Abstract

Using a combination of internal conical diffraction and Mach-Zehnder interferometry we have theoretically and experimentally demonstrated an efficient new technique for the conversion of a linearly polarized Gaussian laser beam to one with radial polarization. These methods that can be adapted to yield either ring-shaped or first order Bessel beams which are radially polarized.

© 2011 OSA

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References

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  1. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
    [Crossref] [PubMed]
  2. Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
    [Crossref]
  3. S. Quabis, R. Dorn, M. Eberler, O. Glokl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
    [Crossref]
  4. S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29(15), 2234–2239 (1990).
    [Crossref] [PubMed]
  5. Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005).
    [Crossref] [PubMed]
  6. W. J. Lai, B. C. Lim, P. B. Phua, K. S. Tiaw, H. H. Teo, and M. H. Hong, “Generation of radially polarized beam with a segmented spiral varying retarder,” Opt. Express 16(20), 15694–15699 (2008).
    [Crossref] [PubMed]
  7. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett. 32(11), 1468–1470 (2007).
    [Crossref] [PubMed]
  8. Y. Tokizane, K. Shimatake, Y. Toda, K. Oka, M. Tsubota, S. Tanda, and R. Morita, “Global evaluation of closed-loop electron dynamics in quasi-one-dimensional conductors using polarization vortices,” Opt. Express 17(26), 24198–24207 (2009).
    [Crossref] [PubMed]
  9. M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
    [Crossref]
  10. A. M. Belsky and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).
  11. W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).
  12. H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Phil. Mag. 1, 112–120 (1833).
  13. H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Phil. Mag. 1207–210 (1833).
  14. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).
  15. C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009).
    [Crossref] [PubMed]
  16. V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
    [Crossref]
  17. D. P. O’Dwyer, C. F. Phelan, K. E. Ballantine, Y. P. Rakovich, J. G. Lunney, and J. F. Donegan, “Conical diffraction of linearly polarised light controls the angular position of a microscopic object,” Opt. Express 18(26), 27319–27326 (2010).
    [Crossref] [PubMed]
  18. M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
    [Crossref]
  19. M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
    [Crossref]

2010 (2)

2009 (2)

2008 (2)

W. J. Lai, B. C. Lim, P. B. Phua, K. S. Tiaw, H. H. Teo, and M. H. Hong, “Generation of radially polarized beam with a segmented spiral varying retarder,” Opt. Express 16(20), 15694–15699 (2008).
[Crossref] [PubMed]

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

2007 (1)

2005 (2)

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005).
[Crossref] [PubMed]

2004 (1)

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[Crossref]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glokl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref] [PubMed]

1999 (1)

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

1990 (1)

1978 (1)

A. M. Belsky and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).

1837 (1)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).

1833 (2)

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Phil. Mag. 1, 112–120 (1833).

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Phil. Mag. 1207–210 (1833).

Aguiló, M.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

Ballantine, K. E.

Belsky, A. M.

A. M. Belsky and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).

Berry, M. V.

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[Crossref]

Brown, T. G.

Díaz, F.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

Donegan, J. F.

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glokl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[Crossref]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glokl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[Crossref]

Ford, D. H.

Fujita, K.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Glokl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glokl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[Crossref]

Hamilton, W. R.

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).

Hiraga, D.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Hong, M. H.

Inouye, Y.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Jackel, S.

Jeffrey, M. R.

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

Kawano, S.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Kawata, S.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Khapaluyk, A. P.

A. M. Belsky and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).

Kimura, W. D.

Kobayashi, M.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Kozawa, Y.

Lai, W. J.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glokl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[Crossref]

Lim, B. C.

Lloyd, H.

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Phil. Mag. 1, 112–120 (1833).

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Phil. Mag. 1207–210 (1833).

Lumer, Y.

Lunney, J. G.

Machavariani, G.

Mansuripur, M.

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

Meir, A.

Morita, R.

Moshe, I.

Nikolov, V.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

O’Dwyer, D. P.

Oka, K.

Peet, V.

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[Crossref]

Phelan, C. F.

Phua, P. B.

Pujol, M. C.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glokl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[Crossref]

Rakovich, Y. P.

Rico, M.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

Saito, Y.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Sato, S.

Shimatake, K.

Smith, N. I.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Solans, X.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

Solé, R.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

Tanda, S.

Teo, H. H.

Tiaw, K. S.

Tidwell, S. C.

Toda, Y.

Tokizane, Y.

Tsubota, M.

Youngworth, K. S.

Zaldo, C.

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

M. C. Pujol, M. Rico, C. Zaldo, R. Solé, V. Nikolov, X. Solans, M. Aguiló, and F. Díaz, “Crystalline structure and optical spectroscopy of Er3+-doped KGd(WO4)2 single crystals,” Appl. Phys. B 68(2), 187–197 (1999).
[Crossref]

J. Opt. (1)

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[Crossref]

J. Opt. A, Pure Appl. Opt. (2)

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[Crossref]

J. Raman Spectrosc. (1)

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, “Z-polarization sensitive detection in micro-Raman spectroscopy by radially polarized incident light,” J. Raman Spectrosc. 39(11), 1643–1648 (2008).
[Crossref]

Opt. Commun. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glokl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Opt. Spectrosc. (1)

A. M. Belsky and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 312–315 (1978).

Phil. Mag. (2)

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Phil. Mag. 1, 112–120 (1833).

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Phil. Mag. 1207–210 (1833).

Trans. R. Irish Acad. (1)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1837).

Other (1)

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).

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Figures (13)

Fig. 1
Fig. 1

Transverse distribution of intensity and polarization (arrows) in (a) radially polarized and (b) azimuthally polarized light beams.

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Fig. 2
Fig. 2

(a) Schematic diagram showing the geometry of internal conical diffraction. (b) The FIP intensity and polarization distribution for a conically diffracted Gaussian beam where ω0:R0 = 1:9.

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Fig. 3
Fig. 3

The FIP intensity distribution for conical diffraction of Gaussian beams: (a) circularly polarized, (b) linearly (horizontal) polarized Gaussian beams and (c) when the (b) propagates through a vertically aligned linear polarizer. (d), (e) and (f) show the far field profiles corresponding to (a), (b) and (c) respectively.

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Fig. 4
Fig. 4

Schematic diagram showing the formation of radially polarized beams by superposition of equal amplitude orthogonal Hermite-Bessel-like beams in (a) the FIP and (b) the far field.

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Fig. 5
Fig. 5

Schematic diagram showing the formation of radially polarized beams by the superposition of a crescent-shaped beam with its mirror image in (a) the FIP and (b) the far field. The ellipses in (b) indicate elliptical polarization.

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Fig. 6
Fig. 6

The basic experimental setup used to convert a linearly polarized Gaussian to a radially polarized beam using conical diffraction and an interferometer. LP is a linear polarizer, BSM is a beam-splitter, HWP is a half wave-plate and CCD is a charge-coupled device camera.

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Fig. 7
Fig. 7

Intensity distributions of (a) the beam from Arm 1 on its own, (b) the beam from Arm 2 on its own, and (c) the superposition beam.

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Fig. 8
Fig. 8

Intensity profiles recorded when the radially polarized beam of method 1 (a) is transmitted through a linear polarizer with the transmission axis set at follows: (b) horizontal, (c) at 45° to horizontal, (d) vertical and (e) 135° to horizontal.

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Fig. 9
Fig. 9

Far-field intensity profiles predicted by Eq. (9) for (a) δ = 0; (b) δ = π/2 and (c) δ = π, which yields the radially polarized beam

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Fig. 10
Fig. 10

(a) CCD image of the radially polarized beam formed by the superposition of crescent beams. (b) Comparison of the measured (solid line) and calculated (dashed line) radial intensity profiles.

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Fig. 11
Fig. 11

Intensity profiles recorded when the radially polarized beam of method 2 (a) is transmitted through a linear polarizer with the transmission axis set at follows: (b) horizontal, (c) at 45° to horizontal, (d) vertical and (e) 135° to horizontal.

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Fig. 12
Fig. 12

The optical system used to relay the FIP to the detector plane.

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Fig. 13
Fig. 13

FIP intensity distributions of the beams transmitted via Arm 1 (a), Arm 2 (b) and the radially polarized superposition beam obtained using method 1 and the imaging system shown in Fig. 12.

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Equations (9)

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

E → (r,θ,Z)= B 0 (r,Z)( e x e y )+ B 1 (r,Z)( cosθ sinθ sinθ −cosθ )( e x e y ),
B 0 (r,Z)= π k 2 ω 0 2 ∫ 0 ∞ P e − 1 2 ik P 2 Z cos(kP R 0 ) J 0 (rkP) e − 1 4 ω 0 2 k 2 P 2 dP ,
B 1 (r,Z)= π k 2 ω 0 2 ∫ 0 ∞ P e − 1 2 ik P 2 Z sin(kP R 0 ) J 1 (rkP) e − 1 4 ω 0 2 k 2 P 2 dP .
B 1 sinθ( 0 1 ),
B 1 sinθ( 0 1 )− e iδ B 1 cosθ( 1 0 ),
B 1 ( cosθ sinθ ).
B 0 ( 1 0 )+ B 1 ( cosθ sinθ ).
B 0 ( 1 0 )− B 1 ( cosθ sinθ ).
B 0 ( 1 0 )+ B 1 ( cosθ sinθ )+ e iδ { B 0 ( 1 0 )− B 1 ( cosθ sinθ ) },

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