Abstract

We report a concise yet efficient experiment to extend the study of full Poincaré beams to incorporate the nonlinear optical effect. The main feature of our scheme is the employment of Type-II phase-matching KTP crystal to implement the second harmonic generation with structured vector light from invisible to visible region. Of particular interest is the revelation and visualization of the hidden topological structures transferred from the input polarization state to the output observable intensity patterns. The experimental results are in good agreement with the numerical simulations. Our present work provides us with the insight into the interaction of full Poincaré beams with media in the nonlinear regime.

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

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References

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2017 (1)

P. Stanislovaitis, A. Matijosius, M. Ivanov, and V. Smilgevicius, “Topological charge transformation of beams with embedded fractional phase step in theprocess of second harmonic generation,” J. Opt. 19(10), 105603 (2017).
[Crossref]

2015 (2)

W. Zhu, V. Shvedov, W. She, and W. Krolikowski, “Transverse spin angular momentum of tightly focused full Poincaré beams,” Opt. Express 23(26), 34029–34041 (2015).
[Crossref] [PubMed]

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

2014 (3)

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

P. Stanislovaitis, A. Matijošius, V. Šetkus, and V. Smilgevičius, “Peculiarities of second harmonic generation by paraxial beams with radial/azimuthal polarization in type II nonlinear crystal,” Lith. J. Phys. 54(3), 142–149 (2014).
[Crossref]

Z. Y. Zhou, D. S. Ding, Y. K. Jiang, Y. Li, S. Shi, X. S. Wang, and B. S. Shi, “Orbital angular momentum light frequency conversion and interference with quasi-phase matching crystals,” Opt. Express 22(17), 20298–20310 (2014).
[Crossref] [PubMed]

2013 (2)

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
[Crossref] [PubMed]

L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A 88(5), 053831 (2013).
[Crossref]

2012 (4)

2010 (5)

2009 (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

2006 (2)

K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16(12), 2603–2607 (2006).
[Crossref]

S. Carrasco, B. E. A. Saleh, M. C. Teich, and J. Fourkas, “Second- and third-harmonic generation with vector Gaussian beams,” J. Opt. Soc. Am. B 23(10), 2134–2141 (2006).
[Crossref]

2005 (1)

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

2002 (2)

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213(4), 201–221 (2002).
[Crossref]

I. Freund, “Second-harmonic generation of polarization singularities,” Opt. Lett. 27(18), 1640–1642 (2002).
[Crossref] [PubMed]

1983 (1)

J. F. Nye, “Lines of circular polarization in electromagnetic wave fields,” Proc. R. Soc. Lond. A Math. Phys. Sci. 389 (1797), 279–290 (1983).
[Crossref]

Ahmed, N.

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

Alexeyev, C. N.

Alonso, M. A.

Anischenko, P. M.

Ashrafi, N.

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

Ashrafi, S.

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

Bao, C.

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

Beckley, A. M.

Borwinska, M.

Brasselet, E.

Brown, T. G.

Cao, Y.

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

Cardano, F.

Carrasco, S.

Chen, J.

Chen, L.

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A 88(5), 053831 (2013).
[Crossref]

de Lisio, C.

Dennis, M. R.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[Crossref] [PubMed]

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213(4), 201–221 (2002).
[Crossref]

Desyatnikov, A.

Ding, D. S.

Ding, J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Fadeyeva, T. A.

Flossmann, F.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[Crossref] [PubMed]

Fourkas, J.

Freund, I.

Guo, C.-S.

Huang, H.

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

Ivanov, M.

P. Stanislovaitis, A. Matijosius, M. Ivanov, and V. Smilgevicius, “Topological charge transformation of beams with embedded fractional phase step in theprocess of second harmonic generation,” J. Opt. 19(10), 105603 (2017).
[Crossref]

Izdebskaya, Y. V.

Jiang, Y. K.

Karimi, E.

Kivshar, Y. S.

Krolikowski, W.

Kurzynowski, P.

Lavery, M. P. J.

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

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Levy, U.

Li, L.

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

Li, Y.

Lin, X.

L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A 88(5), 053831 (2013).
[Crossref]

Lu, Q.

L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A 88(5), 053831 (2013).
[Crossref]

Lu, X.

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

Maier, M.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[Crossref] [PubMed]

Marrucci, L.

Matijosius, A.

P. Stanislovaitis, A. Matijosius, M. Ivanov, and V. Smilgevicius, “Topological charge transformation of beams with embedded fractional phase step in theprocess of second harmonic generation,” J. Opt. 19(10), 105603 (2017).
[Crossref]

Matijošius, A.

P. Stanislovaitis, A. Matijošius, V. Šetkus, and V. Smilgevičius, “Peculiarities of second harmonic generation by paraxial beams with radial/azimuthal polarization in type II nonlinear crystal,” Lith. J. Phys. 54(3), 142–149 (2014).
[Crossref]

Molisch, A. F.

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

Neshev, D. N.

Nye, J. F.

J. F. Nye, “Lines of circular polarization in electromagnetic wave fields,” Proc. R. Soc. Lond. A Math. Phys. Sci. 389 (1797), 279–290 (1983).
[Crossref]

Ohtsu, A.

A. Ohtsu, “Second-harmonic wave induced by vortex beams with radial and azimuthal polarizations,” Opt. Commun. 283(20), 3831–3837 (2010).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Ramachandran, S.

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

Ren, Y.

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

Saleh, B. E. A.

Santamato, E.

Schwarz, U. T.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[Crossref] [PubMed]

Šetkus, V.

P. Stanislovaitis, A. Matijošius, V. Šetkus, and V. Smilgevičius, “Peculiarities of second harmonic generation by paraxial beams with radial/azimuthal polarization in type II nonlinear crystal,” Lith. J. Phys. 54(3), 142–149 (2014).
[Crossref]

She, W.

Shi, B. S.

Shi, S.

Shvedov, V.

Shvedov, V. G.

Smilgevicius, V.

P. Stanislovaitis, A. Matijosius, M. Ivanov, and V. Smilgevicius, “Topological charge transformation of beams with embedded fractional phase step in theprocess of second harmonic generation,” J. Opt. 19(10), 105603 (2017).
[Crossref]

P. Stanislovaitis, A. Matijošius, V. Šetkus, and V. Smilgevičius, “Peculiarities of second harmonic generation by paraxial beams with radial/azimuthal polarization in type II nonlinear crystal,” Lith. J. Phys. 54(3), 142–149 (2014).
[Crossref]

Stanislovaitis, P.

P. Stanislovaitis, A. Matijosius, M. Ivanov, and V. Smilgevicius, “Topological charge transformation of beams with embedded fractional phase step in theprocess of second harmonic generation,” J. Opt. 19(10), 105603 (2017).
[Crossref]

P. Stanislovaitis, A. Matijošius, V. Šetkus, and V. Smilgevičius, “Peculiarities of second harmonic generation by paraxial beams with radial/azimuthal polarization in type II nonlinear crystal,” Lith. J. Phys. 54(3), 142–149 (2014).
[Crossref]

Stern, L.

Tan, B.

K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16(12), 2603–2607 (2006).
[Crossref]

Teich, M. C.

Tur, M.

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

Venkatakrishnan, K.

K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16(12), 2603–2607 (2006).
[Crossref]

Volyar, A. V.

Wang, H.-T.

Wang, J.

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

Wang, L. G.

Wang, X. S.

Wang, X.-L.

Willner, A. E.

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

Wozniak, W. A.

Wu, Z.

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

Xie, G.

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

Yan, Y.

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

Zdunek, M.

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
[Crossref] [PubMed]

Zhang, W.

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A 88(5), 053831 (2013).
[Crossref]

Zhao, Z.

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

Zhou, Z. Y.

Zhu, W.

Adv. Opt. Photonics (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

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

Appl. Opt. (1)

J. Micromech. Microeng. (1)

K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16(12), 2603–2607 (2006).
[Crossref]

J. Opt. (1)

P. Stanislovaitis, A. Matijosius, M. Ivanov, and V. Smilgevicius, “Topological charge transformation of beams with embedded fractional phase step in theprocess of second harmonic generation,” J. Opt. 19(10), 105603 (2017).
[Crossref]

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

Lith. J. Phys. (1)

P. Stanislovaitis, A. Matijošius, V. Šetkus, and V. Smilgevičius, “Peculiarities of second harmonic generation by paraxial beams with radial/azimuthal polarization in type II nonlinear crystal,” Lith. J. Phys. 54(3), 142–149 (2014).
[Crossref]

Opt. Commun. (2)

A. Ohtsu, “Second-harmonic wave induced by vortex beams with radial and azimuthal polarizations,” Opt. Commun. 283(20), 3831–3837 (2010).
[Crossref]

M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213(4), 201–221 (2002).
[Crossref]

Opt. Express (11)

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
[Crossref] [PubMed]

L. G. Wang, “Optical forces on submicron particles induced by full Poincaré beams,” Opt. Express 20(19), 20814–20826 (2012).
[Crossref] [PubMed]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
[Crossref] [PubMed]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams II: partial polarization,” Opt. Express 20(9), 9357–9362 (2012).
[Crossref] [PubMed]

W. Zhu, V. Shvedov, W. She, and W. Krolikowski, “Transverse spin angular momentum of tightly focused full Poincaré beams,” Opt. Express 23(26), 34029–34041 (2015).
[Crossref] [PubMed]

A. Desyatnikov, T. A. Fadeyeva, V. G. Shvedov, Y. V. Izdebskaya, A. V. Volyar, E. Brasselet, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Spatially engineered polarization states and optical vortices in uniaxial crystals,” Opt. Express 18(10), 10848–10863 (2010).
[Crossref] [PubMed]

G. M. Lerman, L. Stern, and U. Levy, “Generation and tight focusing of hybridly polarized vector beams,” Opt. Express 18(26), 27650–27657 (2010).
[Crossref] [PubMed]

H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[Crossref] [PubMed]

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
[Crossref] [PubMed]

P. Kurzynowski, W. A. Woźniak, M. Zdunek, and M. Borwińska, “Singularities of interference of three waves with different polarization states,” Opt. Express 20(24), 26755–26765 (2012).
[Crossref] [PubMed]

Z. Y. Zhou, D. S. Ding, Y. K. Jiang, Y. Li, S. Shi, X. S. Wang, and B. S. Shi, “Orbital angular momentum light frequency conversion and interference with quasi-phase matching crystals,” Opt. Express 22(17), 20298–20310 (2014).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (1)

L. Chen, W. Zhang, Q. Lu, and X. Lin, “Making and identifying optical superpositions of high orbital angular momenta,” Phys. Rev. A 88(5), 053831 (2013).
[Crossref]

Phys. Rev. Lett. (2)

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

J. F. Nye, “Lines of circular polarization in electromagnetic wave fields,” Proc. R. Soc. Lond. A Math. Phys. Sci. 389 (1797), 279–290 (1983).
[Crossref]

Sci. Rep. (1)

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

Other (1)

G. Milione and R. R. Alfano, “Cylindrical vector beam transformations and hybrid vector beams,” in Frontiers in Optics 2010/Laser Science XXVI, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FWC4.

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Figures (4)

Fig. 1
Fig. 1 Experimental setup for SHG of FP beams in KTP, see the text for details.
Fig. 2
Fig. 2 Two trivial cases of SHG with scalar beams. Top panel: α = 0 ° . Bottom panel: α = 45 ° . (a1) and (b1): the intensity and polarization distributions of the fundamental beams. (a2) and (b2): numerical simulations of SHG light field’s intensity patterns. (a3) and (b3): the experimental observations.
Fig. 3
Fig. 3 The results for m = 1 with α = 10 ° , 20 ° , 30 ° , 40 ° , 50 ° , 60 ° , 70 ° and 80 ° .Top panel: transverse intensity and polarization distributions of fundamental FP beams, wherethe red circles indicate L-lines. Middle panel: numerical simulations for the transverse intensity patterns of SHG light field. Bottom panel: experimental observations.
Fig. 4
Fig. 4 The results for m = 2 with α = 10 ° , 20 ° , 30 ° , 40 ° , 50 ° , 60 ° , 70 ° and 80 ° . Top panel: transverse intensity and polarization distributions of fundamental FP beams. Middle panel: numerical simulations for the transverse intensity patterns of SHG light field. Bottom panel: experimental observations.

Equations (8)

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E ( r , φ ) = A L G 0 0 ( r , φ ) e 1 + B L G 0 l ( r , φ ) e 2 ,
L G 0 l ( r , φ ) = E 0 r l L 0 l ( 2 r w 2 ) exp ( r 2 w 2 ) exp ( i l φ ) ,
L G 0 l ( r , φ ) ( 1 0 ) ( 1 i ) sin ( 2 α ) 2 L G 0 l ( r , φ ) ( 1 i ) + ( 1 + i ) cos ( 2 α ) 2 L G 0 l ( r , φ ) ( 1 i ) ,
C V H W P = ( cos m φ sin m φ sin m φ cos m φ ) .
L G 0 l ( r , φ ) ( 1 0 ) ( 1 i ) sin ( 2 α ) 2 L G 0 l + m ( r , φ ) ( 1 i ) + ( 1 + i ) cos ( 2 α ) 2 L G 0 l m ( r , φ ) ( 1 i ) ,
E H = ( 1 + i ) cos ( 2 α ) 2 L G 0 0 + ( 1 i ) sin ( 2 α ) 2 L G 0 l ,
E V = i [ ( 1 + i ) cos ( 2 α ) 2 L G 0 0 ( 1 i ) sin ( 2 α ) 2 L G 0 l ] .
d E S H d z = i ω S H 2 d e f f k S H c 2 E H E V ,

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