Abstract

We report here the generation of a three-dimensional (3D) dark focus from a single focused monochromatic Gaussian beam that undergoes conical refraction when it propagates along one of the optic axes of a biaxial crystal. We study the resulting ring intensity pattern behind the crystal as a function of the ratio between the ring radius and the beam waist and derive the particular parameter values for which a 3D dark focus with null intensity at the ring center is formed. We have performed experiments with a KGd(WO4)2 biaxial crystal, reporting the generation of a bottle beam in full agreement with our theoretical investigations.

© 2013 Optical Society of America

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  1. V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
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    [CrossRef]
  8. M. V. Berry and M. R. Dennis, J. Phys. A 34, 8877 (2001).
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    [CrossRef]
  10. W. T. M. Irvine and D. Bouwmeester, Nat. Phys. 4, 716 (2008).
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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]
  32. C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).
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  34. K. G. Wilcox, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, Appl. Phys. B 99, 619 (2010).
    [CrossRef]

2013 (2)

2012 (2)

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).
[CrossRef]

G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, Opt. Lett. 37, 851 (2012).
[CrossRef]

2010 (5)

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, Nat. Phys. 6, 118 (2010).
[CrossRef]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 18, 2753 (2010).
[CrossRef]

K. G. Wilcox, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, Appl. Phys. B 99, 619 (2010).
[CrossRef]

2009 (2)

2008 (3)

V. G. Shvedov, Y. V. Izdebskaya, A. V. Rode, A. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 20902 (2008).
[CrossRef]

W. T. M. Irvine and D. Bouwmeester, Nat. Phys. 4, 716 (2008).
[CrossRef]

T. Kalkandjiev and M. Bursukova, Proc. SPIE 6994, 69940B (2008).
[CrossRef]

2007 (3)

2004 (4)

C. J. R. Sheppard and A. Choudhury, Appl. Opt. 43, 4322 (2004).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef]

D. Yelin, B. E. Bouma, and G. J. Tearney, Opt. Lett. 29, 661 (2004).
[CrossRef]

M. V. Berry, J. Opt. A 6, 289 (2004).
[CrossRef]

2001 (5)

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, Phys. Rev. A 63, 031602(R) (2001).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 2251 (2001).
[CrossRef]

M. V. Berry and M. R. Dennis, J. Phys. A 34, 8877 (2001).
[CrossRef]

L. Cacciapuoti, M. de Angelis, G. Pierattini, and G. M. Tino, Eur. Phys. J. D 14, 373 (2001).
[CrossRef]

P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N. P. Bigelow, Opt. Express 8, 159 (2001).
[CrossRef]

2000 (1)

1999 (2)

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, R1750 (1999).
[CrossRef]

A. M. Belsky and M. A. Stepanov, Opt. Commun. 167, 1 (1999).
[CrossRef]

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

1995 (1)

N. Davidson, H. J. Lee, Ch. S. Adams, M. Kasevich, and S. Chu, Phys. Rev. Lett. 74, 1311 (1995).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

1978 (1)

A. M. Belskii and A. P. Khapalyuk, Opt. Spectrosc. 44, 436 (1978).

1942 (1)

C. V. Raman and T. M. K. Nedungadi, Nature 149, 552 (1942).
[CrossRef]

Abdolvand, A.

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 18, 2753 (2010).
[CrossRef]

K. G. Wilcox, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, Appl. Phys. B 99, 619 (2010).
[CrossRef]

Adams, Ch. S.

N. Davidson, H. J. Lee, Ch. S. Adams, M. Kasevich, and S. Chu, Phys. Rev. Lett. 74, 1311 (1995).
[CrossRef]

Aiello, A.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Alonso, M. A.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

Arlt, J.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, Phys. Rev. A 63, 031602(R) (2001).
[CrossRef]

J. Arlt and M. J. Padgett, Opt. Lett. 25, 191 (2000).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Belskii, A. M.

A. M. Belskii and A. P. Khapalyuk, Opt. Spectrosc. 44, 436 (1978).

Belsky, A. M.

A. M. Belsky and M. A. Stepanov, Opt. Commun. 167, 1 (1999).
[CrossRef]

Berry, M. V.

M. V. Berry and M. R. Jeffrey, Prog. Opt. 50, 13 (2007).
[CrossRef]

M. V. Berry, J. Opt. A 6, 289 (2004).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 2251 (2001).
[CrossRef]

M. V. Berry and M. R. Dennis, J. Phys. A 34, 8877 (2001).
[CrossRef]

Bigelow, N. P.

Bliokh, K. Y.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

Bongs, K.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, Phys. Rev. A 63, 031602(R) (2001).
[CrossRef]

Bouhelier, A.

Bouma, B. E.

Bouwmeester, D.

W. T. M. Irvine and D. Bouwmeester, Nat. Phys. 4, 716 (2008).
[CrossRef]

Bruyant, A.

Burger, S.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, Phys. Rev. A 63, 031602(R) (2001).
[CrossRef]

Bursukova, M.

T. Kalkandjiev and M. Bursukova, Proc. SPIE 6994, 69940B (2008).
[CrossRef]

Cacciapuoti, L.

L. Cacciapuoti, M. de Angelis, G. Pierattini, and G. M. Tino, Eur. Phys. J. D 14, 373 (2001).
[CrossRef]

Carnegie, D. J.

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 21, 11125 (2013).
[CrossRef]

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).
[CrossRef]

Choudhury, A.

Chu, S.

N. Davidson, H. J. Lee, Ch. S. Adams, M. Kasevich, and S. Chu, Phys. Rev. Lett. 74, 1311 (1995).
[CrossRef]

Colas des Francs, G.

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef]

Dally, A.

Davidson, N.

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, R1750 (1999).
[CrossRef]

N. Davidson, H. J. Lee, Ch. S. Adams, M. Kasevich, and S. Chu, Phys. Rev. Lett. 74, 1311 (1995).
[CrossRef]

de Angelis, M.

L. Cacciapuoti, M. de Angelis, G. Pierattini, and G. M. Tino, Eur. Phys. J. D 14, 373 (2001).
[CrossRef]

Dennis, M. R.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, Nat. Phys. 6, 118 (2010).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef]

M. V. Berry and M. R. Dennis, J. Phys. A 34, 8877 (2001).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 2251 (2001).
[CrossRef]

Dereux, A.

Desyatnikov, A.

Desyatnikov, A. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

Dettmer, S.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, Phys. Rev. A 63, 031602(R) (2001).
[CrossRef]

Ejnisman, R.

Ertmer, W.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, Phys. Rev. A 63, 031602(R) (2001).
[CrossRef]

Feurer, T.

M. Meier, V. Romano, and T. Feurer, Appl. Phys. A 86, 329 (2007).
[CrossRef]

Hellweg, D.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, Phys. Rev. A 63, 031602(R) (2001).
[CrossRef]

Henderson, R.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).
[CrossRef]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Hnatovsky, C.

Huang, C.

Ignatovich, F.

Irvine, W. T. M.

W. T. M. Irvine and D. Bouwmeester, Nat. Phys. 4, 716 (2008).
[CrossRef]

Isenhower, L.

Izdebskaya, Y. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

V. G. Shvedov, Y. V. Izdebskaya, A. V. Rode, A. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 20902 (2008).
[CrossRef]

Jack, B.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, Nat. Phys. 6, 118 (2010).
[CrossRef]

Jeffrey, M. R.

M. V. Berry and M. R. Jeffrey, Prog. Opt. 50, 13 (2007).
[CrossRef]

Kalkandjiev, T.

T. Kalkandjiev and M. Bursukova, Proc. SPIE 6994, 69940B (2008).
[CrossRef]

Kalkandjiev, T. K.

Kasevich, M.

N. Davidson, H. J. Lee, Ch. S. Adams, M. Kasevich, and S. Chu, Phys. Rev. Lett. 74, 1311 (1995).
[CrossRef]

Khapalyuk, A. P.

A. M. Belskii and A. P. Khapalyuk, Opt. Spectrosc. 44, 436 (1978).

Khaykovich, L.

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, R1750 (1999).
[CrossRef]

King, R. P.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, Nat. Phys. 6, 118 (2010).
[CrossRef]

Kivshar, Y. S.

Kivshar, Yu. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

Krolikowski, W.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef]

Lee, H. J.

N. Davidson, H. J. Lee, Ch. S. Adams, M. Kasevich, and S. Chu, Phys. Rev. Lett. 74, 1311 (1995).
[CrossRef]

Lee, S.

Li, G.

Maller, K.

McDougall, C.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).
[CrossRef]

McGloin, D.

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).
[CrossRef]

Meier, M.

M. Meier, V. Romano, and T. Feurer, Appl. Phys. A 86, 329 (2007).
[CrossRef]

Nedungadi, T. M. K.

C. V. Raman and T. M. K. Nedungadi, Nature 149, 552 (1942).
[CrossRef]

Novotny, L.

O’Holleran, K.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, Nat. Phys. 6, 118 (2010).
[CrossRef]

Ostrovskaya, E. A.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

Ozeri, R.

R. Ozeri, L. Khaykovich, and N. Davidson, Phys. Rev. A 59, R1750 (1999).
[CrossRef]

Padgett, M. J.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, Nat. Phys. 6, 118 (2010).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef]

J. Arlt and M. J. Padgett, Opt. Lett. 25, 191 (2000).
[CrossRef]

Pierattini, G.

L. Cacciapuoti, M. de Angelis, G. Pierattini, and G. M. Tino, Eur. Phys. J. D 14, 373 (2001).
[CrossRef]

Rafailov, E. U.

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 21, 11125 (2013).
[CrossRef]

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).
[CrossRef]

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 18, 2753 (2010).
[CrossRef]

K. G. Wilcox, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, Appl. Phys. B 99, 619 (2010).
[CrossRef]

Rahman, A.

Raman, C. V.

C. V. Raman and T. M. K. Nedungadi, Nature 149, 552 (1942).
[CrossRef]

Rode, A. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[CrossRef]

V. G. Shvedov, Y. V. Izdebskaya, A. V. Rode, A. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 20902 (2008).
[CrossRef]

Romano, V.

M. Meier, V. Romano, and T. Feurer, Appl. Phys. A 86, 329 (2007).
[CrossRef]

Rudy, P.

Saffman, M.

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Sengstock, K.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, Phys. Rev. A 63, 031602(R) (2001).
[CrossRef]

Sheppard, C. J. R.

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Shostka, N.

Shvedov, V. G.

Sokolovskii, G. S.

G. S. Sokolovskii, D. J. Carnegie, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 21, 11125 (2013).
[CrossRef]

C. McDougall, R. Henderson, D. J. Carnegie, G. S. Sokolovskii, E. U. Rafailov, and D. McGloin, Proc. SPIE 8458, 845824 (2012).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Stepanov, M. A.

A. M. Belsky and M. A. Stepanov, Opt. Commun. 167, 1 (1999).
[CrossRef]

Tearney, G. J.

Tino, G. M.

L. Cacciapuoti, M. de Angelis, G. Pierattini, and G. M. Tino, Eur. Phys. J. D 14, 373 (2001).
[CrossRef]

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Weeber, J.-C.

Wiederrecht, G. P.

Wilcox, K. G.

K. G. Wilcox, A. Abdolvand, T. K. Kalkandjiev, and E. U. Rafailov, Appl. Phys. B 99, 619 (2010).
[CrossRef]

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rafailov, Opt. Express 18, 2753 (2010).
[CrossRef]

Williams, W.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Yelin, D.

Zhan, Q.

Zhang, S.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. A (1)

M. Meier, V. Romano, and T. Feurer, Appl. Phys. A 86, 329 (2007).
[CrossRef]

Appl. Phys. B (1)

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Figures (4)

Fig. 1.
Fig. 1.

On-axis intensity at the focal plane center, IZ=|BC(ρ=0,Z=0)|2, as given by Eq. (7) as a function of the control parameter ρ0=R0/w0. Black solid circles represent the experimental data obtained when a focused Gaussian beam propagates along the optic axis of a KGd(WO4)2 biaxial crystal. The inset shows the on-axis intensity IZ=|BC(ρ=0,Z)|2.

Fig. 2.
Fig. 2.

Slices of the intensity distribution ICP(ρ,Z) along the propagation direction for an input Gaussian beam of CP as given by Eqs. (2)–(5) for different values of the control parameter ρ0.

Fig. 3.
Fig. 3.

Transverse intensity patterns at the focal plane (a)–(d) obtained experimentally and (e)–(h) calculated theoretically [see Eqs. (2)–(5)], for a circularly polarized input beam of fundamental Gaussian profile with different values of the waist radius w0, which give different values of control parameter ρ0.

Fig. 4.
Fig. 4.

Spatial evolution of the transverse intensity patterns along the propagation distance Z for ρ0(exp)=0.93ρ0DF [see Eq. (8)], as (a)–(d) obtained experimentally and (e)–(h) calculated theoretically [see Eqs. (2)–(5)]. Top insets represent the cross section of the measured intensity distribution along the horizontal axis at the beam center.

Equations (8)

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E(ρ,Z)=(BC+CSSBCC)ein,
BC(ρ,Z)=0ηa(η)eiZ4η2cos(ηρ0)J0(ηρ)dη,
BS(ρ,Z)=0ηa(η)eiZ4η2sin(ηρ0)J1(ηρ)dη,
a(η)=0ρEin(ρ)J0(ηρ)dρ,
ICP(ρ,Z)=|BC|2+|BS|2,
ILP(ρ,Z)=ICP+2Re[BCBS*]cos(2Φ(φ+φC)),
BC(0,Z)=1wZddXF(X)=1wZ[1+iπXeX2erf(iX)],
ρ0DF=0.924,

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