A. Roberts, N. Shivaram, and A. S. Sandhu, “A low-cost spatial light modulator for use in undergraduate and graduate optics labs,” Am. J. Phys. 80(3), 211–215 (2012).
[Crossref]

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

von der Linde, D.

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Wang, C. Y.

Wang, X.

Wang, Z.

J. Yin, Y. Zhu, W. Jhe, and Z. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[Crossref]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

Wu, R.

Yin, J.

J. Yin, Y. Zhu, W. Jhe, and Z. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[Crossref]

Zhang, L.

L. Zhang, X. H. Lu, X. M. Chen, and S. L. He, “Generation of a Dark Hollow Beam inside a Cavity,” Chin. Phys. Lett. 21(2), 298–301 (2004).
[Crossref]

Zhang, Y.

Zheltikov, A. M.

M. L. Hu, C. Y. Wang, Y. J. Song, Y. F. Li, L. Chai, E. E. Serebryannikov, and A. M. Zheltikov, “A hollow beam from a holey fiber,” Opt. Express 14(9), 4128–4134 (2006).
[Crossref] [PubMed]

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Zheng, Z.

Zhou, P.

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Zhu, Y.

J. Yin, Y. Zhu, W. Jhe, and Z. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[Crossref]

Žukauskas, A.

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[Crossref]

Adv. Quantum Chem. (1)

H. Rubinsztein-Dunlop, T. A. Nieminen, M. E. J. Friese, and N. R. Heckenberg, “Optical Trapping of Absorbing Particles,” Adv. Quantum Chem. 30(08), 469–492 (1998).
[Crossref]

Am. J. Phys. (1)

D. Huang, H. Timmers, A. Roberts, N. Shivaram, and A. S. Sandhu, “A low-cost spatial light modulator for use in undergraduate and graduate optics labs,” Am. J. Phys. 80(3), 211–215 (2012).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[Crossref]

Chin. Phys. Lett. (1)

L. Zhang, X. H. Lu, X. M. Chen, and S. L. He, “Generation of a Dark Hollow Beam inside a Cavity,” Chin. Phys. Lett. 21(2), 298–301 (2004).
[Crossref]

J. Mod. Opt. (1)

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43(12), 2485–2491 (1996).
[Crossref]

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

S. Kulin, S. Aubin, S. Christe, B. Peker, S. L. Rolston, and L. A. Orozco, “A single hollow beam optical trap for cold atoms,” J. Opt. B Quantum Semiclassical Opt. 3(6), 353–357 (2001).
[Crossref]

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

J. Opt. Technol. (1)

J. Raman Spectrosc. (1)

A. B. Fedotov, P. Zhou, A. P. Tarasevitch, K. V. Dukel’skii, Yu. N. Kondrat’ev, V. S. Shevandin, V. B. Smirnov, D. von der Linde, and A. M. Zheltikov, “Microstructure-fiber sources of mode-separable supercontinuum emission for wave-mixing spectroscopy,” J. Raman Spectrosc. 33(11–12), 888–895 (2002).
[Crossref]

Opt. Commun. (3)

A. T. O’Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185(1–3), 139–143 (2000).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177(1–6), 297–301 (2000).
[Crossref]

Opt. Eng. (1)

G. Ruffato, M. Massari, M. Carli, and F. Romanato, “Spiral phase plates with radial discontinuities for the generation of multiring orbital angular momentum beams: fabrication, characterization, and application,” Opt. Eng. 54(11), 111307 (2015).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. A (3)

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[Crossref] [PubMed]

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “A Waveguide for bose-einstein condensates,” Phys. Rev. A 63(3), 031602 (2001).
[Crossref]

J. Yin, Y. Zhu, W. Jhe, and Z. Wang, “Atom guiding and cooling in a dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[Crossref]

Phys. Rev. Lett. (2)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel Optical Trap of Atoms with a Doughnut Beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[Crossref] [PubMed]

Quantum Electron. (1)

A. V. Korobtsov, S. P. Kotova, N. N. Losevsky, A. M. Mayorova, and S. A. Samagin, “A. M. Mayorova1 and S. A. Samagin, “Formation of contour optical traps using a four-channel liquid crystal focusing device,” Quantum Electron. 44(12), 1157–1164 (2014).
[Crossref]

Other (2)

J. M. Geary, Introduction to lens design: with practical ZEMAX examples (Richmond: Willmann-Bell, 2002), Chap. 4.

G. H. Smith, Practical Computer-Aided Lens Design (Richmond: Willmann-Bell, 1998), Chap. A.6.12.

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Figures (16)

Fig. 1
Fig. 1 Schematic layout of the proposed beam shaping system.
Fig. 2
Fig. 2 The design of the freeform lens unit.
Fig. 3
Fig. 3 Illustration of Ω0 and Ω1.
Fig. 4
Fig. 4 Discretization of Ω0 and the treatment of the boundary condition 2.
Fig. 5
Fig. 5 Schematic layout of the non-classical zoom system
Fig. 6
Fig. 6 (a) The normalized intensity distribution of the incident collimated beam, and (b) the xoz profile of the exit surface of the lens unit.
Fig. 7
Fig. 7 Optical configurations of the non-classical zoom system at the three zoom positions.
Fig. 8
Fig. 8 Three-dimensional model of the beam shaping system.
Fig. 9
Fig. 9 Performance of the freeform lens unit. (a) The annular illumination pattern produced by the lens unit at the center of the freeform lens array at zoom position 1, and (b) the piercing points of the sampled incident rays on the image plane at zoom position 1.
Fig. 10
Fig. 10 The normalized illuminance along the lines x = 0 mm produced by the lens array for r1 = 30 μm, r2 = 0.4 mm at the three zoom positions. The global coordinate system is placed at the entrance surface of freeform lens array. Then, we know that the z-coordinates of the image plane at three zoom positions equal 150.00mm, 157.49mm and 164.36mm.
Fig. 11
Fig. 11 The annular illumination pattern remains unchanged when the image plane is moved. (a) The change of the spot size and (b) the illuminance distributions along the line x = 0 mm obtained at z = 154.50mm, 160.00mm and 167.00mm.
Fig. 12
Fig. 12 Normalized illuminance profile (r1 = 10μm, r2 = 0.2mm) along the line x = 0 mm obtained with a zoom system of spot radius (a) 3μm, (b) 6μm, and (c) 20μm.
Fig. 13
Fig. 13 The relationship between the uniformity of the illumination pattern and the aperture size of the lens unit.
Fig. 14
Fig. 14 The normalized illuminance distributions along the lines x = 0mm produced by the beam shaping system for r1 = 0.02 mm, r2 = 0.2mm at the three zoom positions (z = 150.00mm, 157.49mm and 164.36mm).
Fig. 15
Fig. 15 The normalized illuminance distribution along the line x = 0mm produced by the beam shaping system. The aperture size of the lens unit equals 4mm × 4mm and the other design parameters are kept unchanged.
Fig. 16
Fig. 16 The influence of diffraction effect on the performance of the proposed beam shaping system.

Tables (3)

Tables Icon

Table 1 Design parameters.

Tables Icon

Table 2 Parameters of the non-classical zoom system at Zoom position 1.

Tables Icon

Table 3 Three zoom positions of the non-classical zoom system.

Equations (20)

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N= 1 z x 2 + z y 2 +1 ( z x , z y ,1)
Ο=nI+pN
O= 1 ( z x 2 + z y 2 +1) ( O x , O y , O z )
{ O x = z x [ a (z x 2 + z y 2 )+1 n] O y = z y [ a (z x 2 + z y 2 )+1 n] O z =n( z x 2 + z y 2 )+ a (z x 2 + z y 2 )+1 ,wherea=1 n 2
t x =f× O x O z , t y =f× O y O z
E( t x , t y )| J( T ) |I( x,y )=0
A 1 ( z xx z yy z xy 2 ) I( x,y ) E( t x , t y ) =0
Boundary condition 1: t x 2 + t y 2 r 2 2 =0
Boundary condition 2: t x 2 + t y 2 r 1 2 =0
t xk = r 1 ×cos[ π 4 ( k1 ) ] and t yk = r 1 ×sin[ π 4 ( k1 ) ], ( k=1,...,8 )
f× O xk O zk t xk =0 and f× O yk O zk t yk =0, ( k=1,...,8 )
z x (k=1)= z( m/2 +2,m/2 )+4z( m/2 +1,m/2 )3z( m/2 ,m/2 ) 2h
z u = z( m/2 +2,m/2 +2 )+4z( m/2 +1,m/2 +1 )3zm/2 ,m/2 2 2 h , z v =0
{ z u = z x cosθ+ z y sinθ z v = z x cos( θ+ π 2 )+ z y sin( θ+ π 2 )
{ z x ( k=2 )= z(m/2 +2,m/2 +2)+4z(m/2 +1,m/2 +1)3z(m/2 ,m/2 ) 4h z y ( k=2 )= z(m/2 +2,m/2 +2)+4z(m/2 +1,m/2 +1)3z(m/2 ,m/2 ) 4h
u i = u i1 y i Φ i and y i+1 = y i + u i d i ,(i=1,2,3)
{ u 1 = y 1 Φ 1 , y 2 = y 1 + u 1 d 1 u 2 = u 1 y 2 Φ 2 , y 3 = y 2 + u 2 d 2 u 3 = u 2 y 3 Φ 3 , y 4 = y 3 + u 3 d 3
Φ=( Φ 1 + Φ 2 d 1 Φ 1 Φ 2 )+[ 1 d 1 Φ 1 d 2 ( Φ 1 + Φ 2 d 1 Φ 1 Φ 2 ) ] Φ 3
d 3 = 1 Φ 1 d 1 ( Φ 1 + Φ 2 d 1 Φ 1 Φ 2 ) d 2 Φ
RSD= 1 M1 k1=1 M ( E k1 E 0 1) 2

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