Abstract

Polarization and spatial phase are independent characteristics for the linearly-polarized plane light wave. These characteristics can be coupled when the light field has an inhomogeneous polarization state in space and time. Inhomogeneous polarization appears in the vector beam. The polarization-phase coupling takes place by introducing the orbital angular momentum to the vector beam. In this paper, the polarization-phase coupling in the vector orbital angular momentum beam has been examined. The polarization-phase coupling induces Laguerre-Gaussian modes with different orders, and the resultant electric field is a superposition of induced Laguerre-Gaussian modes. The analytical expressions for the resultant electric fields have been derived under the paraxial approximation and confirmed by numerical calculation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

2017 (4)

L. Du, Z. Man, Y. Zhang, C. Min, S. Zhu, and X. Yuan, “Manipulating orbital angular momentum of light with tailored in-plane polarization states,” Sci. Rep. 7(1), 41001 (2017).
[Crossref]

M. A. Alonso and M. R. Dennis, “Ray-optical Poincare sphere for structured Gaussian beams,” Optica 4(4), 476–486 (2017).
[Crossref]

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirror,” Phys. Rev. Lett. 118(3), 033902 (2017).
[Crossref]

2016 (4)

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

V. Petrillo, G. Dattoli, I. Drebot, and F. Nguyen, “Compton scattering Gamma rays with orbital momentum,” Phys. Rev. Lett. 117(12), 123903 (2016).
[Crossref]

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularities in tailored vector beams,” J. Opt. 18(7), 074012 (2016).
[Crossref]

2015 (3)

2013 (2)

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

D. J. Kim, J. W. Kim, and W. A. Clarkson, “Q-switched Nd:YAG optical vortex lasers,” Opt. Express 21(24), 29449–29454 (2013).
[Crossref]

2011 (3)

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

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Broadband anisotropy of femtosecond laser induced nanogratings in fused silica,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincare sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref]

2010 (3)

2005 (1)

2000 (1)

1996 (1)

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(5-6), 321–327 (1994).
[Crossref]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[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), 8185–8189 (1992).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[Crossref]

1939 (1)

J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56(1), 99–107 (1939).
[Crossref]

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincare sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref]

Allen, L.

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]

Alonso, M. A.

Alpmann, C.

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularities in tailored vector beams,” J. Opt. 18(7), 074012 (2016).
[Crossref]

Alves, E. P.

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

April, A.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Arissian, L.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Barwick, B.

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(5-6), 321–327 (1994).
[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), 8185–8189 (1992).
[Crossref]

Beresna, M.

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Broadband anisotropy of femtosecond laser induced nanogratings in fused silica,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Bingham, R.

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

Bouchard, F.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Boyadjiev, L.

S. P. Mirevski and L. Boyadjiev, “On some fractional generalizations of the Laguerre polynomials and the Kummer function,” Comput. Math. Appl. 59(3), 1271–1277 (2010).
[Crossref]

Boyd, R. W.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Brabec, T.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Brown, G. G.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Brown, T. G.

Bulanov, S.

Cerjan, A.

Cerjan, C.

Chopineau, L.

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirror,” Phys. Rev. Lett. 118(3), 033902 (2017).
[Crossref]

Chu, L.

J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56(1), 99–107 (1939).
[Crossref]

Clarkson, W. A.

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(5-6), 321–327 (1994).
[Crossref]

Corkum, P. B.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Dattoli, G.

V. Petrillo, G. Dattoli, I. Drebot, and F. Nguyen, “Compton scattering Gamma rays with orbital momentum,” Phys. Rev. Lett. 117(12), 123903 (2016).
[Crossref]

Dennis, M. R.

Denoeud, A.

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirror,” Phys. Rev. Lett. 118(3), 033902 (2017).
[Crossref]

Denz, C.

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularities in tailored vector beams,” J. Opt. 18(7), 074012 (2016).
[Crossref]

Drebot, I.

V. Petrillo, G. Dattoli, I. Drebot, and F. Nguyen, “Compton scattering Gamma rays with orbital momentum,” Phys. Rev. Lett. 117(12), 123903 (2016).
[Crossref]

Du, L.

L. Du, Z. Man, Y. Zhang, C. Min, S. Zhu, and X. Yuan, “Manipulating orbital angular momentum of light with tailored in-plane polarization states,” Sci. Rep. 7(1), 41001 (2017).
[Crossref]

Fonseca, R. A.

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

Fortin, P.-L.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Fourmaux, S.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Gahagan, K. T.

Gecevicius, M.

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Broadband anisotropy of femtosecond laser induced nanogratings in fused silica,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Gertus, T.

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Broadband anisotropy of femtosecond laser induced nanogratings in fused silica,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Gradshteyn, I.S.

I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007), Eq. 6.631.

Hammond, T. J.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Handali, J.

Heckenberg, N. R.

Jeong, T. M.

Karimi, E.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Kazansky, P. G.

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Broadband anisotropy of femtosecond laser induced nanogratings in fused silica,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Kieffer, J.-C.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Kim, D. J.

Kim, J. W.

Ko, D. H.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Kong, F.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Korn, G.

Korneev, P.

R. Nuter, P. Korneev, I. Thiele, and V. Tikhonchuk, “Plasma solenoid driven by a laser carrying an orbital angular momentum,” Phys. Rev. E 98(3), 033211 (2018).
[Crossref]

Kotlyar, V.

Kovalev, A.

Kozawa, Y.

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(5-6), 321–327 (1994).
[Crossref]

Le Garrec, B.

Leblanc, A.

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirror,” Phys. Rev. Lett. 118(3), 033902 (2017).
[Crossref]

Legare, F.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Li, Z.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Man, Z.

L. Du, Z. Man, Y. Zhang, C. Min, S. Zhu, and X. Yuan, “Manipulating orbital angular momentum of light with tailored in-plane polarization states,” Sci. Rep. 7(1), 41001 (2017).
[Crossref]

Marceau, V.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Margarone, D.

McDuff, R.

Mendonca, J. T.

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

Milione, G.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincare sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref]

Min, C.

L. Du, Z. Man, Y. Zhang, C. Min, S. Zhu, and X. Yuan, “Manipulating orbital angular momentum of light with tailored in-plane polarization states,” Sci. Rep. 7(1), 41001 (2017).
[Crossref]

Mirevski, S. P.

S. P. Mirevski and L. Boyadjiev, “On some fractional generalizations of the Laguerre polynomials and the Kummer function,” Comput. Math. Appl. 59(3), 1271–1277 (2010).
[Crossref]

Mocek, T.

Nalimov, A.

Nguyen, F.

V. Petrillo, G. Dattoli, I. Drebot, and F. Nguyen, “Compton scattering Gamma rays with orbital momentum,” Phys. Rev. Lett. 117(12), 123903 (2016).
[Crossref]

Nolan, D. A.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincare sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref]

Norreys, P.

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

Nuter, R.

R. Nuter, P. Korneev, I. Thiele, and V. Tikhonchuk, “Plasma solenoid driven by a laser carrying an orbital angular momentum,” Phys. Rev. E 98(3), 033211 (2018).
[Crossref]

Otte, E.

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularities in tailored vector beams,” J. Opt. 18(7), 074012 (2016).
[Crossref]

Padgett, M. J.

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

Payeur, S.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Petrillo, V.

V. Petrillo, G. Dattoli, I. Drebot, and F. Nguyen, “Compton scattering Gamma rays with orbital momentum,” Phys. Rev. Lett. 117(12), 123903 (2016).
[Crossref]

Piche, M.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Quéré, F.

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirror,” Phys. Rev. Lett. 118(3), 033902 (2017).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[Crossref]

Ryzhik, I.M.

I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007), Eq. 6.631.

Sato, S.

Schmidt, B.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Shakya, P.

Shen, B.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Shi, Y.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Silva, L. O.

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

Smith, C. P.

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]

Stratton, J.

J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56(1), 99–107 (1939).
[Crossref]

Swartzlander, G. A.

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincare sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref]

Thiele, I.

R. Nuter, P. Korneev, I. Thiele, and V. Tikhonchuk, “Plasma solenoid driven by a laser carrying an orbital angular momentum,” Phys. Rev. E 98(3), 033211 (2018).
[Crossref]

Thire, N.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Tikhonchuk, V.

R. Nuter, P. Korneev, I. Thiele, and V. Tikhonchuk, “Plasma solenoid driven by a laser carrying an orbital angular momentum,” Phys. Rev. E 98(3), 033211 (2018).
[Crossref]

Trines, R. M. G. M.

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

Varin, C.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Vieira, J.

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

Wang, J.

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

Wang, W.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Wang, X.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Weber, S.

White, A.

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(5-6), 321–327 (1994).
[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), 8185–8189 (1992).
[Crossref]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[Crossref]

Xu, J.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Xu, Z.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Yao, A. M.

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

Yi, L.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Youngworth, K. S.

Yuan, X.

L. Du, Z. Man, Y. Zhang, C. Min, S. Zhu, and X. Yuan, “Manipulating orbital angular momentum of light with tailored in-plane polarization states,” Sci. Rep. 7(1), 41001 (2017).
[Crossref]

Zhang, C.

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Zhang, L.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Zhang, X.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

Zhang, Y.

L. Du, Z. Man, Y. Zhang, C. Min, S. Zhu, and X. Yuan, “Manipulating orbital angular momentum of light with tailored in-plane polarization states,” Sci. Rep. 7(1), 41001 (2017).
[Crossref]

Zhu, S.

L. Du, Z. Man, Y. Zhang, C. Min, S. Zhu, and X. Yuan, “Manipulating orbital angular momentum of light with tailored in-plane polarization states,” Sci. Rep. 7(1), 41001 (2017).
[Crossref]

Adv. Opt. Photonics (1)

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

Appl. Phys. Lett. (1)

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Broadband anisotropy of femtosecond laser induced nanogratings in fused silica,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Appl. Sci. (1)

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. 3(1), 70–93 (2013).
[Crossref]

Comput. Math. Appl. (1)

S. P. Mirevski and L. Boyadjiev, “On some fractional generalizations of the Laguerre polynomials and the Kummer function,” Comput. Math. Appl. 59(3), 1271–1277 (2010).
[Crossref]

J. Opt. (1)

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularities in tailored vector beams,” J. Opt. 18(7), 074012 (2016).
[Crossref]

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

Nat. Commun. (2)

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonca, R. Bingham, P. Norreys, and L. O. Silva, “Amplications and generation of ultra-intense twisted laser pulses via stimulated Raman scattering,” Nat. Commun. 7(1), 10371 (2016).
[Crossref]

F. Kong, C. Zhang, F. Bouchard, Z. Li, G. G. Brown, D. H. Ko, T. J. Hammond, L. Arissian, R. W. Boyd, E. Karimi, and P. B. Corkum, “Controlling the orbital angular momentum of high harmonic vortices,” Nat. Commun. 8(1), 14970 (2017).
[Crossref]

Opt. Commun. (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(5-6), 321–327 (1994).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Optica (1)

Photonics Res. (1)

J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016).
[Crossref]

Phys. Rev. (1)

J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56(1), 99–107 (1939).
[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), 8185–8189 (1992).
[Crossref]

Phys. Rev. E (1)

R. Nuter, P. Korneev, I. Thiele, and V. Tikhonchuk, “Plasma solenoid driven by a laser carrying an orbital angular momentum,” Phys. Rev. E 98(3), 033211 (2018).
[Crossref]

Phys. Rev. Lett. (4)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincare sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref]

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quéré, “Interaction of ultraintense laser vortices with plasma mirror,” Phys. Rev. Lett. 118(3), 033902 (2017).
[Crossref]

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref]

V. Petrillo, G. Dattoli, I. Drebot, and F. Nguyen, “Compton scattering Gamma rays with orbital momentum,” Phys. Rev. Lett. 117(12), 123903 (2016).
[Crossref]

Proc. R. Soc. Lond. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959).
[Crossref]

Sci. Rep. (1)

L. Du, Z. Man, Y. Zhang, C. Min, S. Zhu, and X. Yuan, “Manipulating orbital angular momentum of light with tailored in-plane polarization states,” Sci. Rep. 7(1), 41001 (2017).
[Crossref]

Other (2)

I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007), Eq. 6.631.

T. G. Brown, Progress in Optics, vol. 56 (Elsevier, 2011), chap. 2.

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Figures (6)

Fig. 1.
Fig. 1. (a) Poincare sphere representing the polarization state (PS) of the beam. S1, S2, S3 mean the stoke parameters. (b) Radial polarization (blue arrows) and Laguerre-Gaussian intensity profile. (c) Helical phase shift dependent on the orientation angle γ. l is the topological charge.
Fig. 2.
Fig. 2. Coordinates used when the electric field distributions are calculated near the focal plane. Definition of coordinates (a) for the source point and (b) for the observation point.
Fig. 3.
Fig. 3. Electric field and Intensity distributions. (a) LP OAM and (b) RP OAM beams. The wavelength (λ) is 0.8 µm, and horizontal and vertical dimension of the calculation window is (12.2λ)×(12.2λ). Red color in the field means a positive value and blue means a negative value.
Fig. 4.
Fig. 4. Graphical calculation of superposed modes. The calculation window is (12.2λ)×(12.2λ) as in Fig. 3.
Fig. 5.
Fig. 5. Electric fields and intensities at different positions showing the propagation property of the linearly-polarized OAM beam with (a) a TC of 1 and (b) a TC of 2. The calculation window is (12.2λ)×(12.2λ) as in Fig. 3.
Fig. 6.
Fig. 6. Electric fields and intensities at different positions showing the propagation property of the cylindrical vector OAM beam with (a) a TC of 1 and (b) a TC of 2. The calculation window is (12.2λ)×(12.2λ) as in Fig. 3.

Equations (11)

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[ φ x ( 2 θ , 2 ϕ ) φ y ( 2 θ , 2 ϕ ) ] = [ cos θ cos ϕ i sin θ sin ϕ cos θ sin ϕ + i sin θ cos ϕ ] .
[ φ x m , l ( 2 θ , 2 ϕ ) φ y m , l ( 2 θ , 2 ϕ ) ] = e i l γ T ( m γ ) [ cos θ cos ϕ i sin θ sin ϕ cos θ sin ϕ + i sin θ cos ϕ ] .
[ φ x m , l ( 2 θ , 2 ϕ ) φ y m , l ( 2 θ , 2 ϕ ) ] = 1 2 ( cos θ cos ϕ i sin θ sin ϕ ) { e i ( l + m ) γ [ 1 i ] + e i ( l m ) γ [ 1 i ] } + i 1 2 ( cos θ sin ϕ + i sin θ cos ϕ ) { e i ( l + m ) γ [ 1 i ] e i ( l m ) γ [ 1 i ] } .
[ E x ( x S , y S , z S ) E y ( x S , y S , z S ) ] = E 0 2 e r S 2 2 ω 0 2 { e i ( l + m ) γ [ 1 i ] + e i ( l m ) γ [ 1 i ] } .
E x ( x P , y P , z P ) = i E 0 2 π 0 α 0 2 π [ e sin 2 ϑ / sin 2 ϑ 2 sin 2 ϑ 0 2 sin 2 ϑ 0 e i ( l + m ) γ cos 1 / 2 ϑ sin ϑ × { cos ϑ + ( 1 cos ϑ ) sin 2 γ } e i k r P cos ε ] d ϑ d γ i E 0 2 π 0 α 0 2 π [ e sin 2 ϑ / sin 2 ϑ 2 sin 2 ϑ 0 2 sin 2 ϑ 0 e i ( l m ) γ cos 1 / 2 ϑ sin ϑ × { cos ϑ + ( 1 cos ϑ ) sin 2 γ } e i k r P cos ε ] d ϑ d γ .
E x ( x P , y P , z P ) = i l + m + 1 2 π E 0 e i k r P cos χ e i ( l + m ) q n = 0 ( 1 ) n ( 2 n + 1 ) ! 0 α e ϑ 2 2 ϑ 0 2 J l + m ( k r P sin χ ϑ ) ϑ 2 n + 1 d ϑ i l m + 1 2 π E 0 e i k r P cos χ e i ( l m ) q n = 0 ( 1 ) n ( 2 n + 1 ) ! 0 α e ϑ 2 2 ϑ 0 2 J l m ( k r P sin χ ϑ ) ϑ 2 n + 1 d ϑ .
0 e x 2 x 2 μ + ν + 1 J ν ( 2 x z ) d x = μ ! 2 e z z ν / ν 2 2 L μ ν ( z ) .
E x ( x P , y P , z P ) = i l + m + 1 2 π E 0 e i k r P cos χ n = 0 2 n ϑ 0 2 n + 2 ( 1 ) n ( 2 n + 1 ) ! ( n l + m 2 ) ! L G n | l + m | 2 l + m e i ( l + m ) q i l m + 1 2 π E 0 e i k r P cos χ n = 0 2 n ϑ 0 2 n + 2 ( 1 ) n ( 2 n + 1 ) ! ( n l m 2 ) ! L G n | l m | 2 l m e i ( l m ) q .
0 ϑ e α ϑ 2 J l ± m ( 2 R p ϑ ) d ϑ = π R p 4 α 3 / 3 2 2 e R p 2 2 α [ I l ± m 2 1 2 ( R p 2 2 α ) I l ± m 2 + 1 2 ( R p 2 2 α ) ] ,
E y ( x P , y P , z P ) i l + m 1 E 0 ( n C 1 , n L G n | l + m + 2 | 2 l + m + 2 e i ( l + m + 2 ) q n C 2 , n L G n | l + m 2 | 2 l + m 2 e i ( l + m 2 ) q ) + i l m 1 E 0 ( n C 3 , n L G n | l m + 2 | 2 l m + 2 e i ( l m + 2 ) q n C 4 , n L G n | l m 2 | 2 l m 2 e i ( l m 2 ) q ) ,
E z ( x P , y P , z P ) i l + m 1 E 0 ( n D 1 , n L G n | l + m + 1 | 2 l + m + 1 e i ( l + m + 1 ) q n D 2 , n L G n | l + m 1 | 2 l + m 1 e i ( l + m 1 ) q ) + i l m 1 E 0 ( n D 3 , n L G n | l m + 1 | 2 l m + 1 e i ( l m + 1 ) q n D 4 , n L G n | l m 1 | 2 l m 1 e i ( l m 1 ) q ) .

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