Abstract

We present results of our observations on the free space evolution of conically diffracted beams from both single and cascade systems using various combinations of four biaxial crystals of the monoclinic double tungstate family [KGd(WO4)2]. Longitudinal shifts and radii of the Hamilton-Lloyd pair of rings were measured. In each case, the symmetric - forward and backward - evolution of the beam in free space from its focal image plane was monitored and quantified. Theoretical ring plane patterns based on a recently presented theoretical model are also compared to experimental patterns and found to be in good agreement.

© 2014 Optical Society of America

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  1. W. R. Hamilton, “Third supplement to an essay on the theory of systems 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).
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    [CrossRef]
  5. M. V. Berry, M. R. Jeffrey, and L. G. Lunney, “Conical diffraction: Observation and theory,” Proc. R. Soc. A 462, 1629–1642 (2006).
    [CrossRef]
  6. M. V. Berry, M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
    [CrossRef]
  7. 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]
  8. J. G. Lunney, D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006).
    [CrossRef]
  9. C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, 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]
  10. V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, H. Tomizawa, J. Mompart, “Wave-vector and polarization dependence of conical refraction,” Opt. Express 21(4), 4503–4511 (2013).
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  13. D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. G. Lunney, J. F. Donegan, “The creation and annihilation of optical vortices using cascade conical diffraction,” Opt. Express 19(3), 2580–2588 (2011).
    [CrossRef] [PubMed]
  14. M. V. Berry, “Conical diffraction from an N-crystal cascade,” J. Opt. 12(7), 075704 (2010).
    [CrossRef]
  15. A. Abdolvand, “Conical diffraction from a multi-crystal cascade: experimental observations,” Appl. Phys. B 103(2), 281–283 (2011).
    [CrossRef]
  16. S. D. Grant, A. Abdolvand, “Left- and right-circularly polarized light in cascade conical diffraction,” Opt. Lett. 37(24), 5226–5228 (2012).
    [CrossRef] [PubMed]
  17. A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, J. Mompart, “Multiple rings formation in cascaded conical refraction,” Opt. Lett. 38(9), 1455–1457 (2013).
    [CrossRef] [PubMed]
  18. V. Peet, “Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams,” Opt. Lett. 36(15), 2913–2915 (2011).
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    [CrossRef] [PubMed]
  20. V. V. Filipov, N. V. Kuleshov, I. T. Bodnar, “Negative thermo-optical coefficient and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
    [CrossRef]
  21. A. M. Belskii, A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 436–439 (1978).

2013 (2)

2012 (2)

2011 (3)

2010 (3)

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

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]

2009 (1)

2007 (2)

V. V. Filipov, N. V. Kuleshov, I. T. Bodnar, “Negative thermo-optical coefficient and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

M. V. Berry, M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

2006 (1)

J. G. Lunney, D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (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, A. P. Khapaluyk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt. Spectrosc. 44, 436–439 (1978).

1942 (1)

C. V. Raman, T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942).
[CrossRef]

1839 (1)

J. C. Poggendorff, “Ueber die konische refraction,” Pogg. Ann. 48, 461–462 (1839).

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 (1)

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.

Ballantine, K. E.

Belskii, A. M.

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

Berry, M. V.

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

M. V. Berry, M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[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]

Bodnar, I. T.

V. V. Filipov, N. V. Kuleshov, I. T. Bodnar, “Negative thermo-optical coefficient and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

Donegan, J. F.

Eastham, P. R.

Filipov, V. V.

V. V. Filipov, N. V. Kuleshov, I. T. Bodnar, “Negative thermo-optical coefficient and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

Grant, S. D.

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).

Jeffrey, M. R.

M. V. Berry, M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

Kalkandjiev, T. K.

Khapaluyk, A. P.

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

Kuleshov, N. V.

V. V. Filipov, N. V. Kuleshov, I. T. Bodnar, “Negative thermo-optical coefficient and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[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).

Loiko, Y. V.

Lunney, J. G.

Mompart, J.

Nedungadi, T. M. K.

C. V. Raman, T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942).
[CrossRef]

O’Dwyer, D. P.

Peet, V.

Phelan, C. F.

Poggendorff, J. C.

J. C. Poggendorff, “Ueber die konische refraction,” Pogg. Ann. 48, 461–462 (1839).

Rafailov, E. U.

Rakovich, Y. P.

Raman, C. V.

C. V. Raman, T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942).
[CrossRef]

Tomizawa, H.

Turpin, A.

Weaire, D. W.

J. G. Lunney, D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006).
[CrossRef]

Wilcox, K. G.

Appl. Phys. B (2)

A. Abdolvand, “Conical diffraction from a multi-crystal cascade: experimental observations,” Appl. Phys. B 103(2), 281–283 (2011).
[CrossRef]

V. V. Filipov, N. V. Kuleshov, I. T. Bodnar, “Negative thermo-optical coefficient and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region,” Appl. Phys. B 87(4), 611–614 (2007).
[CrossRef]

Europhys. News (1)

J. G. Lunney, D. W. Weaire, “The ins and outs of conical refraction,” Europhys. News 37(3), 26–29 (2006).
[CrossRef]

J. Opt. (2)

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

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

Nature (1)

C. V. Raman, T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942).
[CrossRef]

Opt. Express (5)

Opt. Lett. (3)

Opt. Spectrosc. (1)

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

Philos. Mag. (1)

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

Pogg. Ann. (1)

J. C. Poggendorff, “Ueber die konische refraction,” Pogg. Ann. 48, 461–462 (1839).

Prog. Opt. (1)

M. V. Berry, M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[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 (1837).

Other (1)

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

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Figures (5)

Fig. 1
Fig. 1

The collimated beam from a 635 nm laser diode was focused using a lens before passing through the conical diffraction crystals and arriving at the beam profiler. The two crystals depicted comprised the cascade system.

Fig. 2
Fig. 2

The Ring plane patterns for (a) single crystal with unpolarized incident light, (b) single crystal with vertically polarized light, (c) cascade with unpolarized light and (d) cascade with vertically polarized light. The top row represents the theoretical patterns while the bottom row are experimental patterns.

Fig. 3
Fig. 3

The conical diffraction pattern - the ring plane and free space evolution - for a single crystal (here L3) configuration.

Fig. 4
Fig. 4

The 2Zf values – full free space evolution - for (a) single crystal and (b) cascade experiments.

Fig. 5
Fig. 5

The ring plane pattern and free space evolution for a two-crystal cascade - here consisting of L1 and L3 - and the cross section of the beam evolution in free space.

Tables (2)

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Table 1 Theoretical and Measured Values for Longitudinal Shifts and Ring Radii

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Table 2 Theoretical and Measured Values for Inner and Outer Ring Radii

Equations (3)

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I = 2 ρ 0 ( 1 + ζ 2 ) 3 4 | f ( ρ ρ 0 1 + i ζ ) | 2 ,
I LP =I 2 π cos 2 ( χ+ φ 1 2 Φ 0 ),
Z f = 2 π λ A ω 0 L 2 3 ,

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