Abstract

An analytical model for the conversion efficiency from a TEM00 mode to an arbitrary Laguerre-Gaussian (LG) mode with null radial index spiral phase optics is presented. We extend this model to include the effects of stepped spiral phase optics, spiral phase optics of non-integer topological charge, and the reduction in conversion efficiency due to broad laser bandwidth. We find that through optimization, an optimal beam waist ratio of the input and output modes exists and is dependent upon the output azimuthal mode number.

© 2017 Optical Society of America

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References

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  7. T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
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  22. 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]
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    [Crossref]
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    [Crossref]

2017 (1)

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirrors,” Phys. Rev. Lett. 118, 033902 (2017).
[Crossref] [PubMed]

2016 (3)

T. V. Liseykina, S. V. Popruzhenko, and A. Macchi, “Inverse Faraday effect driven by radiation friction,” New J. Phys. 18, 072001 (2016).
[Crossref]

Zs. Lecz, I. V. Konoplev, A. Seryi, and A. Andreev, “GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma,” Sci. Rep. 6, 36139 (2016).
[Crossref] [PubMed]

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

2015 (3)

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (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. Photon. 7(1), 66–106 (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 (3)

J. Vieira and J. T. Mendonça, “Nonlinear laser driven donut wakefields for positron and electron acceleration,” Phys. Rev. Lett. 112, 215001 (2014).
[Crossref]

G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates,” Opt. Lett. 39, 5094–5097 (2014).
[Crossref] [PubMed]

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

2012 (4)

G. Campbell, B. Hage, B. Buchler, and P. K. Lam, “Generation of high-order optical vortices using directly machined spiral phase mirrors,” Appl. Opt. 51(7), 873–876 (2012).
[Crossref] [PubMed]

Y. Iketaki and N. Bokor, “Super-resolution microscope using a two-color phase plate for generating quasi-Laguerre-Gaussian beam,” Opt. Commun. 285(18), 3798–3804 (2012).
[Crossref]

J. T. Mendonça, “Twisted waves in a plasma,” Plasma Phys. Control. Fusion 54, 124031 (2012).
[Crossref]

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nature Phys. 8, 743–745 (2012).
[Crossref]

2011 (3)

2010 (1)

S. Ali, J. R. Davies, and J. T. Mendonça, “Inverse Faraday effect with linearly polarized laser pulses,” Phys. Rev. Lett. 105, 035001 (2010).
[Crossref] [PubMed]

2009 (2)

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref] [PubMed]

J. T. Mendonça, B. Thiede, and H. Then, “Stimulated Raman and Brillouin backscattering of collimated beams carrying orbital angular momentum,” Phys. Rev. Lett. 102, 185005 (2009).
[Crossref] [PubMed]

2008 (1)

Q. Xie and D. Zhao, “Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams,” Opt. Commun. 281, 7–11 (2008).
[Crossref]

2007 (2)

2004 (1)

1998 (1)

S. Backus, C. G. Durfee, M. M. Murname, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (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, 4713–4716 (1997).
[Crossref]

1995 (1)

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

1993 (1)

M. W. Beijersbergen, L. Allen, H.E.L.O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converotrs and transfer of orbital angular momentum,” Opt. Commun. 96(1,2,3), 123–132 (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), 8185–8190 (1992).
[Crossref] [PubMed]

Ahmed, N.

Ali, S.

S. Ali, J. R. Davies, and J. T. Mendonça, “Inverse Faraday effect with linearly polarized laser pulses,” Phys. Rev. Lett. 105, 035001 (2010).
[Crossref] [PubMed]

Allen, L.

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

M. W. Beijersbergen, L. Allen, H.E.L.O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converotrs and transfer of orbital angular momentum,” Opt. Commun. 96(1,2,3), 123–132 (1993).
[Crossref]

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), 8185–8190 (1992).
[Crossref] [PubMed]

Andreev, A.

Zs. Lecz, I. V. Konoplev, A. Seryi, and A. Andreev, “GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma,” Sci. Rep. 6, 36139 (2016).
[Crossref] [PubMed]

Ashrafi, N.

Ashrafi, S.

Backus, S.

S. Backus, C. G. Durfee, M. M. Murname, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).
[Crossref]

Bagnoud, V.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Bao, C.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H.E.L.O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converotrs and transfer of orbital angular momentum,” Opt. Commun. 96(1,2,3), 123–132 (1993).
[Crossref]

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), 8185–8190 (1992).
[Crossref] [PubMed]

Bokor, N.

Y. Iketaki and N. Bokor, “Super-resolution microscope using a two-color phase plate for generating quasi-Laguerre-Gaussian beam,” Opt. Commun. 285(18), 3798–3804 (2012).
[Crossref]

Bowman, C. N.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref] [PubMed]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nature Photon. 5, 343–348 (2011).
[Crossref]

Brabetz, C.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Buchler, B.

Busold, S.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Campbell, G.

Cao, Y.

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]

Chen, M.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Chopineau, L.

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirrors,” Phys. Rev. Lett. 118, 033902 (2017).
[Crossref] [PubMed]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Cowan, T.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Davies, J. R.

S. Ali, J. R. Davies, and J. T. Mendonça, “Inverse Faraday effect with linearly polarized laser pulses,” Phys. Rev. Lett. 105, 035001 (2010).
[Crossref] [PubMed]

Denoeud, A.

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirrors,” Phys. Rev. Lett. 118, 033902 (2017).
[Crossref] [PubMed]

Deppert, O.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Dreischuh, A.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nature Phys. 8, 743–745 (2012).
[Crossref]

Durfee, C. G.

S. Backus, C. G. Durfee, M. M. Murname, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).
[Crossref]

Esarey, E.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Ghai, D. P.

Gradshteyn, I.

I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Elsevier, 2007).

Hage, B.

Hansinger, P.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nature Phys. 8, 743–745 (2012).
[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, 4713–4716 (1997).
[Crossref]

Huang, H.

Iketaki, Y.

Y. Iketaki and N. Bokor, “Super-resolution microscope using a two-color phase plate for generating quasi-Laguerre-Gaussian beam,” Opt. Commun. 285(18), 3798–3804 (2012).
[Crossref]

Jahn, D.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Kapteyn, H. C.

S. Backus, C. G. Durfee, M. M. Murname, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).
[Crossref]

Kern, C.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nature Phys. 8, 743–745 (2012).
[Crossref]

Kester, O.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Konoplev, I. V.

Zs. Lecz, I. V. Konoplev, A. Seryi, and A. Andreev, “GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma,” Sci. Rep. 6, 36139 (2016).
[Crossref] [PubMed]

Kowalski, B. A.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref] [PubMed]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

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, 4713–4716 (1997).
[Crossref]

Lam, P. K.

Lavery, M. P. J.

Leblanc, A.

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirrors,” Phys. Rev. Lett. 118, 033902 (2017).
[Crossref] [PubMed]

Lecz, Zs.

Zs. Lecz, I. V. Konoplev, A. Seryi, and A. Andreev, “GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma,” Sci. Rep. 6, 36139 (2016).
[Crossref] [PubMed]

Li, F. Y.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Li, L.

Liseykina, T. V.

T. V. Liseykina, S. V. Popruzhenko, and A. Macchi, “Inverse Faraday effect driven by radiation friction,” New J. Phys. 18, 072001 (2016).
[Crossref]

Luo, J.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Ma, Y. Y.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Macchi, A.

T. V. Liseykina, S. V. Popruzhenko, and A. Macchi, “Inverse Faraday effect driven by radiation friction,” New J. Phys. 18, 072001 (2016).
[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]

G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates,” Opt. Lett. 39, 5094–5097 (2014).
[Crossref] [PubMed]

McLeod, R. R.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref] [PubMed]

Mendonça, J. T.

J. Vieira and J. T. Mendonça, “Nonlinear laser driven donut wakefields for positron and electron acceleration,” Phys. Rev. Lett. 112, 215001 (2014).
[Crossref]

J. T. Mendonça, “Twisted waves in a plasma,” Plasma Phys. Control. Fusion 54, 124031 (2012).
[Crossref]

S. Ali, J. R. Davies, and J. T. Mendonça, “Inverse Faraday effect with linearly polarized laser pulses,” Phys. Rev. Lett. 105, 035001 (2010).
[Crossref] [PubMed]

J. T. Mendonça, B. Thiede, and H. Then, “Stimulated Raman and Brillouin backscattering of collimated beams carrying orbital angular momentum,” Phys. Rev. Lett. 102, 185005 (2009).
[Crossref] [PubMed]

Miyaji, G.

Miyanaga, N.

Molina Terriza, G.

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

Molisch, A. F.

Murname, M. M.

S. Backus, C. G. Durfee, M. M. Murname, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).
[Crossref]

Nakatsuka, M.

Padgett, M.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nature Photon. 5, 343–348 (2011).
[Crossref]

Padgett, M. J.

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

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

Popruzhenko, S. V.

T. V. Liseykina, S. V. Popruzhenko, and A. Macchi, “Inverse Faraday effect driven by radiation friction,” New J. Phys. 18, 072001 (2016).
[Crossref]

Quéré, F.

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirrors,” Phys. Rev. Lett. 118, 033902 (2017).
[Crossref] [PubMed]

Ramachandran, S.

Ren, Y.

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]

G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates,” Opt. Lett. 39, 5094–5097 (2014).
[Crossref] [PubMed]

Roth, M.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[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]

G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates,” Opt. Lett. 39, 5094–5097 (2014).
[Crossref] [PubMed]

Ryzhik, I.

I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Elsevier, 2007).

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, 4713–4716 (1997).
[Crossref]

Scarborough, T. D.

Schroeder, C. B.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Schumacher, D.

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Scott, T. F.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref] [PubMed]

Seryi, A.

Zs. Lecz, I. V. Konoplev, A. Seryi, and A. Andreev, “GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma,” Sci. Rep. 6, 36139 (2016).
[Crossref] [PubMed]

Shen, B.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Sheng, Z. M.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Shi, Y.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

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, 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, 4713–4716 (1997).
[Crossref]

Siegman, A. E.

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

Spielmann, Ch.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nature Phys. 8, 743–745 (2012).
[Crossref]

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), 8185–8190 (1992).
[Crossref] [PubMed]

Strohaber, J.

Sueda, K.

Sullivan, A. C.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref] [PubMed]

Then, H.

J. T. Mendonça, B. Thiede, and H. Then, “Stimulated Raman and Brillouin backscattering of collimated beams carrying orbital angular momentum,” Phys. Rev. Lett. 102, 185005 (2009).
[Crossref] [PubMed]

Thiede, B.

J. T. Mendonça, B. Thiede, and H. Then, “Stimulated Raman and Brillouin backscattering of collimated beams carrying orbital angular momentum,” Phys. Rev. Lett. 102, 185005 (2009).
[Crossref] [PubMed]

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, 4713–4716 (1997).
[Crossref]

Torner, L.

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

Torres, J. P.

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

Tur, M.

Uiterwaal, C. J. G. J.

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 converotrs and transfer of orbital angular momentum,” Opt. Commun. 96(1,2,3), 123–132 (1993).
[Crossref]

Vieira, J.

J. Vieira and J. T. Mendonça, “Nonlinear laser driven donut wakefields for positron and electron acceleration,” Phys. Rev. Lett. 112, 215001 (2014).
[Crossref]

Wang, J.

Wang, W.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Weng, S. M.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Willner, A. E.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H.E.L.O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converotrs and transfer of orbital angular momentum,” Opt. Commun. 96(1,2,3), 123–132 (1993).
[Crossref]

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), 8185–8190 (1992).
[Crossref] [PubMed]

Xie, G.

Xie, Q.

Q. Xie and D. Zhao, “Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams,” Opt. Commun. 281, 7–11 (2008).
[Crossref]

Xu, Z.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Yan, Y.

Yao, A. M.

Yu, L. L.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Yu, T. P.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Zeng, M.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Zhang, G. B.

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

Zhang, L.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Zhang, X.

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Zhao, D.

Q. Xie and D. Zhao, “Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams,” Opt. Commun. 281, 7–11 (2008).
[Crossref]

Zhao, Z.

Zürch, M.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nature Phys. 8, 743–745 (2012).
[Crossref]

Adv. Opt. Photon. (2)

Appl. Opt. (3)

Nature Photon. (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nature Photon. 5, 343–348 (2011).
[Crossref]

Nature Phys. (2)

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, “Strong-field physics with singular light beams,” Nature Phys. 8, 743–745 (2012).
[Crossref]

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

New J. Phys. (1)

T. V. Liseykina, S. V. Popruzhenko, and A. Macchi, “Inverse Faraday effect driven by radiation friction,” New J. Phys. 18, 072001 (2016).
[Crossref]

Opt. Commun. (5)

Y. Iketaki and N. Bokor, “Super-resolution microscope using a two-color phase plate for generating quasi-Laguerre-Gaussian beam,” Opt. Commun. 285(18), 3798–3804 (2012).
[Crossref]

Q. Xie and D. Zhao, “Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams,” Opt. Commun. 281, 7–11 (2008).
[Crossref]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H.E.L.O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converotrs and transfer of orbital angular momentum,” Opt. Commun. 96(1,2,3), 123–132 (1993).
[Crossref]

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[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 (1)

Opt. Lett. (1)

Phys. Plasmas (2)

G. B. Zhang, M. Chen, C. B. Schroeder, J. Luo, M. Zeng, F. Y. Li, L. L. Yu, S. M. Weng, Y. Y. Ma, T. P. Yu, Z. M. Sheng, and E. Esarey, “Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse,” Phys. Plasmas 23, 033114 (2016).
[Crossref]

C. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud, “Laser-driven ion acceleration with hollow laser beams,” Phys. Plasmas 22, 013105 (2015)
[Crossref]

Phys. Rev. A (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), 8185–8190 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

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, 4713–4716 (1997).
[Crossref]

J. T. Mendonça, B. Thiede, and H. Then, “Stimulated Raman and Brillouin backscattering of collimated beams carrying orbital angular momentum,” Phys. Rev. Lett. 102, 185005 (2009).
[Crossref] [PubMed]

S. Ali, J. R. Davies, and J. T. Mendonça, “Inverse Faraday effect with linearly polarized laser pulses,” Phys. Rev. Lett. 105, 035001 (2010).
[Crossref] [PubMed]

J. Vieira and J. T. Mendonça, “Nonlinear laser driven donut wakefields for positron and electron acceleration,” Phys. Rev. Lett. 112, 215001 (2014).
[Crossref]

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirrors,” Phys. Rev. Lett. 118, 033902 (2017).
[Crossref] [PubMed]

Y. Shi, B. Shen, L. Zhang, X. Zhang, W. Wang, and Z. Xu, “Light fan driven by a relativistic laser pulse,” Phys. Rev. Lett. 112, 235001 (2014).
[Crossref] [PubMed]

Plasma Phys. Control. Fusion (1)

J. T. Mendonça, “Twisted waves in a plasma,” Plasma Phys. Control. Fusion 54, 124031 (2012).
[Crossref]

Rev. Sci. Instrum. (1)

S. Backus, C. G. Durfee, M. M. Murname, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).
[Crossref]

Sci. Rep. (1)

Zs. Lecz, I. V. Konoplev, A. Seryi, and A. Andreev, “GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma,” Sci. Rep. 6, 36139 (2016).
[Crossref] [PubMed]

Science (1)

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref] [PubMed]

Other (2)

I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Elsevier, 2007).

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

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Figures (7)

Fig. 1
Fig. 1 (a) Continuous spiral phase optic with L = 1 and P = 0 also indicating the total spiral height H. (b) 16 step spiral phase optic with L = 1 and P = 0. Both plates shown with an 800nm step height.
Fig. 2
Fig. 2 Conversion efficiency of a continuous spiral phase optic with L = 1 to the first 5 LGℓp modes. The peak of the LG10 mode is located at γ = 1 / 2 where γ is the ratio of the output beam waist to the input beam waist.
Fig. 3
Fig. 3 Conversion efficiency of a continuous spiral phase optic with charge L to the L = LG mode assuming the optimum output beam waist given by Eq. (11). Displayed are the results for the first four even modes: p = 0, 2, 4, 6 on a log-log scale.
Fig. 4
Fig. 4 Multiplicative scaling factor |ΦLN|2 as a function of the number of SSPO steps N for the L = = 1, 2, 3 cases, normalized to 4π2. As the number of steps approaches ∞, all cases approach a value of 1.
Fig. 5
Fig. 5 Multiplicative scaling factor |ΦLN|2 as a function of intrinsic topological charge of the spiral phase optic L to the LG10 mode. Inset into the image is a wider field of view showing the behavior away from ( = L = 1), note the zeros of the function at all integer charges not equal to .
Fig. 6
Fig. 6 Laguerre-Gauss mode spectrum (LGip) emanating from a continuous L = 1.2, P = 0 SPO. The azimuthal mode number i is on the x-axis, the radial mode number p is on the y-axis and the total conversion efficiency ηLℓp is displayed on the vertical z-axis on a log scale.
Fig. 7
Fig. 7 Conversion efficiency scaling factor ΦℓLNν as a function of laser bandwidth in nanometers for the case of = L and N = ∞. Four central wavelengths λ0 are plotted: 1064nm, 800nm, 532nm, 400nm.

Tables (1)

Tables Icon

Table 1 Conversion efficiencies from a TEM00 mode to various LG modes for given SPO step numbers N. The SPO carries a null radial index (P = 0) and results are shown for both L = 1 and L = 2 optics. The N = ∞ corresponds to a continuous phase optic.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

T = exp ( i L ϕ )
u p = 2 p ! π ( p + | | ) ! 1 w ( z ) [ r 2 w ( z ) ] | | exp [ r 2 w 2 ( z ) ] L p | | ( 2 r 2 w 2 ( z ) ) × exp [ i ϕ ] exp [ i k 0 r 2 z 2 ( z 2 + z R 2 ) ] exp [ i ψ ( z ) ]
L p ( x ) = n = 0 p ( 1 ) n ( p + ) ! ( p n ) ! ( + n ) ! n ! x n
η p = | u p | T | u m n | 2 = | 0 2 π 0 u p * ( r , ϕ , z ) T ( r , ϕ ) u m n ( r , ϕ , z ) r d r d ϕ | 2
u p | T | u 00 = 2 π p ! ( p + | | ) ! 1 w 0 w 1 0 2 π 0 [ r 2 w 1 ] | | exp [ r 2 ( 1 w 0 2 + 1 w 1 2 ) ] × L p | | ( 2 r 2 w 1 2 ) exp [ i ( L ) ϕ ] r d r d ϕ = R | | p Φ L
R | | p = 2 π p ! ( p + | | ) ! 2 | | 2 w 0 w 1 | | + 1 × 0 r | | + 1 exp ( β r 2 ) m = 0 p ( 1 ) m ( | | + p ) ! ( p m ) ! ( | | + m ) ! m ! 2 m r 2 m w 1 2 m d r
β = 1 w 0 2 + 1 w 1 2
0 x n exp ( a x b ) d x = 1 b a 1 / b ( n + 1 ) Γ ( n + 1 b )
Φ L = 0 2 π exp ( i ( L ) ϕ ) d ϕ = 2 π | = L
η p = | R | | p Φ = L | 2 = 2 | | + 2 p ! ( | | + p ) ! γ 2 [ m = 0 p ( 2 ) m Γ ( μ ) ( p m ) ! ( | | + m ) ! m ! ( 1 + γ 2 ) μ ] 2
γ = 1 | | + 1
T = exp [ i L ( 2 π n N ) ]
Φ L N = n = 0 N 1 2 π n / N 2 π ( n + 1 ) / N exp [ i ( ϕ L 2 π n N ) ] d ϕ
Φ L N = i N L [ exp ( i L 2 π N ) 1 ]
Φ L N = i [ exp ( i 2 π N ) 1 ] exp ( i 2 π ( L ) ) 1 exp ( i 2 π ( L ) / N ) 1
lim N Φ L N = i L [ exp ( i 2 π ( L ) ) 1 ]
T = exp [ i L ( 2 π n ν N ν 0 ) ]
| Φ L N ν | 2 = 1 σ 2 π exp [ 1 2 ( ν ν 0 σ ) 2 ] × | n = 0 N 1 2 π n / N 2 π ( n + 1 ) / N exp [ i ( ϕ L 2 π n ν N ν 0 ) ] d ϕ | 2 d ν
| Φ L N ν | 2 = 1 σ 2 π exp [ 1 2 ( ν ν 0 σ ) 2 ] × | i [ exp ( i 2 π N ) 1 ] exp ( i 2 π ( L ν ν 0 ) ) 1 exp ( i 2 π ( L ν ν 0 ) / N ) 1 | 2 d ν

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