Abstract

In theory, there are analogous transformations of light’s spin and orbital angular momentum [Allen and Padgett, J. Mod. Opt. 54, 487 (2007)]; however, none have been observed experimentally yet. In particular, it is unknown if there exists for the orbital angular momentum of light an effect analogous to the spin angular momentum-based optical rotation; this would manifest itself as a rotation of the corresponding Hermite-Gauss mode. Here we report an experimental search for this effect in a cholesteric liquid crystal polymer, using strongly focussed, spin-orbit coupled light. We find that the relative phase velocities of the orbital modes constituting the Hermite-Gauss mode agree to within 10−5.

© 2011 OSA

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    [CrossRef] [PubMed]
  27. D. J. Broer and I. Heynderickx, “Three-dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules 23, 2474–2477 (1990).
    [CrossRef]
  28. R. A. M. Hikmet, J. Lub, and D. J. Broer, “Anisotropic networks formed by photopolymerization of liquid-crystalline molecules,” Adv. Mater. 3, 392–394 (1991).
    [CrossRef]
  29. D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
    [CrossRef]
  30. S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
    [CrossRef]
  31. T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused gaussian beam,” J. Opt. A 10, 115005 (2008).
    [CrossRef]
  32. J. Pastrnak and K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
    [CrossRef]
  33. A. G. Serebryakov and F. Bociort, “Spatial dispersion of crystals as a critical problem for deep uv lithography,” J. Opt. Technol. 70, 566–569 (2003).
    [CrossRef]
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    [CrossRef]

2010 (3)

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73, 096501 (2010).
[CrossRef]

A. Picón, J. Mompart, J. R. V. de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express 18, 3660–3671 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (3)

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused gaussian beam,” J. Opt. A 10, 115005 (2008).
[CrossRef]

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

R. Grinter, “Photon angular momentum: selection rules and multipolar transition moments,” J. Phys. B 41, 095001 (2008).
[CrossRef]

2007 (1)

L. Allen and M. Padgett, “Equivalent geometric transformations for spin and orbital angular momentum of light,” J. Mod. Opt. 54, 487–491 (2007).
[CrossRef]

2006 (3)

A. Alexandrescu, D. Cojoc, and E. D. Fabrizio, “Mechanism of angular momentum exchange between molecules and laguerre-gaussian beams,” Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

M. Padgett, G. Whyte, J. Girkin, A. Wright, L. Allen, P. Öhberg, and S. M. Barnett, “Polarization and image rotation induced by a rotating dielectric rod: an optical angular momentum interpretation,” Opt. Lett. 31, 2205–2207 (2006).
[CrossRef] [PubMed]

2005 (1)

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[CrossRef]

2004 (2)

R. Jáuregui, “Rotational effects of twisted light on atoms beyond the paraxial approximation,” Phys. Rev. A 70, 033415 (2004).
[CrossRef]

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[CrossRef]

2003 (2)

A. G. Serebryakov and F. Bociort, “Spatial dispersion of crystals as a critical problem for deep uv lithography,” J. Opt. Technol. 70, 566–569 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef] [PubMed]

2002 (2)

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, “A quantum electrodynamics framework for the nonlinear optics of twisted beams,” J. Opt. B 4, S66 (2002).
[CrossRef]

1999 (2)

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
[CrossRef]

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

1998 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

1997 (1)

1995 (2)

W. D. St. John, W. J. Fritz, Z. J. Lu, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E 51, 1191–1198 (1995).
[CrossRef]

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, 826–829 (1995).
[CrossRef] [PubMed]

1994 (2)

S. J. van Enk and G. Nienhuis, “Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields,” J. Mod. Opt. 41, 963–977 (1994).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

1993 (1)

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

1992 (1)

G. Nienhuis, J. P. Woerdman, and I. Kuščer, “Magnetic and mechanical faraday effects,” Phys. Rev. A 46, 7079–7092 (1992).
[CrossRef] [PubMed]

1991 (1)

R. A. M. Hikmet, J. Lub, and D. J. Broer, “Anisotropic networks formed by photopolymerization of liquid-crystalline molecules,” Adv. Mater. 3, 392–394 (1991).
[CrossRef]

1990 (1)

D. J. Broer and I. Heynderickx, “Three-dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules 23, 2474–2477 (1990).
[CrossRef]

1971 (1)

J. Pastrnak and K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

1970 (1)

D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
[CrossRef]

Alexandrescu, A.

A. Alexandrescu, D. Cojoc, and E. D. Fabrizio, “Mechanism of angular momentum exchange between molecules and laguerre-gaussian beams,” Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Allen, L.

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

L. Allen and M. Padgett, “Equivalent geometric transformations for spin and orbital angular momentum of light,” J. Mod. Opt. 54, 487–491 (2007).
[CrossRef]

M. Padgett, G. Whyte, J. Girkin, A. Wright, L. Allen, P. Öhberg, and S. M. Barnett, “Polarization and image rotation induced by a rotating dielectric rod: an optical angular momentum interpretation,” Opt. Lett. 31, 2205–2207 (2006).
[CrossRef] [PubMed]

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, 52–54 (1997).
[CrossRef] [PubMed]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

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

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Andrews, D. L.

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[CrossRef]

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, “A quantum electrodynamics framework for the nonlinear optics of twisted beams,” J. Opt. B 4, S66 (2002).
[CrossRef]

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Araoka, F.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef] [PubMed]

Babiker, M.

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[CrossRef]

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, “A quantum electrodynamics framework for the nonlinear optics of twisted beams,” J. Opt. B 4, S66 (2002).
[CrossRef]

Barnett, S. M.

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

M. Padgett, G. Whyte, J. Girkin, A. Wright, L. Allen, P. Öhberg, and S. M. Barnett, “Polarization and image rotation induced by a rotating dielectric rod: an optical angular momentum interpretation,” Opt. Lett. 31, 2205–2207 (2006).
[CrossRef] [PubMed]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

Baudisch, M.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Beijersbergen, M. W.

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

Bennett, C. R.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Berreman, D. W.

D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
[CrossRef]

Bloch, D.

Bloch, J.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Bociort, F.

Broer, D. J.

R. A. M. Hikmet, J. Lub, and D. J. Broer, “Anisotropic networks formed by photopolymerization of liquid-crystalline molecules,” Adv. Mater. 3, 392–394 (1991).
[CrossRef]

D. J. Broer and I. Heynderickx, “Three-dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules 23, 2474–2477 (1990).
[CrossRef]

Calvo, G. F.

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Clays, K.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Cojoc, D.

A. Alexandrescu, D. Cojoc, and E. D. Fabrizio, “Mechanism of angular momentum exchange between molecules and laguerre-gaussian beams,” Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Courtial, J.

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef] [PubMed]

Dávila Romero, L. C.

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[CrossRef]

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, “A quantum electrodynamics framework for the nonlinear optics of twisted beams,” J. Opt. B 4, S66 (2002).
[CrossRef]

de Aldana, J. R. V.

Dholakia, K.

Ducloy, M.

Fabrizio, E. D.

A. Alexandrescu, D. Cojoc, and E. D. Fabrizio, “Mechanism of angular momentum exchange between molecules and laguerre-gaussian beams,” Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef] [PubMed]

Franke-Arnold, S.

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

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, 826–829 (1995).
[CrossRef] [PubMed]

Fritz, W. J.

W. D. St. John, W. J. Fritz, Z. J. Lu, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E 51, 1191–1198 (1995).
[CrossRef]

Girkin, J.

Girkin, J. M.

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

Götte, J. B.

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

Grinter, R.

R. Grinter, “Photon angular momentum: selection rules and multipolar transition moments,” J. Phys. B 41, 095001 (2008).
[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, 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused gaussian beam,” J. Opt. A 10, 115005 (2008).
[CrossRef]

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, 826–829 (1995).
[CrossRef] [PubMed]

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Heynderickx, I.

D. J. Broer and I. Heynderickx, “Three-dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules 23, 2474–2477 (1990).
[CrossRef]

Hikmet, R. A. M.

R. A. M. Hikmet, J. Lub, and D. J. Broer, “Anisotropic networks formed by photopolymerization of liquid-crystalline molecules,” Adv. Mater. 3, 392–394 (1991).
[CrossRef]

Jáuregui, R.

R. Jáuregui, “Rotational effects of twisted light on atoms beyond the paraxial approximation,” Phys. Rev. A 70, 033415 (2004).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Khoo, I.

I. Khoo, Liquid Crystals , Wiley series in pure and applied optics (Wiley-Interscience, 2007).
[CrossRef]

Klimov, V.

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Krizhanovskii, D. N.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Kušcer, I.

G. Nienhuis, J. P. Woerdman, and I. Kuščer, “Magnetic and mechanical faraday effects,” Phys. Rev. A 46, 7079–7092 (1992).
[CrossRef] [PubMed]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, 1975), Vol. 8.

Laussy, F. P.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Leach, J.

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

Leite, J. R. R.

Lemaitre, A.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, 1975), Vol. 8.

Lu, Z. J.

W. D. St. John, W. J. Fritz, Z. J. Lu, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E 51, 1191–1198 (1995).
[CrossRef]

Lub, J.

R. A. M. Hikmet, J. Lub, and D. J. Broer, “Anisotropic networks formed by photopolymerization of liquid-crystalline molecules,” Adv. Mater. 3, 392–394 (1991).
[CrossRef]

Marchetti, F. M.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Marrucci, L.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Mompart, J.

Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Nieminen, T. A.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused gaussian beam,” J. Opt. A 10, 115005 (2008).
[CrossRef]

Nienhuis, G.

S. J. van Enk and G. Nienhuis, “Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields,” J. Mod. Opt. 41, 963–977 (1994).
[CrossRef]

G. Nienhuis, J. P. Woerdman, and I. Kuščer, “Magnetic and mechanical faraday effects,” Phys. Rev. A 46, 7079–7092 (1992).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73, 096501 (2010).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Öhberg, P.

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef] [PubMed]

Padgett, M.

Padgett, M. J.

Pastrnak, J.

J. Pastrnak and K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

Persoons, A.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Petrov, D. V.

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Picón, A.

Plaja, L.

Roso, L.

Rubinsztein-Dunlop, H.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused gaussian beam,” J. Opt. A 10, 115005 (2008).
[CrossRef]

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, 826–829 (1995).
[CrossRef] [PubMed]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Sanvitto, D.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Scheffer, T. J.

D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
[CrossRef]

Serebryakov, A. G.

Simpson, N. B.

Skolnick, M. S.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Soukoulis, C. M.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef] [PubMed]

St. John, W. D.

W. D. St. John, W. J. Fritz, Z. J. Lu, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E 51, 1191–1198 (1995).
[CrossRef]

Stilgoe, A. B.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused gaussian beam,” J. Opt. A 10, 115005 (2008).
[CrossRef]

Szymanska, M. H.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Tabosa, J. W. R.

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Tejedor, C.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Tosi, G.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

van der Veen, H. E. L. O.

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

van Enk, S. J.

S. J. van Enk and G. Nienhuis, “Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields,” J. Mod. Opt. 41, 963–977 (1994).
[CrossRef]

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Vedam, K.

J. Pastrnak and K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

Verbiest, T.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Vina, L.

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Whyte, G.

Woerdman, J. P.

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

G. Nienhuis, J. P. Woerdman, and I. Kuščer, “Magnetic and mechanical faraday effects,” Phys. Rev. A 46, 7079–7092 (1992).
[CrossRef] [PubMed]

Wright, A.

Wright, A. J.

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

Yang, D.-K.

W. D. St. John, W. J. Fritz, Z. J. Lu, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E 51, 1191–1198 (1995).
[CrossRef]

Adv. Mater. (1)

R. A. M. Hikmet, J. Lub, and D. J. Broer, “Anisotropic networks formed by photopolymerization of liquid-crystalline molecules,” Adv. Mater. 3, 392–394 (1991).
[CrossRef]

J. Mod. Opt. (2)

S. J. van Enk and G. Nienhuis, “Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields,” J. Mod. Opt. 41, 963–977 (1994).
[CrossRef]

L. Allen and M. Padgett, “Equivalent geometric transformations for spin and orbital angular momentum of light,” J. Mod. Opt. 54, 487–491 (2007).
[CrossRef]

J. Opt. A (1)

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Angular momentum of a strongly focused gaussian beam,” J. Opt. A 10, 115005 (2008).
[CrossRef]

J. Opt. B (1)

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, “A quantum electrodynamics framework for the nonlinear optics of twisted beams,” J. Opt. B 4, S66 (2002).
[CrossRef]

J. Opt. Technol. (1)

J. Phys. B (1)

R. Grinter, “Photon angular momentum: selection rules and multipolar transition moments,” J. Phys. B 41, 095001 (2008).
[CrossRef]

Macromolecules (1)

D. J. Broer and I. Heynderickx, “Three-dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules 23, 2474–2477 (1990).
[CrossRef]

Nat. Phys. (1)

D. Sanvitto, F. M. Marchetti, M. H. Szymanska, G. Tosi, M. Baudisch, F. P. Laussy, D. N. Krizhanovskii, M. S. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Vina, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[CrossRef]

Nature (1)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604–605 (2003).
[CrossRef] [PubMed]

Opt. Commun. (3)

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

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, “On optical vortex interactions with chiral matter,” Opt. Commun. 237, 133–139 (2004).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (3)

R. Jáuregui, “Rotational effects of twisted light on atoms beyond the paraxial approximation,” Phys. Rev. A 70, 033415 (2004).
[CrossRef]

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, “Interactions of twisted light with chiral molecules: an experimental investigation,” Phys. Rev. A 71, 055401 (2005).
[CrossRef]

G. Nienhuis, J. P. Woerdman, and I. Kuščer, “Magnetic and mechanical faraday effects,” Phys. Rev. A 46, 7079–7092 (1992).
[CrossRef] [PubMed]

Phys. Rev. B (2)

J. Pastrnak and K. Vedam, “Optical anisotropy of silicon single crystals,” Phys. Rev. B 3, 2567–2571 (1971).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Phys. Rev. E (1)

W. D. St. John, W. J. Fritz, Z. J. Lu, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E 51, 1191–1198 (1995).
[CrossRef]

Phys. Rev. Lett. (7)

D. W. Berreman and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970).
[CrossRef]

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83, 4967–4970 (1999).
[CrossRef]

J. Leach, A. J. Wright, J. B. Götte, J. M. Girkin, L. Allen, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “‘aether drag’ and moving images,” Phys. Rev. Lett. 100, 153902 (2008).
[CrossRef] [PubMed]

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, 826–829 (1995).
[CrossRef] [PubMed]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

A. Alexandrescu, D. Cojoc, and E. D. Fabrizio, “Mechanism of angular momentum exchange between molecules and laguerre-gaussian beams,” Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73, 096501 (2010).
[CrossRef]

Other (2)

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, 1975), Vol. 8.

I. Khoo, Liquid Crystals , Wiley series in pure and applied optics (Wiley-Interscience, 2007).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Cholesteric liquid crystal. (a) Optical properties: If the wavelength of the incident light matches the pitch p 0 of the cholesteric liquid crystal (black bar), the reflected (transmitted) light has the same (opposite) handedness as the CLC. (b) Experimentally measured optical rotation (in transmission, normal incidence) of linear polarized light, showing the expected dispersive behavior around the resonant reflection band (gray box).

Fig. 2
Fig. 2

Scheme of the experiment. Pol.: linear polarizers; PEM: photo-elastic modulator; SLM: spatial light modulator; PD: photo diode; SMF: single-mode fiber. The CCD is used to record the profile of the transmitted mode.

Fig. 3
Fig. 3

Demonstration of the fit algorithm used to determine the nodal line orientation of the Hermite-Gauss type mode: (a) 2D intensity profile; (b) example fit (intensity as a function of CCD column) of a horizontal cross section of this profile; and (c) linear regression (as a function of the CCD row) to find the global angle of this nodal line.

Fig. 4
Fig. 4

Measurement of the HG 1,0-mode rotation angle (inset) at different wavelengths for focussed probe light (NA=0.4).

Equations (2)

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

cos ( ϕ ) | H G 1 , 0 + sin ( ϕ ) | H G 0 , 1 e i ϕ | L G 1 , 0 + e i ϕ | L G + 1 , 0
J z E = σ z + ω + σ z ω ( 4 / θ 0 2 2 p + + 1 + 1 ) 1

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