Abstract

Cascade conical refraction occurs when a beam of light travels through two or more biaxial crystals arranged in series. The output beam can be altered by varying the relative azimuthal orientation of the two biaxial crystals. For two identical crystals, in general the output beam comprises a ring beam with a spot at its centre. The relative intensities of the spot and ring can be controlled by varying the azimuthal angle between the refracted cones formed in each crystal. We have used this beam arrangement to trap one microsphere within the central spot and a second microsphere on the ring. Using linearly polarized light, we can rotate the microsphere on the ring with respect to the central sphere. Finally, using a half wave-plate between the two crystals, we can create a unique beam profile that has two intensity peaks on the ring, and thereby trap two microspheres on diametrically opposite points on the ring and rotate them around the central sphere. Such a versatile optical trap should find application in optical trapping setups.

© 2012 OSA

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References

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  1. W. R. Hamilton, “Third supplement to an essay on the theory of system of rays,” Trans. R. Irish Acad.17, 1–144 (1837).
  2. H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Philos. Mag.1, 112–120 (1833).
  3. A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc.44, 312–315 (1978).
  4. M. V. Berry, “Conical refraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt.6(4), 289–300 (2004).
    [CrossRef]
  5. 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. Express17(15), 12891–12899 (2009).
    [CrossRef] [PubMed]
  6. D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express18(16), 16480–16485 (2010).
    [CrossRef] [PubMed]
  7. V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt.12(9), 095706 (2010).
    [CrossRef]
  8. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett.11(5), 288–290 (1986).
    [CrossRef] [PubMed]
  9. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature330(6150), 769–771 (1987).
    [CrossRef] [PubMed]
  10. K. Dholakia and T. Ĉižmár, “Shaping the future of manipulation,” Nat. Photonics5(6), 335–342 (2011).
    [CrossRef]
  11. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5(6), 343–348 (2011).
    [CrossRef]
  12. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner,” Opt. Lett.22(1), 52–54 (1997).
    [CrossRef] [PubMed]
  13. K. Volke-Sepúlveda, S. Chavez-Cerda, V. Garces-Chavez, and K. Dholakia, “Three-dimensional optical forces and transfer of orbital angular momentum from multiringed light beams to spherical microparticles,” J. Opt. Soc. Am. B21, 1749–1757 (2004).
    [CrossRef]
  14. R. Bowman, A. Jesacher, G. Thalhammer, G. Gibson, M. Ritsch-Marte, and M. Padgett, “Position clamping in a holographic counterpropagating optical trap,” Opt. Express19(10), 9908–9914 (2011).
    [CrossRef] [PubMed]
  15. E. McLeod and C. B. Arnold, “Array-based optical nanolithography using optically trapped microlenses,” Opt. Express17(5), 3640–3650 (2009).
    [CrossRef] [PubMed]
  16. K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron.2(4), 1066–1076 (1996).
    [CrossRef]
  17. K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys.30(Part 2, No. 5B), L907–L909 (1991).
    [CrossRef]
  18. M. Capitanio, R. Cicchi, and F. S. Pavone, “Continuous and time-shared multiple optical tweezers for the study of single motor proteins,” Opt. Lasers Eng.45(4), 450–457 (2007).
    [CrossRef]
  19. E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
    [CrossRef]
  20. 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. Express18(26), 27319–27326 (2010).
    [CrossRef] [PubMed]
  21. M. V. Berry, “Conical diffraction from an N-crystal cascade,” J. Opt.12(7), 075704 (2010).
    [CrossRef]
  22. A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express18(3), 2753–2759 (2010).
    [CrossRef] [PubMed]
  23. D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “The creation and annihilation of optical vortices using cascade conical diffraction,” Opt. Express19(3), 2580–2588 (2011).
    [CrossRef] [PubMed]
  24. C. F. Phelan, K. E. Ballantine, P. R. Eastham, J. F. Donegan, and J. G. Lunney, “Conical diffraction of a Gaussian beam with a two crystal cascade,” Opt. Express20, 13201–13207 (2012).
    [CrossRef] [PubMed]

2012

2011

2010

2009

2007

M. Capitanio, R. Cicchi, and F. S. Pavone, “Continuous and time-shared multiple optical tweezers for the study of single motor proteins,” Opt. Lasers Eng.45(4), 450–457 (2007).
[CrossRef]

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
[CrossRef]

2004

1997

1996

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron.2(4), 1066–1076 (1996).
[CrossRef]

1991

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys.30(Part 2, No. 5B), L907–L909 (1991).
[CrossRef]

1987

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature330(6150), 769–771 (1987).
[CrossRef] [PubMed]

1986

1978

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

1837

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

1833

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

Abdolvand, A.

Allen, L.

Andilla, J.

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
[CrossRef]

Arnold, C. B.

Ashkin, A.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature330(6150), 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett.11(5), 288–290 (1986).
[CrossRef] [PubMed]

Ballantine, K. E.

Belskii, A. M.

A. M. Belskii 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, “Conical diffraction from an N-crystal cascade,” J. Opt.12(7), 075704 (2010).
[CrossRef]

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

Bjorkholm, J. E.

Block, S. M.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron.2(4), 1066–1076 (1996).
[CrossRef]

Bowman, R.

Capitanio, M.

M. Capitanio, R. Cicchi, and F. S. Pavone, “Continuous and time-shared multiple optical tweezers for the study of single motor proteins,” Opt. Lasers Eng.45(4), 450–457 (2007).
[CrossRef]

Carnicer, A.

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
[CrossRef]

Chavez-Cerda, S.

Chu, S.

Cicchi, R.

M. Capitanio, R. Cicchi, and F. S. Pavone, “Continuous and time-shared multiple optical tweezers for the study of single motor proteins,” Opt. Lasers Eng.45(4), 450–457 (2007).
[CrossRef]

Cižmár, T.

K. Dholakia and T. Ĉižmár, “Shaping the future of manipulation,” Nat. Photonics5(6), 335–342 (2011).
[CrossRef]

Dholakia, K.

Donegan, J. F.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature330(6150), 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett.11(5), 288–290 (1986).
[CrossRef] [PubMed]

Eastham, P. R.

Garces-Chavez, V.

Gibson, G.

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron.2(4), 1066–1076 (1996).
[CrossRef]

Hamilton, W. R.

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

Jesacher, A.

Juvells, I.

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
[CrossRef]

Kalkandjiev, T. K.

Khapaluyk, A. P.

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

Kitamura, N.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys.30(Part 2, No. 5B), L907–L909 (1991).
[CrossRef]

Koshioka, M.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys.30(Part 2, No. 5B), L907–L909 (1991).
[CrossRef]

Lloyd, H.

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

Lunney, J. G.

Martín-Badosa, E.

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
[CrossRef]

Masuhara, H.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys.30(Part 2, No. 5B), L907–L909 (1991).
[CrossRef]

McLeod, E.

Misawa, H.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys.30(Part 2, No. 5B), L907–L909 (1991).
[CrossRef]

Montes-Usategui, M.

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
[CrossRef]

O’Dwyer, D. P.

Padgett, M.

Padgett, M. J.

Pavone, F. S.

M. Capitanio, R. Cicchi, and F. S. Pavone, “Continuous and time-shared multiple optical tweezers for the study of single motor proteins,” Opt. Lasers Eng.45(4), 450–457 (2007).
[CrossRef]

Peet, V.

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

Phelan, C. F.

Pleguezuelos, E.

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
[CrossRef]

Rafailov, E. U.

Rakovich, Y. P.

Ritsch-Marte, M.

Sasaki, K.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys.30(Part 2, No. 5B), L907–L909 (1991).
[CrossRef]

Simpson, N. B.

Thalhammer, G.

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron.2(4), 1066–1076 (1996).
[CrossRef]

Volke-Sepúlveda, K.

Wilcox, K. G.

Yamane, T.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature330(6150), 769–771 (1987).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron.2(4), 1066–1076 (1996).
[CrossRef]

J. Opt.

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

M. V. Berry, “Conical diffraction from an N-crystal cascade,” J. Opt.12(7), 075704 (2010).
[CrossRef]

J. Opt. A

E. Martín-Badosa, M. Montes-Usategui, A. Carnicer, J. Andilla, E. Pleguezuelos, and I. Juvells, “Design strategies for optimizing holographic optical tweezers set-ups,” J. Opt. A9(8), S267–S277 (2007).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

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

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, “Laser-scanning micromanipulation and spatial patterning of fine particles,” Jpn. J. Appl. Phys.30(Part 2, No. 5B), L907–L909 (1991).
[CrossRef]

Nat. Photonics

K. Dholakia and T. Ĉižmár, “Shaping the future of manipulation,” Nat. Photonics5(6), 335–342 (2011).
[CrossRef]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5(6), 343–348 (2011).
[CrossRef]

Nature

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature330(6150), 769–771 (1987).
[CrossRef] [PubMed]

Opt. Express

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. Express17(15), 12891–12899 (2009).
[CrossRef] [PubMed]

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction,” Opt. Express18(16), 16480–16485 (2010).
[CrossRef] [PubMed]

R. Bowman, A. Jesacher, G. Thalhammer, G. Gibson, M. Ritsch-Marte, and M. Padgett, “Position clamping in a holographic counterpropagating optical trap,” Opt. Express19(10), 9908–9914 (2011).
[CrossRef] [PubMed]

E. McLeod and C. B. Arnold, “Array-based optical nanolithography using optically trapped microlenses,” Opt. Express17(5), 3640–3650 (2009).
[CrossRef] [PubMed]

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. Express18(26), 27319–27326 (2010).
[CrossRef] [PubMed]

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express18(3), 2753–2759 (2010).
[CrossRef] [PubMed]

D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, and J. F. Donegan, “The creation and annihilation of optical vortices using cascade conical diffraction,” Opt. Express19(3), 2580–2588 (2011).
[CrossRef] [PubMed]

C. F. Phelan, K. E. Ballantine, P. R. Eastham, J. F. Donegan, and J. G. Lunney, “Conical diffraction of a Gaussian beam with a two crystal cascade,” Opt. Express20, 13201–13207 (2012).
[CrossRef] [PubMed]

Opt. Lasers Eng.

M. Capitanio, R. Cicchi, and F. S. Pavone, “Continuous and time-shared multiple optical tweezers for the study of single motor proteins,” Opt. Lasers Eng.45(4), 450–457 (2007).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

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

Philos. Mag.

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

Trans. R. Irish Acad.

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

Supplementary Material (2)

» Media 1: MPEG (688 KB)     
» Media 2: MPEG (422 KB)     

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Figures (8)

Fig. 1
Fig. 1

Schematic of conical refraction. A beam traversing a crystal of length (L) is refracted through a semi-angle (A) to give a ring radius of R0. The beam shift direction (γ) is in the direction of the parallel polarization component towards the orthogonally polarized component at the opposite side of the ring.

Fig. 2
Fig. 2

Experimental setup for observation of focal image plane profiles. The two biaxial crystals are located between the two lenses, one rotated at an angle α around the beam axis; optical elements can be placed after the laser or in between the crystals and include linear polarizer, quarter or half wave-plate, or some combination of these.

Fig. 3
Fig. 3

CCD images of the FIP with (a) α = 0°,(b) α = 20°, (c) α = 45°, (d) α = 90°. (e) Processed image of all frames from α = 0 to 180°. The path of the Gaussian central spot travels along the patch of the ring generated from the first crystal and increases in intensity. is

Fig. 4
Fig. 4

Optical setup for cascade conical diffraction optical trap. The dichroic mirror prevents the 532 nm trapping beam entering the CCD. Sample illumination for CCD recording is provided by the light source below the sample. Optical elements can include linear polarizer, quarter or half wave-plate, or some combination.

Fig. 5
Fig. 5

(a) Intensity profile of cascade conical refraction beam in the FIP with linearly polarized 532nm light incident on the first crystal. (b) 3-D plot of the intensity distribution in (a).

Fig. 6
Fig. 6

Several individual frames showing how a particle trapped in the crescent beam orbits around the particle trapped in central beam spot. Media 1 shows the rotation of the outer microsphere with respect to the centrally trap microsphere as the plane of polarization of the incident beam is rotated.

Fig. 7
Fig. 7

Beam profile in the FIP with a half-wave plate between the two biaxial crystals.

Fig. 8
Fig. 8

Frames from rotation of two diametrically opposed particles trapped in lobes around a stationary particle trapped in the centre. Media 2 shows the continuous anti-clockwise rotation of the two microparticles around the central particle trapped in the Gaussian spot.

Equations (3)

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A= 1 n 2 ( n 3 n 2 )( n 2 n 1 )
D t =2 f 3 ( R 01 + R 02 ) f 2 .
F=6π R p ηv,

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