Abstract

Linearly and circularly polarized terahertz (THz) vortex beams are generated by adopting a THz quarter wave plate and spiral phase plates with topological charges 1 and 2. Taking advantage of a THz digital holographic imaging system, longitudinal components of THz vortices with different polarizations and topological charges are coherently measured and systemically analyzed in a focusing condition. The application potential of circularly polarized THz vortex beams in microscopy is experimentally demonstrated and the transformation between the spin angular momentums and orbital angular momentums of THz waves is also checked. Modified Richards-Wolf vector diffraction integration equations are applied to successfully simulate experimental phenomena.

© 2016 Optical Society of America

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2016 (1)

2015 (3)

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

N. Tian, L. Fu, and M. Gu, “Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam,” Sci. Rep. 5, 13580 (2015).
[Crossref] [PubMed]

Z. Zhang, H. Fan, H. F. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).
[Crossref]

2014 (3)

2013 (2)

S. N. Khonina, S. V. Karpeev, S. V. Alferov, D. A. Savelyev, J. Laukkanen, and J. Turnnen, “Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams,” J. Opt. 15(8), 085704 (2013).
[Crossref]

J. He, X. Wang, D. Hu, J. Ye, S. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express 21(17), 20230–20239 (2013).
[Crossref] [PubMed]

2012 (3)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

2011 (2)

S. N. Khonina, N. L. Kazanskiy, and S. G. Volotovsky, “Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system,” J. Mod. Opt. 58(9), 748–760 (2011).
[Crossref]

F. Tamburini, B. Thide, G. M. Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[Crossref]

2010 (3)

2009 (1)

2008 (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

2007 (2)

A. Nahata and W. Zhu, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express 15(9), 5616–5624 (2007).
[Crossref] [PubMed]

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

B. H. Jia, X. S. Gan, and M. Gu, “Direct observation of a pure focused evanescent field of a high numerical aperture objective lens by scanning near-field optical microscopy,” Appl. Phys. Lett. 86(13), 131110 (2005).
[Crossref]

2003 (3)

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597(2), 1266–1270 (2003).
[Crossref]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[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]

2002 (1)

J. W. M. Chon, X. S. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

2001 (1)

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6(4), 480–484 (2001).
[Crossref] [PubMed]

2000 (3)

1997 (1)

1996 (1)

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

1995 (3)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

M. J. Padgett and L. Allen, “The poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

J. Rosenzweig, A. Murokh, and C. Pellegrini, “A proposed dielectric-loaded resonant laser accelerator,” Phys. Rev. Lett. 74(13), 2467–2470 (1995).
[Crossref] [PubMed]

1990 (1)

R. D. Romea and W. D. Kimura, “Modeling of inverse C-caronerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D Part. Fields 42(5), 1807–1818 (1990).
[Crossref] [PubMed]

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 Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Alferov, S. V.

S. N. Khonina, S. V. Karpeev, S. V. Alferov, D. A. Savelyev, J. Laukkanen, and J. Turnnen, “Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams,” J. Opt. 15(8), 085704 (2013).
[Crossref]

Allen, L.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[Crossref] [PubMed]

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

M. J. Padgett and L. Allen, “The poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

Anzolin, G.

F. Tamburini, B. Thide, G. M. Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[Crossref]

Bergman, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Bianchini, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

Brown, T.

Carozzi, T. D.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Chen, B.

Chon, J. W. M.

J. W. M. Chon, X. S. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Cui, Y.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref] [PubMed]

Dholakia, K.

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

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]

Fallahi, A.

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Fan, H.

Z. Zhang, H. Fan, H. F. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).
[Crossref]

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Feng, S.

Fischer, B. M.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Fu, L.

N. Tian, L. Fu, and M. Gu, “Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam,” Sci. Rep. 5, 13580 (2015).
[Crossref] [PubMed]

Gan, X. S.

B. H. Jia, X. S. Gan, and M. Gu, “Direct observation of a pure focused evanescent field of a high numerical aperture objective lens by scanning near-field optical microscopy,” Appl. Phys. Lett. 86(13), 131110 (2005).
[Crossref]

J. W. M. Chon, X. S. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Grier, D. G.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref] [PubMed]

Gu, M.

N. Tian, L. Fu, and M. Gu, “Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam,” Sci. Rep. 5, 13580 (2015).
[Crossref] [PubMed]

B. H. Jia, X. S. Gan, and M. Gu, “Direct observation of a pure focused evanescent field of a high numerical aperture objective lens by scanning near-field optical microscopy,” Appl. Phys. Lett. 86(13), 131110 (2005).
[Crossref]

J. W. M. Chon, X. S. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Harwit, M.

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597(2), 1266–1270 (2003).
[Crossref]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

He, J.

Hecht, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Hell, S. W.

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6(4), 480–484 (2001).
[Crossref] [PubMed]

Helm, H.

Helm, M.

K. J. Kaltenecker, J. C. Konig-Otto, M. Mittendorff, S. Winnerl, H. Schneider, M. Helm, H. Helm, M. Walther, and B. M. Fischer, “Gouy phase shift of a tightly focused, radially polarized beam,” Optica 3(1), 35–41 (2016).
[Crossref]

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Hong, K. H.

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Hu, D.

Huang, H.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Huang, W.

Z. Zhang, H. Fan, H. F. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).
[Crossref]

Huang, W. R.

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Hubrich, R.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Huse, N.

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6(4), 480–484 (2001).
[Crossref] [PubMed]

Ibragimov, N. H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Istomin, Y. N.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Jia, B. H.

B. H. Jia, X. S. Gan, and M. Gu, “Direct observation of a pure focused evanescent field of a high numerical aperture objective lens by scanning near-field optical microscopy,” Appl. Phys. Lett. 86(13), 131110 (2005).
[Crossref]

Jiang, Z.

Kaltenecker, K. J.

Kan, Q.

Karpeev, S. V.

S. N. Khonina, S. V. Karpeev, S. V. Alferov, D. A. Savelyev, J. Laukkanen, and J. Turnnen, “Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams,” J. Opt. 15(8), 085704 (2013).
[Crossref]

Kärtner, F. X.

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Kazanskiy, N. L.

S. N. Khonina, N. L. Kazanskiy, and S. G. Volotovsky, “Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system,” J. Mod. Opt. 58(9), 748–760 (2011).
[Crossref]

Khamitova, R.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Khonina, S. N.

S. N. Khonina, S. V. Karpeev, S. V. Alferov, D. A. Savelyev, J. Laukkanen, and J. Turnnen, “Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams,” J. Opt. 15(8), 085704 (2013).
[Crossref]

S. N. Khonina, N. L. Kazanskiy, and S. G. Volotovsky, “Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system,” J. Mod. Opt. 58(9), 748–760 (2011).
[Crossref]

Kimura, W. D.

R. D. Romea and W. D. Kimura, “Modeling of inverse C-caronerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D Part. Fields 42(5), 1807–1818 (1990).
[Crossref] [PubMed]

Konig-Otto, J. C.

Korotkova, O.

Laukkanen, J.

S. N. Khonina, S. V. Karpeev, S. V. Alferov, D. A. Savelyev, J. Laukkanen, and J. Turnnen, “Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams,” J. Opt. 15(8), 085704 (2013).
[Crossref]

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]

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Maccalli, S.

Maffei, B.

Mari, E.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

Miller, R. J.

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Mittendorff, M.

K. J. Kaltenecker, J. C. Konig-Otto, M. Mittendorff, S. Winnerl, H. Schneider, M. Helm, H. Helm, M. Walther, and B. M. Fischer, “Gouy phase shift of a tightly focused, radially polarized beam,” Optica 3(1), 35–41 (2016).
[Crossref]

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Moriena, G.

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Murokh, A.

J. Rosenzweig, A. Murokh, and C. Pellegrini, “A proposed dielectric-loaded resonant laser accelerator,” Phys. Rev. Lett. 74(13), 2467–2470 (1995).
[Crossref] [PubMed]

Nahata, A.

Nanni, E. A.

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Ng, M. W. R.

Novotny, L.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Padgett, M. J.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[Crossref] [PubMed]

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

M. J. Padgett and L. Allen, “The poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

Palmer, K.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Pellegrini, C.

J. Rosenzweig, A. Murokh, and C. Pellegrini, “A proposed dielectric-loaded resonant laser accelerator,” Phys. Rev. Lett. 74(13), 2467–2470 (1995).
[Crossref] [PubMed]

Pisano, G.

Pu, J.

Qu, J.

Z. Zhang, H. Fan, H. F. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).
[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]

Ravi, K.

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Ren, Y. X.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[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 Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Robertson, D. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

Romanato, F.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

Romea, R. D.

R. D. Romea and W. D. Kimura, “Modeling of inverse C-caronerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D Part. Fields 42(5), 1807–1818 (1990).
[Crossref] [PubMed]

Rosenzweig, J.

J. Rosenzweig, A. Murokh, and C. Pellegrini, “A proposed dielectric-loaded resonant laser accelerator,” Phys. Rev. Lett. 74(13), 2467–2470 (1995).
[Crossref] [PubMed]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
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Savelyev, D. A.

S. N. Khonina, S. V. Karpeev, S. V. Alferov, D. A. Savelyev, J. Laukkanen, and J. Turnnen, “Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams,” J. Opt. 15(8), 085704 (2013).
[Crossref]

Schemmel, P.

Schneider, H.

K. J. Kaltenecker, J. C. Konig-Otto, M. Mittendorff, S. Winnerl, H. Schneider, M. Helm, H. Helm, M. Walther, and B. M. Fischer, “Gouy phase shift of a tightly focused, radially polarized beam,” Optica 3(1), 35–41 (2016).
[Crossref]

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Schönle, A.

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6(4), 480–484 (2001).
[Crossref] [PubMed]

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Sick, B.

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

Simpson, N. B.

Sjöholm, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Smith, G. M.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

Sponselli, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

Sun, W.

Sun, W. F.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[Crossref] [PubMed]

Tamburini, F.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

F. Tamburini, B. Thide, G. M. Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[Crossref]

Terriza, G. M.

F. Tamburini, B. Thide, G. M. Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[Crossref]

Then, H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Thide, B.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

F. Tamburini, B. Thide, G. M. Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[Crossref]

Thidé, B.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Tian, N.

N. Tian, L. Fu, and M. Gu, “Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam,” Sci. Rep. 5, 13580 (2015).
[Crossref] [PubMed]

Tur, M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Turnbull, G. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

Turnnen, J.

S. N. Khonina, S. V. Karpeev, S. V. Alferov, D. A. Savelyev, J. Laukkanen, and J. Turnnen, “Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams,” J. Opt. 15(8), 085704 (2013).
[Crossref]

Volotovsky, S. G.

S. N. Khonina, N. L. Kazanskiy, and S. G. Volotovsky, “Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system,” J. Mod. Opt. 58(9), 748–760 (2011).
[Crossref]

Walther, M.

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Wang, J.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wang, S.

Wang, X.

Wang, X. K.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[Crossref] [PubMed]

Willner, A. E.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Winnerl, S.

K. J. Kaltenecker, J. C. Konig-Otto, M. Mittendorff, S. Winnerl, H. Schneider, M. Helm, H. Helm, M. Walther, and B. M. Fischer, “Gouy phase shift of a tightly focused, radially polarized beam,” Optica 3(1), 35–41 (2016).
[Crossref]

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[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 Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Xie, Z.

Xu, H. F.

Z. Zhang, H. Fan, H. F. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).
[Crossref]

Xu, X. G.

Yan, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Ye, J.

Ye, J. S.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[Crossref] [PubMed]

Youngworth, K.

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Zhan, Q.

Zhang, X.-C.

Zhang, Y.

Zhang, Z.

Z. Zhang, H. Fan, H. F. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).
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B. Chen, Z. Zhang, and J. Pu, “Tight focusing of partially coherent and circularly polarized vortex beams,” J. Opt. Soc. Am. A 26(4), 862–869 (2009).
[Crossref] [PubMed]

Zhu, W.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

J. W. M. Chon, X. S. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
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B. H. Jia, X. S. Gan, and M. Gu, “Direct observation of a pure focused evanescent field of a high numerical aperture objective lens by scanning near-field optical microscopy,” Appl. Phys. Lett. 86(13), 131110 (2005).
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Astrophys. J. (1)

M. Harwit, “Photon orbital angular momentum in astrophysics,” Astrophys. J. 597(2), 1266–1270 (2003).
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J. Biomed. Opt. (1)

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6(4), 480–484 (2001).
[Crossref] [PubMed]

J. Mod. Opt. (1)

S. N. Khonina, N. L. Kazanskiy, and S. G. Volotovsky, “Vortex phase transmission function as a factor to reduce the focal spot of high-aperture focusing system,” J. Mod. Opt. 58(9), 748–760 (2011).
[Crossref]

J. Opt. (2)

S. N. Khonina, S. V. Karpeev, S. V. Alferov, D. A. Savelyev, J. Laukkanen, and J. Turnnen, “Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams,” J. Opt. 15(8), 085704 (2013).
[Crossref]

Z. Zhang, H. Fan, H. F. Xu, J. Qu, and W. Huang, “Three-dimensional focus shaping of partially coherent circularly polarized vortex beams using a binary optic,” J. Opt. 17(6), 065611 (2015).
[Crossref]

J. Opt. Soc. Am. A (2)

Nat. Commun. (1)

E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Nat. Photonics (2)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Nat. Phys. (1)

F. Tamburini, B. Thide, G. M. Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7(3), 195–197 (2011).
[Crossref]

New J. Phys. (2)

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Opt. Commun. (3)

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[Crossref] [PubMed]

M. J. Padgett and L. Allen, “The poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Optica (1)

Phys. Rev. D Part. Fields (1)

R. D. Romea and W. D. Kimura, “Modeling of inverse C-caronerenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D Part. Fields 42(5), 1807–1818 (1990).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

J. Rosenzweig, A. Murokh, and C. Pellegrini, “A proposed dielectric-loaded resonant laser accelerator,” Phys. Rev. Lett. 74(13), 2467–2470 (1995).
[Crossref] [PubMed]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[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]

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

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[Crossref]

Sci. Rep. (1)

N. Tian, L. Fu, and M. Gu, “Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam,” Sci. Rep. 5, 13580 (2015).
[Crossref] [PubMed]

Other (1)

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Figures (9)

Fig. 1
Fig. 1 (a) Refractive index spectrum of a polylactic acid medium. (b) Photos of spiral phase plates with l = 1 (left) and 2 (right). (c) THz digital holographic imaging system.
Fig. 2
Fig. 2 (a) Amplitude and (b) wrapped phase distributions of the Ex component at 0.62 THz for a linearly polarized THz vortex beam with l = 1 on the focal plane. Corresponding (c) amplitude and (d) phase images of Ex with l = 2.
Fig. 3
Fig. 3 (a) Transverse and (b) longitudinal amplitude distributions of Ez at 0.62 THz for a linearly polarized THz vortex beam with l = 1 on the focal plane and cross-sectional plane (y = 0 mm), respectively. Corresponding (c) transverse and (d) longitudinal wrapped phase patterns. (e), (f), (g) and (h) are simulated amplitude and phase maps of Ez with l = 1 on the focal plane and cross-sectional plane by using the Richards-Wolf vector diffraction equation. (i) Normalized amplitude profile curves extracted from (a) and (e) on the line of y = 0 mm. The red solid line is the experimental result and the blue square dot line is the simulation one.
Fig. 4
Fig. 4 (a) Amplitude and (c) wrapped phase distributions of Ez at 0.62 THz for a linearly polarized THz vortex beam with l = 2 on the focal plane. Corresponding (b) amplitude and (d) wrapped phase maps of Ez on the x-z plane. (e), (f), (g) and (h) are transverse and longitudinal patterns of the amplitude and wrapped phase of Ez with l = 2 calculated by the modified Richards-Wolf equation. (i) Normalized experimental and simulation amplitude profile curves extracted from (a) and (e) along the y = 0 mm direction.
Fig. 5
Fig. 5 (a) Amplitude and (b) wrapped phase images of the Ex component at 0.62 THz for a right circularly polarized (RCP) THz vortex beam with l = 1 on the focal plane. Corresponding (c) amplitude and (d) phase patterns of the Ey component. (e), (f), (g), and (h) present the amplitude and wrapped phase distributions of Ex and Ey at 0.62 THz for a RCP THz beam with a vortex wave front of l = 2 on the focal plane.
Fig. 6
Fig. 6 (a) and (b) show the amplitude distributions of Ez at 0.62 THz for a converging right circularly polarized (RCP) THz vortex beam with l = 1 on the focal plane and x-z plane. (c) and (d) show the corresponding transverse and longitudinal wrapped phase patterns. (e), (f), (g), and (f) give simulated amplitude and phase images of Ez at 0.62 THz for a focused radially polarized beam with l = 1 on the transverse and longitudinal cross-sectional planes. (i) Comparison of normalized experimental and simulation Ez amplitude distribution plots obtained from (a) and (e) on the line of y = 0 mm.
Fig. 7
Fig. 7 (a) and (b) are the transverse and longitudinal amplitude patterns of Ez at 0.62 THz for a RCP THz vortex beam with l = 2. (c) and (d) are the corresponding wrapped phase maps of Ez on the transverse and longitudinal cross-sectional planes. (e), (f), (g), and (h) present simulated amplitude and phase distributions of Ez at 0.62 THz for a focused radially polarized vortex beam with a topological charge 1 on the focal plane and x-z plane, respectively. (i) Comparison of normalized experimental and simulation Ez amplitude distribution plots obtained from (a) and (e) along the y = 0 mm direction.
Fig. 8
Fig. 8 Normalized Ez amplitude profile curves of the RCP THz vortex beams with l = 1 (a) and 2 (b). These lines are obtained from Figs. 6(i) and 7(i). The blue dashed line is the amplitude profile of Ex for a converging linearly polarized THz beam at 0.62 THz on the focal plane.
Fig. 9
Fig. 9 (a) and (b) are the amplitude and wrapped phase images of Ez at 0.62 THz for a converging left circularly polarized (LCP) THz vortex beam with l = 1 on the focal plane. (c) and (d) are the corresponding amplitude and phase maps of Ez with l = 2. (e)-(h) present the simulated complex field distributions of Ez components of radially polarized vortex beams with charges 2 and 3.

Equations (4)

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h= lλ Δn ,
E z = i l+1 kf 0 α exp( ilφ ) B l ( t,φ ) sin 2 θ cosθ exp( ikzcosθ )dθ,
B l ( t,φ )= i 2 [ exp( iφ ) J l+1 ( t )exp( iφ ) J l1 ( t ) ],
E z = i l kf 0 α exp[ i( l1 )φ ] J l1 ( t ) sin 2 θ cosθ exp( ikzcosθ )dθ.

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