Abstract

The study of light fields near nanophotonic structures continually reveals new fundamental features of light–matter interactions on the nanoscale, driving advances in fields ranging from nonlinear and quantum optics to biosensing. Here, we have succeeded in separately mapping the electric and magnetic fields. This allows us to present the first fully three-dimensional maps of the in-plane electromagnetic near fields of a photonic crystal waveguide, in experiment and theory. In these fields, we identify and study the spatial evolution of infinitesimally small optical entities: optical singularities. We discuss the topological properties of the local light fields in the vicinity of the singularities and show that the trajectory traced by each singularity through three-dimensional space is distinct. These results are an important step toward understanding the behavior of light at the nanoscale, opening up new avenues for on-chip control and detection of nanoscopic or quantum objects with structured light fields.

© 2015 Optical Society of America

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References

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    [Crossref]

2015 (1)

B. le Feber, N. Rotenberg, L. Kuipers, “Nanophotonic countrol of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

2014 (7)

A. de Hoogh, N. Rotenberg, L. Kuipers, “Optical singularities in plasmonic fields near single subwavelength holes,” J. Opt. 16, 114004 (2014).
[Crossref]

BICEP2 Collaboration, “Detection of B-mode polarization at degree angular scales by BICEP2,” Phys. Rev. Lett. 112, 241101 (2014).
[Crossref]

S. Hashiyada, T. Narushima, H. Okamoto, “Local optical activity in achiral two-dimensional gold nanostructures,” J. Phys. Chem. C 118, 22229–22233 (2014).
[Crossref]

N. Rotenberg, L. Kuipers, “Mapping nanoscale light fields,” Nat. Photonics 8, 919–926 (2014), and references therein.

A. Libster-Hershko, I. Epstein, A. Arie, “Rapidly accelerating Mathieu and Weber surface plasmon beams,” Phys. Rev. Lett. 113, 123902 (2014).
[Crossref]

J. Petersen, J. Volz, A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

2013 (4)

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

B. le Feber, N. Rotenberg, D. M. Beggs, L. Kuipers, “Simultaneous measurement of nanoscale electric and magnetic optical fields,” Nat. Photonics 8, 43–46 (2013).
[Crossref]

H. Kedia, I. Bialynicki-Birula, D. Peralta-Salas, W. T. Irvine, “Tying knots in light fields,” Phys. Rev. Lett. 111, 150404 (2013).
[Crossref]

T. J. Davis, E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).

2012 (2)

I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

2011 (2)

A. Minovich, A. E. Klein, N. Januts, T. Pertsch, D. N. Neshev, Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[Crossref]

Y. Tang, A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

2010 (2)

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
[Crossref]

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
[Crossref]

2009 (2)

M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
[Crossref]

2008 (1)

W. T. M. Irvine, D. Bouwmeester, “Linked and knotted beams of light,” Nat. Phys. 4, 716–720 (2008).
[Crossref]

2006 (1)

2005 (1)

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94, 123901 (2005).
[Crossref]

2004 (2)

H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, H. Blok, “Connection between phase singularities and the radiation pattern of a slit in a metal plate,” Phys. Rev. Lett. 93, 173901 (2004).
[Crossref]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[Crossref]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref]

2002 (1)

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

2001 (2)

M. V. Berry, M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. A 457, 141–155 (2001).

S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref]

2000 (1)

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[Crossref]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, 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]

Albrecht, B.

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

Andrews, D. L.

D. L. Andrews, Structured Light and Its Applications (Academic, 2008).

Arie, A.

A. Libster-Hershko, I. Epstein, A. Arie, “Rapidly accelerating Mathieu and Weber surface plasmon beams,” Phys. Rev. Lett. 113, 123902 (2014).
[Crossref]

Baba, T.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
[Crossref]

Balistreri, M. L. M.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[Crossref]

Barnett, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref]

Barron, L. D.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
[Crossref]

Beggs, D. M.

B. le Feber, N. Rotenberg, D. M. Beggs, L. Kuipers, “Simultaneous measurement of nanoscale electric and magnetic optical fields,” Nat. Photonics 8, 43–46 (2013).
[Crossref]

A. B. Young, A. Thijssen, D. M. Beggs, L. Kuipers, J. G. Rarity, R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” arXiv: 1406.0714 (2014).

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Berry, M. V.

M. V. Berry, M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. A 457, 141–155 (2001).

Bialynicki-Birula, I.

H. Kedia, I. Bialynicki-Birula, D. Peralta-Salas, W. T. Irvine, “Tying knots in light fields,” Phys. Rev. Lett. 111, 150404 (2013).
[Crossref]

Blok, H.

H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, H. Blok, “Connection between phase singularities and the radiation pattern of a slit in a metal plate,” Phys. Rev. Lett. 93, 173901 (2004).
[Crossref]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94, 123901 (2005).
[Crossref]

Bouwmeester, D.

W. T. M. Irvine, D. Bouwmeester, “Linked and knotted beams of light,” Nat. Phys. 4, 716–720 (2008).
[Crossref]

Burresi, M.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
[Crossref]

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

Carpy, T.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
[Crossref]

Christodoulides, D. N.

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
[Crossref]

Cohen, A. E.

Y. Tang, A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[Crossref]

Davis, T. J.

T. J. Davis, E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).

de Hoogh, A.

A. de Hoogh, N. Rotenberg, L. Kuipers, “Optical singularities in plasmonic fields near single subwavelength holes,” J. Opt. 16, 114004 (2014).
[Crossref]

Dennis, M. R.

M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

J. Leach, M. R. Dennis, J. Courtial, M. J. Padgett, “Laser beams: knotted threads of darkness,” Nature 432, 165 (2004).
[Crossref]

M. V. Berry, M. R. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. R. Soc. A 457, 141–155 (2001).

El-Ella, H.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” arXiv: 1406.4295 (2015).

Engelen, R. J. P.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
[Crossref]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94, 123901 (2005).
[Crossref]

Epstein, I.

A. Libster-Hershko, I. Epstein, A. Arie, “Rapidly accelerating Mathieu and Weber surface plasmon beams,” Phys. Rev. Lett. 113, 123902 (2014).
[Crossref]

Fleischer, J. W.

S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
[Crossref]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, 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]

Gadegaard, N.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
[Crossref]

Gbur, G.

H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, H. Blok, “Connection between phase singularities and the radiation pattern of a slit in a metal plate,” Phys. Rev. Lett. 93, 173901 (2004).
[Crossref]

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94, 123901 (2005).
[Crossref]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref]

Hansen, S. L.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” arXiv: 1406.4295 (2015).

Hashiyada, S.

S. Hashiyada, T. Narushima, H. Okamoto, “Local optical activity in achiral two-dimensional gold nanostructures,” J. Phys. Chem. C 118, 22229–22233 (2014).
[Crossref]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, 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]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, 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]

Hendry, E.

T. J. Davis, E. Hendry, “Superchiral electromagnetic fields created by surface plasmons in nonchiral metallic nanostructures,” Phys. Rev. B 87, 085405 (2013).

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
[Crossref]

Irvine, W. T.

H. Kedia, I. Bialynicki-Birula, D. Peralta-Salas, W. T. Irvine, “Tying knots in light fields,” Phys. Rev. Lett. 111, 150404 (2013).
[Crossref]

Irvine, W. T. M.

W. T. M. Irvine, D. Bouwmeester, “Linked and knotted beams of light,” Nat. Phys. 4, 716–720 (2008).
[Crossref]

Januts, N.

A. Minovich, A. E. Klein, N. Januts, T. Pertsch, D. N. Neshev, Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
[Crossref]

Javadi, A.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” arXiv: 1406.4295 (2015).

Jia, S.

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

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N. Rotenberg, L. Kuipers, “Mapping nanoscale light fields,” Nat. Photonics 8, 919–926 (2014), and references therein.

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A. B. Young, A. Thijssen, D. M. Beggs, L. Kuipers, J. G. Rarity, R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” arXiv: 1406.0714 (2014).

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S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
[Crossref]

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

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I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” arXiv: 1406.4295 (2015).

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E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
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M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
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A. B. Young, A. Thijssen, D. M. Beggs, L. Kuipers, J. G. Rarity, R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” arXiv: 1406.0714 (2014).

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M. P. J. Lavery, F. C. Speirits, S. M. Barnett, M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
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M. R. Dennis, K. O’Holleran, M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
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A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
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H. Kedia, I. Bialynicki-Birula, D. Peralta-Salas, W. T. Irvine, “Tying knots in light fields,” Phys. Rev. Lett. 111, 150404 (2013).
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A. Minovich, A. E. Klein, N. Januts, T. Pertsch, D. N. Neshev, Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. 107, 116802 (2011).
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E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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A. B. Young, A. Thijssen, D. M. Beggs, L. Kuipers, J. G. Rarity, R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” arXiv: 1406.0714 (2014).

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B. le Feber, N. Rotenberg, L. Kuipers, “Nanophotonic countrol of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
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A. de Hoogh, N. Rotenberg, L. Kuipers, “Optical singularities in plasmonic fields near single subwavelength holes,” J. Opt. 16, 114004 (2014).
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B. le Feber, N. Rotenberg, D. M. Beggs, L. Kuipers, “Simultaneous measurement of nanoscale electric and magnetic optical fields,” Nat. Photonics 8, 43–46 (2013).
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H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, H. Blok, “Connection between phase singularities and the radiation pattern of a slit in a metal plate,” Phys. Rev. Lett. 93, 173901 (2004).
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I. Kaminer, R. Bekenstein, J. Nemirovsky, M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
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S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media,” Phys. Rev. Lett. 104, 253904 (2010).
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I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” arXiv: 1406.4295 (2015).

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I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” arXiv: 1406.4295 (2015).

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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[Crossref]

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M. P. J. Lavery, F. C. Speirits, S. M. Barnett, M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
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I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” arXiv: 1406.4295 (2015).

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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
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M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
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J. Petersen, J. Volz, A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
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A. B. Young, A. Thijssen, D. M. Beggs, L. Kuipers, J. G. Rarity, R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” arXiv: 1406.0714 (2014).

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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
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X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
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A. de Hoogh, N. Rotenberg, L. Kuipers, “Optical singularities in plasmonic fields near single subwavelength holes,” J. Opt. 16, 114004 (2014).
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R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
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N. Rotenberg, L. Kuipers, “Mapping nanoscale light fields,” Nat. Photonics 8, 919–926 (2014), and references therein.

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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1.

Three-dimensional near-field microscopy. (a) Schematic of the near-field scanning optical microscope used to create three dimensional near-field maps above a PhCW. A polarizing beam splitter (PBS) splits the light into the signal branch, which is coupled into the PhCW, and a reference branch. The aperture probe tip scatters some of the near field into the fiber, where it is combined with the light in the reference branch and then detected on two photodiodes. A set of half-wave plates (HWPs) and a quarter-wave plate (QWP) ensure that the detector and sample frames are identical. (b) Measured field amplitudes of the in-plane electromagnetic near fields over 2 unit cells of the PhCW, at heights ranging from 20 to 280 nm above the waveguide surface. The scaling of each measurement, relative to the 20 nm plane, is indicated by the multiplication factor in the bottom left corner of each frame.

Fig. 2.
Fig. 2.

Complex in-plane electromagnetic near fields above a PhCW: the calculated and measured amplitude (a)–(d) and corresponding phase (e)–(h) distributions of the in-plane electromagnetic field components 110 nm above the photonic crystal waveguide. The relative scaling of the amplitudes is shown the bottom right corner of (a)–(d) and the locations of the holes of the PhCW are indicated by the dashed blue curves. In (e)–(h), lines of constant phase are shown, and the phase singularities (denoted by solid symbols on all frames) occur where these lines intersect. In each frame we show the fields of two unit cells, marking the singularities in one of the unit cells. Calculations are shown on the left half of each frame, while the right half depicts the measurements.

Fig. 3.
Fig. 3.

Trajectories of phase singularities above the PhCW: the y position of the p1 (a) and the p2 (b) phase singularities for all in-plane field components as a function of height. In both panels the trajectories of the singularities determined from theoretical modeling are given by the solid curves, while the corresponding experimentally measured positions are shown by the symbols. The error bars represent the resolution of our measurements, and the period of the PhCW is a=420nm.

Fig. 4.
Fig. 4.

Polarization state of the light 110 nm above the PhCW. (a) The polarization ellipse for the in-plane electric field, showing the ellipticity, ε, and the angle of orientation α; (b)–(g), the amplitude, angle of orientation, and ellipticity of the in-plane electric fields (b)–(d) and in-plane magnetic fields (e)–(g). The scaling factors of the field amplitudes are shown in the bottom right corner of (b) and (e). The polarization singularities (C-points), c1,r and c2,r, are marked by symbols in (b)–(g). Lines of constant α, which intersect at the singularities, are shown in (c) and (f), as are lines of linear polarization (L-lines) in (d) and (g).

Fig. 5.
Fig. 5.

Trajectories of the polarization singularities. The left side shows two of the singularities associated with the in-plane electric field, and the right side shows two associated with the in-plane magnetic field. Both calculations (curves) and measurements (symbols) are shown, and the error bars on the latter are due to the experimental resolution. The bottom axis denotes the position of each singularity, while in the top we show the separation between each singularity pair.

Tables (1)

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Table 1. OAM Charge of the Phase Singularities in the In-Plane Fieldsa

Equations (3)

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s=12πCdφ,
ε(r)=tan{sin1[sin(2ψ(r))sin(δ(r))]/2},
α(r)={tan1[tan(2ψ(r))cos(δ(r))]}/2,

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