Abstract

Optical singularities have attracted much interest in the past decades, enabling advancements in nano-manipulation, bio-sensing, and quantum optics, owing to their ability to carry and transfer angular momentum on the nano scale. Optical vortices (OVs), in this respect, are phase singularities useful for many applications, such as particle trapping and manipulation, optical communication, and super-resolution. Vectorial OVs also exhibit polarization singularities, known as C-points, which have been used in recent years to control emission from quantum emitters. Here, we present continuous nanoscale spatial control over optical singularities on a metal–air interface by varying the polarization state of the light exciting surface plasmon polaritons through a spiral slit. We demonstrate our method using phase-resolved near-field microscopy. Such control over optical singularities opens up exciting possibilities for light in two dimensions, ranging from new light–matter interactions on a chip to efficiently controlled nanomotors.

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

Full Article  |  PDF Article
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References

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    [Crossref]

2017 (2)

G. Spektor, D. Kilbane, A. K. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein, and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science 355, 1187–1191 (2017).
[Crossref]

E. Maguid, M. Yannai, A. Faerman, I. Yulevich, V. Kleiner, and E. Hasman, “Disorder-induced optical transition from spin Hall to random Rashba effect,” Science 358, 1411–1415 (2017).

2016 (3)

A. David, B. Gjonaj, and G. Bartal, “Two-dimensional optical nanovortices at visible light,” Phys. Rev. B 93, 121302 (2016).
[Crossref]

N. Rivera, I. Kaminer, B. Zhen, J. D. Joannopoulos, and M. Soljačić, “Shrinking light to allow forbidden transitions on the atomic scale,” Science 353, 263–269 (2016).
[Crossref]

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

2015 (4)

A. David, B. Gjonaj, Y. Blau, S. Dolev, and G. Bartal, “Nanoscale shaping and focusing of visible light in planar metal-oxide–silicon waveguides,” Optica 2, 1045–1048 (2015).
[Crossref]

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

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. E. Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

A. de Hoogh, L. Kuipers, T. D. Visser, and N. Rotenberg, “Creating and controlling polarization singularities in plasmonic fields,” Photonics 2, 553–567 (2015).
[Crossref]

2014 (3)

R. Neo, S. J. Tan, X. Z. Puyalto, S. L. Saval, J. B. Hawthorn, and G. M. Terriza, “Correcting vortex splitting in higher order vortex beams,” Opt. Express 22, 9920–9931 (2014).
[Crossref]

W. Y. Tsai, J. S. Huang, and C. B. Huang, “Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic Archimedes spiral,” Nano Lett. 14, 547–552 (2014).
[Crossref]

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

2013 (2)

M. V. Berry, “A note on superoscillations associated with Bessel beams,” J. Opt. 15, 044006 (2013).
[Crossref]

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Y. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt. 15, 073001 (2013).
[Crossref]

2012 (4)

N. Shitrit, S. Nechayev, V. Kleiner, and E. Hasman, “Spin-dependent plasmonics based on interfering topological defects,” Nano Lett. 12, 1620–1623 (2012).
[Crossref]

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

Z. Shen, Z. J. Hu, G. H. Yuan, C. J. Min, H. Fang, and X.-C. Yuan, “Visualizing orbital angular momentum of plasmonic vortices,” Opt. Lett. 37, 4627–4629 (2012).
[Crossref]

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

2011 (1)

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Active spatial control of plasmonic fields,” Nat. Photonics 5, 360–363 (2011).
[Crossref]

2010 (2)

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5, 570–573 (2010).
[Crossref]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref]

2008 (1)

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

2006 (5)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31, 1325–1327 (2006).
[Crossref]

J. Gore, Z. Bryant, M. Nöllmann, M. U. Le, N. R. Cozzarelli, and C. Bustamante, “DNA overwinds when stretched,” Nature 442, 836–839 (2006).
[Crossref]

R. Eelkema, M. M. Pollard, J. Vicario, N. Katsonis, B. S. Ramon, C. W. M. Bastiaansen, D. J. Broer, and B. L. Feringa, “Nanomotor rotates microscale objects,” Nature 440, 163 (2006).
[Crossref]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006).
[Crossref]

2004 (2)

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

P. Lodahl, A. F. V. Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[Crossref]

2003 (1)

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

2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. A 457, 2251–2263 (2001).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

Aeschlimann, M.

G. Spektor, D. Kilbane, A. K. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein, and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science 355, 1187–1191 (2017).
[Crossref]

Ahmed, N.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

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

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Aulbach, J.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, “Active spatial control of plasmonic fields,” Nat. Photonics 5, 360–363 (2011).
[Crossref]

Bao, C.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Barnett, S. M.

Bartal, G.

A. David, B. Gjonaj, and G. Bartal, “Two-dimensional optical nanovortices at visible light,” Phys. Rev. B 93, 121302 (2016).
[Crossref]

A. David, B. Gjonaj, Y. Blau, S. Dolev, and G. Bartal, “Nanoscale shaping and focusing of visible light in planar metal-oxide–silicon waveguides,” Optica 2, 1045–1048 (2015).
[Crossref]

M. Liu, T. Zentgraf, Y. Liu, G. Bartal, and X. Zhang, “Light-driven nanoscale plasmonic motors,” Nat. Nanotechnol. 5, 570–573 (2010).
[Crossref]

Bastiaansen, C. W. M.

R. Eelkema, M. M. Pollard, J. Vicario, N. Katsonis, B. S. Ramon, C. W. M. Bastiaansen, D. J. Broer, and B. L. Feringa, “Nanomotor rotates microscale objects,” Nature 440, 163 (2006).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Berry, M. V.

M. V. Berry, “A note on superoscillations associated with Bessel beams,” J. Opt. 15, 044006 (2013).
[Crossref]

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. A 457, 2251–2263 (2001).
[Crossref]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

Blau, Y.

Broer, D. J.

R. Eelkema, M. M. Pollard, J. Vicario, N. Katsonis, B. S. Ramon, C. W. M. Bastiaansen, D. J. Broer, and B. L. Feringa, “Nanomotor rotates microscale objects,” Nature 440, 163 (2006).
[Crossref]

Bryant, Z.

J. Gore, Z. Bryant, M. Nöllmann, M. U. Le, N. R. Cozzarelli, and C. Bustamante, “DNA overwinds when stretched,” Nature 442, 836–839 (2006).
[Crossref]

Buljan, H.

F. Machado, N. Rivera, H. Buljan, M. Soljačić, and I. Kaminer, “Shaping polaritons to reshape selection rules,” arXiv:1610.01668 (2016).

Bustamante, C.

J. Gore, Z. Bryant, M. Nöllmann, M. U. Le, N. R. Cozzarelli, and C. Bustamante, “DNA overwinds when stretched,” Nature 442, 836–839 (2006).
[Crossref]

Cai, X.

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

Cao, Y.

Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5, 4876 (2014).
[Crossref]

Cho, S. W.

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref]

Clarke, E.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Coles, R. J.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Courtial, J.

Cozzarelli, N. R.

J. Gore, Z. Bryant, M. Nöllmann, M. U. Le, N. R. Cozzarelli, and C. Bustamante, “DNA overwinds when stretched,” Nature 442, 836–839 (2006).
[Crossref]

David, A.

de Hoogh, A.

A. de Hoogh, L. Kuipers, T. D. Visser, and N. Rotenberg, “Creating and controlling polarization singularities in plasmonic fields,” Photonics 2, 553–567 (2015).
[Crossref]

A. de Hoogh, “Optical singularities and nonlinear effects near plasmonic nanostructures,” Ph.D. dissertation (Delft University of Technology, 2016), pp. 13–14.

Dennis, M. R.

M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31, 1325–1327 (2006).
[Crossref]

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. A 457, 2251–2263 (2001).
[Crossref]

Dixon, J. E.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Dolev, S.

Dolinar, S.

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

Driel, A. F. V.

P. Lodahl, A. F. V. Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[Crossref]

Eelkema, R.

R. Eelkema, M. M. Pollard, J. Vicario, N. Katsonis, B. S. Ramon, C. W. M. Bastiaansen, D. J. Broer, and B. L. Feringa, “Nanomotor rotates microscale objects,” Nature 440, 163 (2006).
[Crossref]

Ella, H. E.

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[Crossref]

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G. Spektor, D. Kilbane, A. K. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein, and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science 355, 1187–1191 (2017).
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A. de Hoogh, L. Kuipers, T. D. Visser, and N. Rotenberg, “Creating and controlling polarization singularities in plasmonic fields,” Photonics 2, 553–567 (2015).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Hang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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X. Cai, J. Wang, M. J. Strain, B. J. Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
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Yuan, X.-C.

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Hang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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E. Maguid, M. Yannai, A. Faerman, I. Yulevich, V. Kleiner, and E. Hasman, “Disorder-induced optical transition from spin Hall to random Rashba effect,” Science 358, 1411–1415 (2017).

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N. Rivera, I. Kaminer, B. Zhen, J. D. Joannopoulos, and M. Soljačić, “Shrinking light to allow forbidden transitions on the atomic scale,” Science 353, 263–269 (2016).
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X. Cai, J. Wang, M. J. Strain, B. J. Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
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Supplementary Material (4)

NameDescription
» Supplement 1       Supplemental document
» Visualization 1       Continuous control over optical vortices for plasmonic slit of topological charge of 2
» Visualization 2       Continuous control over optical vortices for plasmonic slit of topological charge of 1
» Visualization 3       Simulation of in-plane electrical field in time domain. C-points can be distinguished as points with circular polarization.

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Figures (6)

Fig. 1.
Fig. 1. Control over phase singularities. Coupling plane waves into surface plasmon polaritons by a spiral slit allows the mapping of any polarization state, represented by the Poincaré sphere, into the location of plasmonic phase singularities in a 2D plane. The amplitude of the out-of-plane electric field resulting from coupling plane waves of different polarization states is shown along with their position on the Poincaré sphere. The black spots correspond to the phase singularities, with their separation and rotation angle controlled by varying only the polarization state of the incident light. Polarization variation along the longitudinal lines of the Poincaré sphere results in a control over the separation of the OVs, while along the latitudinal lines it results in a rotation of their shared axis. The super-oscillatory nature of OVs enables such control in precision much higher than allowed by the diffraction limit.
Fig. 2.
Fig. 2. Experimental setup. (a) A linearly polarized laser beam propagates through λ/2 and λ/4 plates which provide complete control over the polarization state. The beam is then incident upon a metal–dielectric interface and is coupled to the interface via a spiral slit [for example, a scanning electron microscope image of a l=2 slit is presented in (b)]. The polarization state is translated to two Bessel modes of different orders, creating a controlled interference pattern. The full field distribution is mapped by phase-resolved s-NSOM showing both the amplitude and phase at 15 nm resolution.
Fig. 3.
Fig. 3. Controlling the distance between OVs. Amplitude (upper row) and phase (lower row) of near-field mapping for l=1(left columns) and l=2(right columns). The orientations of the λ/4 and λ/2 plates are indicated above the amplitude images. The singularities are marked by black circles in the phase maps. The distance between the singularities is indicated above the phase images.
Fig. 4.
Fig. 4. Controlling the rotation angle of the OVs. Amplitude (upper row) and phase (lower row) of near-field mapping for l=1 (left columns) and l=2 (right columns). The orientations of the λ/4 and λ/2 plates are indicated above the amplitude images. The singularities are marked by black circles in the phase maps. The rotation angle of the singularities is indicated above the phase images.
Fig. 5.
Fig. 5. Experimental in-plane field. In-plane field components Eρ, Eθ (c)–(f), (i)–(l) derived out of the measured out-of-plane field component Ez (a), (b), (g), (h) for l=1. Two polarization states examined: ϑλ/2=160, ϑλ/4=0 (a)–(f) and ϑλ/2=175, ϑλ/4=0 (g)–(l). Amplitude (upper row) and phase (bottom row) presented.
Fig. 6.
Fig. 6. Analytical in-plane field and control over C-points location. Numerical simulations fitted to two polarization states depicted in Fig. 5 respectively. Amplitude (upper row) and phase (bottom row) of the out-of-plane field component Ez and the in-plain field component Eρ, Eθ are presented. The polarization states expressed by the polarization ellipse orientation α and handedness ϵ of the two states have also been calculated [(g), (h) and (o), (p), respectively]. The distance between the C-points, marked by black circles, is indicated above the α image.

Equations (7)

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E(ρ,θ,z)=eikzz(Ez(ρ,θ)z^+Eρ(ρ,θ)ρ^+Eθ(ρ,θ)θ^),
Ez(ρ,θ)=Jm(ksppρ)eimθ,
Ez(ρ,θ)=J(l±1)(ksppρ)ei(l±1)θ.
σ+1+|a0|eiϕ0σ1,
Ez(ρ,θ)=Jl+1(ksppρ)ei(l+1)θ+|a0|eiϕ0Jl1(ksppρ)ei(l1)θ,
|a0|=fa0(ϑλ/4,ϑλ/2);ϕ0=fϕ0(ϑλ/4,ϑλ/2),
Eρ=ξρEz;Eθ=ξ1ρθEz,

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