Abstract

A Potassium Titanyl Phosphate (KTP) crystal has been used in conjunction with a 10-ps pulsed laser to produce a frequency-doubled conically-refracted Gaussian beam. The ‘free’ and ‘forced’ beams that make up the scheme for nonlinear conical refraction were readily observable in non-phase-matched conditions. The dependency of the frequency-doubled beam patterns on the incident beam polarization, which until now has remained unexplored, was examined in detail. We have also revealed the existence of two orthogonally polarized ‘free’ rays for particular orientations of the incident beam polarization.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  6. 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. Express 19(3), 2580–2588 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  32. M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical refraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  34. J. Kroupa, “Second-harmonic conical refraction in GUHP,” J. Opt. 12(4), 045706 (2010).
    [CrossRef]
  35. S. A. Zolotovskaya, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, “Second-Harmonic conical refraction: observation of free and forced harmonic waves,” Appl. Phys. B 103(1), 9–12 (2011).
    [CrossRef]
  36. A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, J. Trull, C. Cojocaru, and J. Mompart, “Type I and type II second harmonic generation of conically refracted beams,” Opt. Lett. 38(14), 2484–2486 (2013).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2014 (2)

2013 (6)

2012 (3)

2011 (4)

S. A. Zolotovskaya, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, “Second-Harmonic conical refraction: observation of free and forced harmonic waves,” Appl. Phys. B 103(1), 9–12 (2011).
[CrossRef]

V. Peet, “Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams,” Opt. Lett. 36(15), 2913–2915 (2011).
[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. Express 19(3), 2580–2588 (2011).
[CrossRef] [PubMed]

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

2010 (5)

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

V. Peet and D. Zolotukhin, “Free-space evolution of focused Gaussian beams transformed by conical diffraction in a biaxial crystal,” Opt. Commun. 283(15), 3011–3016 (2010).
[CrossRef]

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

J. Kroupa, “Second-harmonic conical refraction in GUHP,” J. Opt. 12(4), 045706 (2010).
[CrossRef]

2009 (1)

2008 (1)

T. K. Kalkandjiev and M. Bursukova, “Conical Refraction: an experimental introduction,” Proc. SPIE 6994, 69940B (2008).
[CrossRef]

2007 (1)

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

2006 (3)

R. A. Indik and A. C. Newell, “Conical refraction and nonlinearity,” Opt. Express 14(22), 10614–10620 (2006).
[CrossRef] [PubMed]

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

M. V. Berry and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8(12), 1043–1051 (2006).
[CrossRef]

2005 (1)

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

2004 (1)

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]

2002 (1)

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
[CrossRef]

1980 (1)

V. I. Stroganov, A. I. Illarionov, and B. I. Kidyarov, “Conical refraction in second harmonic generation in a crystal of lithium formate,” J. Appl. Spectrosc. 32(4), 341–344 (1980).
[CrossRef]

1978 (2)

A. J. Schell and N. Bloembergen, “Laser studies of internal conical refraction. III. Second-harmonic conical refraction in α-iodic acid,” Phys. Rev. A 18(6), 2592–2602 (1978).
[CrossRef]

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

1977 (1)

A. J. Schell and N. Bloembergen, “Second harmonic conical refraction,” Opt. Commun. 21(1), 150–153 (1977).
[CrossRef]

1969 (1)

H. Shih and N. Bloembergen, “Conical Refraction in Second-Harmonic Generation,” Phys. Rev. 184(3), 895–904 (1969).
[CrossRef]

1942 (1)

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

Belsky, A. M.

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
[CrossRef]

Berry, M. V.

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

M. V. Berry and 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 and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8(12), 1043–1051 (2006).
[CrossRef]

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

Bloembergen, N.

A. J. Schell and N. Bloembergen, “Laser studies of internal conical refraction. III. Second-harmonic conical refraction in α-iodic acid,” Phys. Rev. A 18(6), 2592–2602 (1978).
[CrossRef]

A. J. Schell and N. Bloembergen, “Second harmonic conical refraction,” Opt. Commun. 21(1), 150–153 (1977).
[CrossRef]

H. Shih and N. Bloembergen, “Conical Refraction in Second-Harmonic Generation,” Phys. Rev. 184(3), 895–904 (1969).
[CrossRef]

Bursukova, M.

T. K. Kalkandjiev and M. Bursukova, “Conical Refraction: an experimental introduction,” Proc. SPIE 6994, 69940B (2008).
[CrossRef]

Carnegie, D. J.

Cojocaru, C.

Darcy, R. T.

Donegan, J. F.

Eastham, P. R.

Gillespie, W. A.

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).

Hnatovsky, C.

Illarionov, A. I.

V. I. Stroganov, A. I. Illarionov, and B. I. Kidyarov, “Conical refraction in second harmonic generation in a crystal of lithium formate,” J. Appl. Spectrosc. 32(4), 341–344 (1980).
[CrossRef]

Indik, R. A.

Jeffrey, M. R.

M. V. Berry and 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 and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8(12), 1043–1051 (2006).
[CrossRef]

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

Jennings, B. D.

Kalkandjiev, T. K.

S. D. Grant, S. A. Zolotovskaya, W. A. Gillespie, T. K. Kalkandjiev, and A. Abdolvand, “Azimuthally and radially polarized light in conical diffraction,” Opt. Lett. 39(7), 1988–1991 (2014).
[CrossRef] [PubMed]

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] [PubMed]

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, H. Tomizawa, and J. Mompart, “Wave-vector and polarization dependence of conical refraction,” Opt. Express 21(4), 4503–4511 (2013).
[CrossRef] [PubMed]

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, and J. Mompart, “Multiple rings formation in cascaded conical refraction,” Opt. Lett. 38(9), 1455–1457 (2013).
[CrossRef] [PubMed]

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, J. Trull, C. Cojocaru, and J. Mompart, “Type I and type II second harmonic generation of conically refracted beams,” Opt. Lett. 38(14), 2484–2486 (2013).
[CrossRef] [PubMed]

A. Turpin, Y. Loiko, T. K. Kalkandjiev, and J. Mompart, “Free-space optical polarization demultiplexing and multiplexing by means of conical refraction,” Opt. Lett. 37(20), 4197–4199 (2012).
[CrossRef] [PubMed]

S. A. Zolotovskaya, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, “Second-Harmonic conical refraction: observation of free and forced harmonic waves,” Appl. Phys. B 103(1), 9–12 (2011).
[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] [PubMed]

T. K. Kalkandjiev and M. Bursukova, “Conical Refraction: an experimental introduction,” Proc. SPIE 6994, 69940B (2008).
[CrossRef]

Khapaluyk, A. P.

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

Kidyarov, B. I.

V. I. Stroganov, A. I. Illarionov, and B. I. Kidyarov, “Conical refraction in second harmonic generation in a crystal of lithium formate,” J. Appl. Spectrosc. 32(4), 341–344 (1980).
[CrossRef]

Krolikowski, W.

Kroupa, J.

J. Kroupa, “Second-harmonic conical refraction in GUHP,” J. Opt. 12(4), 045706 (2010).
[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.

Loiko, Y. V.

Lunney, J. G.

Mansuripur, M.

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

McCloskey, D.

Mompart, J.

Nedungadi, T. M. K.

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

Newell, A. C.

O’Dwyer, D. P.

Peet, V.

V. Peet, “Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams,” Opt. Lett. 36(15), 2913–2915 (2011).
[CrossRef] [PubMed]

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

V. Peet and D. Zolotukhin, “Free-space evolution of focused Gaussian beams transformed by conical diffraction in a biaxial crystal,” Opt. Commun. 283(15), 3011–3016 (2010).
[CrossRef]

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

Schell, A. J.

A. J. Schell and N. Bloembergen, “Laser studies of internal conical refraction. III. Second-harmonic conical refraction in α-iodic acid,” Phys. Rev. A 18(6), 2592–2602 (1978).
[CrossRef]

A. J. Schell and N. Bloembergen, “Second harmonic conical refraction,” Opt. Commun. 21(1), 150–153 (1977).
[CrossRef]

Shih, H.

H. Shih and N. Bloembergen, “Conical Refraction in Second-Harmonic Generation,” Phys. Rev. 184(3), 895–904 (1969).
[CrossRef]

Shvedov, V.

Sokolovskii, G. S.

Stepanov, M. A.

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
[CrossRef]

Stroganov, V. I.

V. I. Stroganov, A. I. Illarionov, and B. I. Kidyarov, “Conical refraction in second harmonic generation in a crystal of lithium formate,” J. Appl. Spectrosc. 32(4), 341–344 (1980).
[CrossRef]

Tomizawa, H.

Trull, J.

Turpin, A.

Weaire, D. W.

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

Wilcox, K. G.

Zolotovskaya, S. A.

S. D. Grant, S. A. Zolotovskaya, W. A. Gillespie, T. K. Kalkandjiev, and A. Abdolvand, “Azimuthally and radially polarized light in conical diffraction,” Opt. Lett. 39(7), 1988–1991 (2014).
[CrossRef] [PubMed]

S. A. Zolotovskaya, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, “Second-Harmonic conical refraction: observation of free and forced harmonic waves,” Appl. Phys. B 103(1), 9–12 (2011).
[CrossRef]

Zolotukhin, D.

V. Peet and D. Zolotukhin, “Free-space evolution of focused Gaussian beams transformed by conical diffraction in a biaxial crystal,” Opt. Commun. 283(15), 3011–3016 (2010).
[CrossRef]

Appl. Phys. B (2)

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

S. A. Zolotovskaya, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, “Second-Harmonic conical refraction: observation of free and forced harmonic waves,” Appl. Phys. B 103(1), 9–12 (2011).
[CrossRef]

Europhys. News (1)

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

J. Appl. Spectrosc. (1)

V. I. Stroganov, A. I. Illarionov, and B. I. Kidyarov, “Conical refraction in second harmonic generation in a crystal of lithium formate,” J. Appl. Spectrosc. 32(4), 341–344 (1980).
[CrossRef]

J. Opt. (3)

J. Kroupa, “Second-harmonic conical refraction in GUHP,” J. Opt. 12(4), 045706 (2010).
[CrossRef]

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 (1)

M. V. Berry and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8(12), 1043–1051 (2006).
[CrossRef]

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

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

Nature (1)

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

Opt. Commun. (3)

A. J. Schell and N. Bloembergen, “Second harmonic conical refraction,” Opt. Commun. 21(1), 150–153 (1977).
[CrossRef]

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
[CrossRef]

V. Peet and D. Zolotukhin, “Free-space evolution of focused Gaussian beams transformed by conical diffraction in a biaxial crystal,” Opt. Commun. 283(15), 3011–3016 (2010).
[CrossRef]

Opt. Express (10)

A. Turpin, Y. V. Loiko, T. K. Kalkandjiev, H. Tomizawa, and J. Mompart, “Wave-vector and polarization dependence of conical refraction,” Opt. Express 21(4), 4503–4511 (2013).
[CrossRef] [PubMed]

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] [PubMed]

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]

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] [PubMed]

R. A. Indik and A. C. Newell, “Conical refraction and nonlinearity,” Opt. Express 14(22), 10614–10620 (2006).
[CrossRef] [PubMed]

S. D. Grant and A. Abdolvand, “Evolution of conically diffracted Gaussian beams in free space,” Opt. Express 22(4), 3880–3886 (2014).
[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. Express 19(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. Express 20(12), 13201–13207 (2012).
[CrossRef] [PubMed]

A. Turpin, V. Shvedov, C. Hnatovsky, Y. V. Loiko, J. Mompart, and W. Krolikowski, “Optical vault: A reconfigurable bottle beam based on conical refraction of light,” Opt. Express 21(22), 26335–26340 (2013).
[CrossRef] [PubMed]

R. T. Darcy, D. McCloskey, K. E. Ballantine, B. D. Jennings, J. G. Lunney, P. R. Eastham, and J. F. Donegan, “White Light Conical Diffraction,” Opt. Express 21(17), 20394–20403 (2013).
[CrossRef] [PubMed]

Opt. Lett. (6)

Opt. Spectrosc. (1)

A. M. Belskii and 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).

Phys. Rev. (1)

H. Shih and N. Bloembergen, “Conical Refraction in Second-Harmonic Generation,” Phys. Rev. 184(3), 895–904 (1969).
[CrossRef]

Phys. Rev. A (1)

A. J. Schell and N. Bloembergen, “Laser studies of internal conical refraction. III. Second-harmonic conical refraction in α-iodic acid,” Phys. Rev. A 18(6), 2592–2602 (1978).
[CrossRef]

Pogg. Ann. (1)

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

Proc. SPIE (1)

T. K. Kalkandjiev and M. Bursukova, “Conical Refraction: an experimental introduction,” Proc. SPIE 6994, 69940B (2008).
[CrossRef]

Prog. Opt. (1)

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

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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 J. G. Lunney, “Conical refraction: Observation and theory,” Proc. R. Soc. A, 462, 1629–1642 (2007).

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Figures (4)

Fig. 1
Fig. 1

Linear conical refraction free space evolution of a circularly polarized incident laser beam at 632.8 nm. The quarter-wave plate (λ/4 plate) was used to produce circularly polarized light. The Ring Plane is a symmetry plane about which Poggendorff splitting and the Raman spot become visible. The full free space evolution shows the intersecting cones of oppositely propagating light which form the typical conical refraction pattern.

Fig. 2
Fig. 2

Linear conical refraction: the linearly polarized incident beam at 1064 nm. The polarization of the incident beam is changed to four polarization angles, shown by the red arrows. The evolutions of the beam in each case show the Poggendorff splitting and Raman spot further from the Ring Plane. The missing section of the ring is polarized orthogonally to the incident polarization.

Fig. 3
Fig. 3

The Ring Plane: (a) linear conical refraction at 1064 nm and nonlinear conical refraction (b-d). The red arrows show incident beam polarization direction, the yellow arrows show analyser position. The experimental results in (a) were registered under the condition of internal CR of the incident beam. Therefore the forced harmonic beam reproduced the CR pattern as seen in (b). The free harmonic beam propagates out of the optic axis at 532 nm and is confined in the plane perpendicular to the (G)-vector which produces double refraction along the horizontal abscissa.

Fig. 4
Fig. 4

Free’ and ‘forced’ beams: (a) and (d) the transition for 1064-nm beam from conical refraction to double refraction as the crystal is rotated, (b) the transition from double refraction to conical refraction for an incident 532-nm beam, (c) and (e) the transition between a ‘forced’ cone and ‘free’ rays to a ‘free’ cone and ‘forced’ rays for a SHCR beam. The red arrows show the incident beam polarization direction.

Equations (2)

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G=R[ sinφ,cosφ ]
Z f = 2π λ A ω 0 4 3 L

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