Abstract

In this study, we propose a new approach to construct metasurfaces for the generation of inverse energy flux near the optical axis. We derive new equations intended to create continuous subwavelength relief for transformation of a linearly polarized input field into a radially polarized beam with an arbitrary order. Proposed metasurfaces combine the polarization converter as subwavelength gratings with a varying period and the focusing element as additional structure. Such a combination increases polarization conversion efficiency and decreases the number of optical elements in an arrangement. Numerical simulations of the proposed metasurfaces, based on the finite element method, show that the higher-order polarization conversion provides the greater integrated inverse energy flux. Moreover, the shape of the inverse flux area achieved with the higher-order metasurface is annular and has bigger force area.

© 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 (2)

S. N. Khonina, A. V. Ustinov, and S. A. Degtyarev, “Inverse energy flux of focused radially polarized optical beams,” Phys. Rev. A (Coll. Park) 98(4), 043823 (2018).
[Crossref]

S. A. Degtyarev, S. G. Volotovsky, and S. N. Khonina, “Sublinearly chirped metalenses for forming abruptly autofocusing cylindrically polarized beams,” J. Opt. Soc. Am. B 35(8), 1963–1969 (2018).
[Crossref]

2017 (2)

S. S. Stafeev, V. V. Kotlyar, A. G. Nalimov, M. V. Kotlyar, and L. O’Faolain, “Subwavelength gratings for polarization conversion and focusing of laser light,” Photon. Nanostructures 27, 32–41 (2017).
[Crossref]

V. V. Kotlyar and A. G. Nalimov, “A vector optical vortex generated and focused using a metalens,” Comput. Opt. 41(5), 645–654 (2017).
[Crossref]

2016 (2)

2015 (3)

Z. Zhou and L. Zhu, “Tight focusing of axially symmetric polarized beams with fractional orders,” Opt. Quantum Electron. 48, 1–9 (2015).

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic Field Invisibility Cloak,” Sci. Rep. 5(1), 16416 (2015).
[Crossref] [PubMed]

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40(21), 4887–4890 (2015).
[Crossref] [PubMed]

2014 (1)

2011 (2)

2009 (1)

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

2007 (2)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

A. V. Novitsky and D. V. Novitsky, “Negative propagation of vector Bessel beams,” J. Opt. Soc. Am. A 24(9), 2844–2849 (2007).
[Crossref] [PubMed]

2004 (1)

2002 (1)

1999 (1)

A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

1996 (1)

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

Alfano, R. R.

Balakrishnan, K.

Beresna, M.

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Biener, G.

Bomzon, Z.

Degtyarev, S. A.

S. N. Khonina, A. V. Ustinov, and S. A. Degtyarev, “Inverse energy flux of focused radially polarized optical beams,” Phys. Rev. A (Coll. Park) 98(4), 043823 (2018).
[Crossref]

S. A. Degtyarev, S. G. Volotovsky, and S. N. Khonina, “Sublinearly chirped metalenses for forming abruptly autofocusing cylindrically polarized beams,” J. Opt. Soc. Am. B 35(8), 1963–1969 (2018).
[Crossref]

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Gecevicius, M.

Geng, Z.

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic Field Invisibility Cloak,” Sci. Rep. 5(1), 16416 (2015).
[Crossref] [PubMed]

Gibson, D.

Hasman, E.

Hsu, W.-L.

Huang, B.

Ibn-Elhaj, M.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Kazansky, P. G.

Ke, Y.

Khonina, S. N.

S. A. Degtyarev, S. G. Volotovsky, and S. N. Khonina, “Sublinearly chirped metalenses for forming abruptly autofocusing cylindrically polarized beams,” J. Opt. Soc. Am. B 35(8), 1963–1969 (2018).
[Crossref]

S. N. Khonina, A. V. Ustinov, and S. A. Degtyarev, “Inverse energy flux of focused radially polarized optical beams,” Phys. Rev. A (Coll. Park) 98(4), 043823 (2018).
[Crossref]

Kleiner, V.

Kotlyar, M. V.

S. S. Stafeev, V. V. Kotlyar, A. G. Nalimov, M. V. Kotlyar, and L. O’Faolain, “Subwavelength gratings for polarization conversion and focusing of laser light,” Photon. Nanostructures 27, 32–41 (2017).
[Crossref]

S. S. Stafeev, A. G. Nalimov, M. V. Kotlyar, D. Gibson, S. Song, L. O’Faolain, and V. V. Kotlyar, “Microlens-aided focusing of linearly and azimuthally polarized laser light,” Opt. Express 24(26), 29800–29813 (2016).
[Crossref] [PubMed]

Kotlyar, V. V.

S. S. Stafeev, V. V. Kotlyar, A. G. Nalimov, M. V. Kotlyar, and L. O’Faolain, “Subwavelength gratings for polarization conversion and focusing of laser light,” Photon. Nanostructures 27, 32–41 (2017).
[Crossref]

V. V. Kotlyar and A. G. Nalimov, “A vector optical vortex generated and focused using a metalens,” Comput. Opt. 41(5), 645–654 (2017).
[Crossref]

S. S. Stafeev, A. G. Nalimov, M. V. Kotlyar, D. Gibson, S. Song, L. O’Faolain, and V. V. Kotlyar, “Microlens-aided focusing of linearly and azimuthally polarized laser light,” Opt. Express 24(26), 29800–29813 (2016).
[Crossref] [PubMed]

Lalanne, P.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

Lan, C.

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic Field Invisibility Cloak,” Sci. Rep. 5(1), 16416 (2015).
[Crossref] [PubMed]

Leach, J.

Lemercier-Lalanne, D.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

Li, B.

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic Field Invisibility Cloak,” Sci. Rep. 5(1), 16416 (2015).
[Crossref] [PubMed]

Ling, X.

Liu, Y.

Liu, Z.

Luo, H.

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Milione, G.

Nalimov, A. G.

S. S. Stafeev, V. V. Kotlyar, A. G. Nalimov, M. V. Kotlyar, and L. O’Faolain, “Subwavelength gratings for polarization conversion and focusing of laser light,” Photon. Nanostructures 27, 32–41 (2017).
[Crossref]

V. V. Kotlyar and A. G. Nalimov, “A vector optical vortex generated and focused using a metalens,” Comput. Opt. 41(5), 645–654 (2017).
[Crossref]

S. S. Stafeev, A. G. Nalimov, M. V. Kotlyar, D. Gibson, S. Song, L. O’Faolain, and V. V. Kotlyar, “Microlens-aided focusing of linearly and azimuthally polarized laser light,” Opt. Express 24(26), 29800–29813 (2016).
[Crossref] [PubMed]

Nesterov, A. V.

A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

Nguyen, T. A.

Niv, A.

Niziev, V. G.

A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

Nolan, D. A.

Novitsky, A. V.

Novitsky, D. V.

O’Faolain, L.

S. S. Stafeev, V. V. Kotlyar, A. G. Nalimov, M. V. Kotlyar, and L. O’Faolain, “Subwavelength gratings for polarization conversion and focusing of laser light,” Photon. Nanostructures 27, 32–41 (2017).
[Crossref]

S. S. Stafeev, A. G. Nalimov, M. V. Kotlyar, D. Gibson, S. Song, L. O’Faolain, and V. V. Kotlyar, “Microlens-aided focusing of linearly and azimuthally polarized laser light,” Opt. Express 24(26), 29800–29813 (2016).
[Crossref] [PubMed]

Pau, S.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Sáenz, J. J.

J. J. Sáenz, “Laser tractor beams,” Nat. Photonics 5(9), 514–515 (2011).
[Crossref]

Shu, W.

Song, S.

Stafeev, S. S.

S. S. Stafeev, V. V. Kotlyar, A. G. Nalimov, M. V. Kotlyar, and L. O’Faolain, “Subwavelength gratings for polarization conversion and focusing of laser light,” Photon. Nanostructures 27, 32–41 (2017).
[Crossref]

S. S. Stafeev, A. G. Nalimov, M. V. Kotlyar, D. Gibson, S. Song, L. O’Faolain, and V. V. Kotlyar, “Microlens-aided focusing of linearly and azimuthally polarized laser light,” Opt. Express 24(26), 29800–29813 (2016).
[Crossref] [PubMed]

Ustinov, A. V.

S. N. Khonina, A. V. Ustinov, and S. A. Degtyarev, “Inverse energy flux of focused radially polarized optical beams,” Phys. Rev. A (Coll. Park) 98(4), 043823 (2018).
[Crossref]

Volotovsky, S. G.

Yakunin, V. P.

A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

Yang, Y.

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic Field Invisibility Cloak,” Sci. Rep. 5(1), 16416 (2015).
[Crossref] [PubMed]

Yin, X.

Zhan, Q.

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

Zhou, J.

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic Field Invisibility Cloak,” Sci. Rep. 5(1), 16416 (2015).
[Crossref] [PubMed]

Zhou, Z.

Z. Zhou and L. Zhu, “Tight focusing of axially symmetric polarized beams with fractional orders,” Opt. Quantum Electron. 48, 1–9 (2015).

Zhu, L.

Z. Zhou and L. Zhu, “Tight focusing of axially symmetric polarized beams with fractional orders,” Opt. Quantum Electron. 48, 1–9 (2015).

Adv. Opt. Photonics (1)

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

Appl. Opt. (1)

Comput. Opt. (1)

V. V. Kotlyar and A. G. Nalimov, “A vector optical vortex generated and focused using a metalens,” Comput. Opt. 41(5), 645–654 (2017).
[Crossref]

J. Mod. Opt. (1)

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

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

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

J. Phys. D Appl. Phys. (1)

A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

Nat. Photonics (1)

J. J. Sáenz, “Laser tractor beams,” Nat. Photonics 5(9), 514–515 (2011).
[Crossref]

New J. Phys. (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Opt. Mater. Express (1)

Opt. Quantum Electron. (1)

Z. Zhou and L. Zhu, “Tight focusing of axially symmetric polarized beams with fractional orders,” Opt. Quantum Electron. 48, 1–9 (2015).

Photon. Nanostructures (1)

S. S. Stafeev, V. V. Kotlyar, A. G. Nalimov, M. V. Kotlyar, and L. O’Faolain, “Subwavelength gratings for polarization conversion and focusing of laser light,” Photon. Nanostructures 27, 32–41 (2017).
[Crossref]

Phys. Rev. A (Coll. Park) (1)

S. N. Khonina, A. V. Ustinov, and S. A. Degtyarev, “Inverse energy flux of focused radially polarized optical beams,” Phys. Rev. A (Coll. Park) 98(4), 043823 (2018).
[Crossref]

Sci. Rep. (1)

C. Lan, Y. Yang, Z. Geng, B. Li, and J. Zhou, “Electrostatic Field Invisibility Cloak,” Sci. Rep. 5(1), 16416 (2015).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1 Subwavelength grating as an inhomogeneous half-wave plate; (a) general view of the subwavelength grating; (b) mutual arrangement of the following vectors and angles between them: grating vector K , electric vector E in of the incident beam, and electric vector E out of the output beam. The order of polarization (m) is 5 and polar angle (φ) is 10°.
Fig. 2
Fig. 2 Curves of fast (orange) and slow (black) axes of the subwavelength grating that transforms linearly polarized beams into radially polarized beams with order m. In the first row, the period of curves repetition depends only on the azimuthal angle φ. In the second row, the period of curves repetition depends only on the radius r.
Fig. 3
Fig. 3 The working of metasurface of (a) second and (d) third order; (b, e) longitudinal and (c, f) transverse cross-sections of power flux longitudinal component distributions Sz; graphs of Sz versus the y-axis of the focal spot are shown in the insets on the right.

Equations (7)

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n eff TE = [ Q n 1 2 +( 1Q ) n 2 2 ] 1/2 , n eff TM = [ Q n 1 2 +(1Q) n 2 2 ] 1/2 ,
h( r )= h 0 2 ( 1+sign( cos( f( r ) ) ) ),
E out (r,φ)=E( r )( cos( mφ ) sin( mφ ) ), K ( x,y )=( K x ( x,y ) K y ( x,y ) )= 2π d ( cos( mφ 2 ) sin( mφ 2 ) ),
d( φ )= d 0 cos ( m m2 ) ( m2 2 φ ),f( r,φ )= 2π d 0 r cos ( 2 m2 ) ( m2 2 φ ).
d( r )= d 0 r m 2 ,f( r,φ )= 4π ( m2 )d 0 r 2m 2 cos( m2 2 φ ).
r angle =С cos ( 2 m2 ) ( m2 2 φ ), r rad = С ( 2 2m ) cos ( 2 m2 ) ( m2 2 φ ),
r angle =С sin ( 2 m2 ) ( m2 2 φ ), r rad = С ( 2 2m ) sin ( 2 m2 ) ( m2 2 φ ).

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