Abstract

We report on conical refraction (CR) with low-coherence light sources, such as light-emitting diodes and decoherentized HeNe laser radiation, and demonstrate different CR patterns. In our experiments, a variation of the pinhole sizes from 25 to 100 µm and the distances to pinhole from 50 to 5 cm reduced spatial coherence of radiation that resulted in the disappearance of the dark Poggendorff’s ring in the Lloyd’s plane. This is attributed to the interference nature of the Lloyd’s distribution and found to be in excellent agreement with the paraxial dual-cone model of conical refraction.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (1)

2017 (2)

2016 (2)

D. G. Papazoglou, V. Yu. Fedorov, and S. Tzortzakis, “Janus waves,” Opt. Lett. 41(20), 4656–4659 (2016).
[Crossref]

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Conical refraction: Fundamentals and applications,” Laser Photonics Rev. 10(5), 750–771 (2016).
[Crossref]

2015 (2)

2013 (5)

2012 (1)

2011 (1)

2010 (2)

2006 (1)

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[Crossref]

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]

1978 (1)

A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44(4), 436–439 (1978).

1941 (1)

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “The phenomena of conical refraction,” Nature 147(3722), 268 (1941).
[Crossref]

1905 (1)

W. Voigt, “Bemerkung zur theorie der konischen refraction,” Phys. Z. 6, 672–673 (1905).

1839 (1)

J. C. Poggendorff, “Ueber die konische Refraction,” Ann. Phys. (Berlin, Ger.) 124(11), 461–462 (1839).
[Crossref]

1833 (2)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1833).

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Philos. Mag. 1(1), 112–114 (1833).

Abdolvand, A.

Agranat, A. J.

Ahmed, N.

Akbari, R.

Ashrafi, S.

Ballantine, K. E.

Bao, C.

Belafhal, A.

F. Saad and A. Belafhal, “A detailed study of internal conical refraction phenomenon of flattened Gaussian beams propagating in a biaxial crystal,” Optik 138, 145–152 (2017).
[Crossref]

Belskii, A. M.

A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44(4), 436–439 (1978).

Berry, M. V.

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[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]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Campos, J.

Carnegie, D. J.

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, “Conical Refraction: New observations and a dual cone model,” Opt. Express 21(9), 11125–11131 (2013).
[Crossref]

Yu. V. Loiko, G. S. Sokolovskii, D. J. Carnegie, A. Turpin, J. Mompart, and E. U. Rafailov, “Laser beams with conical refraction patterns,” Proc. SPIE 8960, 89601Q (2014).

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, “Flexible particle manipulation techniques with conical refraction-based optical tweezers,” Proc. SPIE 8458, 845824 (2012).

Dai, K.

Darcy, R. T.

Donegan, J. F.

Eastham, P. R.

Fedorov, V. Yu.

Fedorova, K. A.

Fernandez, E.

Fu, S.

Gao, C.

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 (1833).

Henderson, R.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, “Flexible particle manipulation techniques with conical refraction-based optical tweezers,” Proc. SPIE 8458, 845824 (2012).

Hnatovsky, C.

Howlader, C.

Ilan, H.

Jeffrey, M. R.

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[Crossref]

Jennings, B. D.

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(4), 436–439 (1978).

Krolikowski, W.

Li, L.

Liu, C.

Lizana, A.

Lloyd, H.

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Philos. Mag. 1(1), 112–114 (1833).

Loiko, Y. V.

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Conical refraction: Fundamentals and applications,” Laser Photonics Rev. 10(5), 750–771 (2016).
[Crossref]

Loiko, Yu.

Loiko, Yu. V.

Lunney, J. G.

Major, A.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

McCloskey, D.

McDougall, C.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, “Flexible particle manipulation techniques with conical refraction-based optical tweezers,” Proc. SPIE 8458, 845824 (2012).

McGloin, D.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, “Flexible particle manipulation techniques with conical refraction-based optical tweezers,” Proc. SPIE 8458, 845824 (2012).

Mompart, J.

Mompart Turpin, J.

Nedungadi, T. M. K.

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “The phenomena of conical refraction,” Nature 147(3722), 268 (1941).
[Crossref]

O’Dwyer, D. P.

Pang, K.

Papazoglou, D. G.

Peinado, A.

Phelan, C. F.

Poggendorff, J. C.

J. C. Poggendorff, “Ueber die konische Refraction,” Ann. Phys. (Berlin, Ger.) 124(11), 461–462 (1839).
[Crossref]

Rafailov, E. U.

R. Akbari, C. Howlader, K. A. Fedorova, G. S. Sokolovskii, E. U. Rafailov, and A. Major, “Conical refraction output from a Nd:YVO4 laser with an intracavity conerefringent element,” Opt. Lett. 44(3), 642–645 (2019).
[Crossref]

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, “Conical Refraction: New observations and a dual cone model,” Opt. Express 21(9), 11125–11131 (2013).
[Crossref]

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, “Conical refraction Nd:KGd(WO4)2 laser,” Opt. Express 18(3), 2753–2759 (2010).
[Crossref]

Yu. V. Loiko, G. S. Sokolovskii, D. J. Carnegie, A. Turpin, J. Mompart, and E. U. Rafailov, “Laser beams with conical refraction patterns,” Proc. SPIE 8960, 89601Q (2014).

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, “Flexible particle manipulation techniques with conical refraction-based optical tweezers,” Proc. SPIE 8458, 845824 (2012).

Rajagopalan, V. S.

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “The phenomena of conical refraction,” Nature 147(3722), 268 (1941).
[Crossref]

Rakovich, Y. P.

Raman, C. V.

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “The phenomena of conical refraction,” Nature 147(3722), 268 (1941).
[Crossref]

Ren, Y.

Rosen, S.

Saad, F.

F. Saad and A. Belafhal, “A detailed study of internal conical refraction phenomenon of flattened Gaussian beams propagating in a biaxial crystal,” Optik 138, 145–152 (2017).
[Crossref]

Shi, Y.

Shvedov, V.

Sirat, G. Y.

Sokolovskii, G. S.

R. Akbari, C. Howlader, K. A. Fedorova, G. S. Sokolovskii, E. U. Rafailov, and A. Major, “Conical refraction output from a Nd:YVO4 laser with an intracavity conerefringent element,” Opt. Lett. 44(3), 642–645 (2019).
[Crossref]

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, “Conical Refraction: New observations and a dual cone model,” Opt. Express 21(9), 11125–11131 (2013).
[Crossref]

Yu. V. Loiko, G. S. Sokolovskii, D. J. Carnegie, A. Turpin, J. Mompart, and E. U. Rafailov, “Laser beams with conical refraction patterns,” Proc. SPIE 8960, 89601Q (2014).

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, “Flexible particle manipulation techniques with conical refraction-based optical tweezers,” Proc. SPIE 8458, 845824 (2012).

Song, H.

Tomizawa, H.

Tur, M.

Turpin, A.

Tzortzakis, S.

Voigt, W.

W. Voigt, “Bemerkung zur theorie der konischen refraction,” Phys. Z. 6, 672–673 (1905).

Wang, Z.

Wilcox, K. G.

Willner, A. E.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Xie, G.

Yan, Y.

Zhang, R.

Zhang, S.

Zhao, Z.

Zhong, L.

Ann. Phys. (Berlin, Ger.) (1)

J. C. Poggendorff, “Ueber die konische Refraction,” Ann. Phys. (Berlin, Ger.) 124(11), 461–462 (1839).
[Crossref]

J. Opt. A: Pure Appl. Opt. (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]

Laser Photonics Rev. (1)

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Conical refraction: Fundamentals and applications,” Laser Photonics Rev. 10(5), 750–771 (2016).
[Crossref]

Nature (1)

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “The phenomena of conical refraction,” Nature 147(3722), 268 (1941).
[Crossref]

Opt. Express (7)

Opt. Lett. (7)

Opt. Spectrosc. (1)

A. M. Belskii and A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44(4), 436–439 (1978).

Optik (1)

F. Saad and A. Belafhal, “A detailed study of internal conical refraction phenomenon of flattened Gaussian beams propagating in a biaxial crystal,” Optik 138, 145–152 (2017).
[Crossref]

Philos. Mag. (1)

H. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals,” Philos. Mag. 1(1), 112–114 (1833).

Phys. Z. (1)

W. Voigt, “Bemerkung zur theorie der konischen refraction,” Phys. Z. 6, 672–673 (1905).

Proc. R. Soc. A (1)

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[Crossref]

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 (1833).

Other (4)

Yu. V. Loiko, G. S. Sokolovskii, D. J. Carnegie, A. Turpin, J. Mompart, and E. U. Rafailov, “Laser beams with conical refraction patterns,” Proc. SPIE 8960, 89601Q (2014).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, “Flexible particle manipulation techniques with conical refraction-based optical tweezers,” Proc. SPIE 8458, 845824 (2012).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Supplementary Material (1)

NameDescription
» Visualization 1       Visualization shows experimental conically refracted beam transformation in the Lloyd's plane with spatial coherence degree varying from 0.07 to 0.95.

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Figures (6)

Fig. 1.
Fig. 1. Evolution of a light beam loosely focused through a conically refracting crystal (CRC).
Fig. 2.
Fig. 2. Lloyd’s distribution of the CR beam intensity computed numerically from the dual-cone model with the Gaussian beam and coherence degree α=1 (a) or the flattened Gaussian beam and α=0 (b). Conical refraction pattern in the Lloyd`s plane for coherent (c) and decoherentized laser beam (d). Laser beam is decoherentized by the rotating blurry plate. Beam intensity profiles are shown on the right of each pattern.
Fig. 3.
Fig. 3. (a) LED emission spectrum; (b) Schematic of the optical setup used for the CR experiments with low-coherence light sources. Pinholed LED radiation was collimated by a Lens 1 (of variable focal length) and then focused by a Lens 2 (focal length 100 mm) through a CRC. The CCD camera detecting an output pattern was mounted on a long-range translation stage enabling registration of the spatial evolution of the conically refracted LED radiation.
Fig. 4.
Fig. 4. The axial distribution of the CR beam intensity computed numerically from the dual-cone model with the Gaussian beam and coherence degree α=1 (a) or α=0 (b) and coherently illuminated pinhole (c). Conical refraction pattern with LED light along the beam propagation axis with a pinhole size and distance to pinhole of 25 µm and 5 cm (d), 100 µm and 5 cm (e), 100 µm and 50 cm (f), correspondingly. Note the difference in the horizontal and vertical scales: the distance between Raman spots (horizontal) is ∼50 mm, the diameter of the Lloyd ring (vertical) is ∼0.6 mm.
Fig. 5.
Fig. 5. Transverse intensity distributions of the CR beam at Z = 0 (Lloyd’s plane) obtained experimentally (first row) and from numerical simulations (second row) for a 100 µm pinhole diameter and a distance from the LED to pinhole L1 ∼ 17 cm (α=0.85, first column), 12 cm (α=0.74, second column), 8 cm (α=0.54, third column) and 3 cm (α=0.07, fourth column), correspondingly. Beam intensity profiles are shown on the right of each pattern. Visualization 1 shows experimental transformation of the Lloyd’s distribution with α varying from 0.07 to 0.95.
Fig. 6.
Fig. 6. Measured Lloyd’s pattern for unpolarized LED radiation (a) and linear polarized light (b). Parameter ρ0 = R0/w0 ≈10 (first row), ρ0 ≈ 4.5 (second row), ρ0 ≈ 2.7 (third row), ρ0 ≈ 1.7 (fourth row) and ρ0 ≈ 1.2 (fifth row). For each box, the first column corresponds to coherent light (α≈1), while the second column to incoherent (α≈0). Beam intensity profiles are shown on the right of each pattern.

Equations (9)

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

I = | B 0 | 2 + | B 1 | 2 .
B m = k 0 P a ( P ) e i k Z P 2 / i k Z P 2 2 2 cos ( k R 0 P m π 2 ) J m ( k R P ) d P .
C q = s = ± 1 e s ( φ ) ( e s ( φ ) e i n ) [ k 2 0 P a ( P ) e i k Z P 2 / i k Z P 2 2 2 + i q k R 0 P { J 0 ( k R P ) i q s J 1 ( k R P ) } d P ] .
e 1 ( φ ) = ( c o s ( φ / 2 ) , s i n ( φ / 2 ) ) , e 1 ( φ ) = ( s i n ( φ / 2 ) , c o s ( φ / 2 ) ) .
I = | C 1 + C 1 | 2
I = | C 1 | 2 + | C 1 | 2 + α ( C 1 C 1 + C 1 C 1 ) .
I α 1 | C 1 | 2 + | C 1 | 2 + C 1 C 1 + C 1 C 1 .
I = | C 1 | 2 + | C 1 | 2 .
α = | 2 J 1 ( x ) x | ; x = k D r s L 1

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