Abstract

We demonstrate the transformation of Gaussian input beams into super-Gaussian beams with a quasi flat-top transverse profile by means of the conical refraction phenomenon by adjusting the ratio between the ring radius and the waist radius of the input beam to 0.445. We discuss the beam propagation of the super-Gaussian beam and show that it has a confocal parameter three times larger than the one that would be obtained from a Gaussian beam. The experiments performed with a KGd(WO4)2 biaxial crystal are in good agreement with the theoretical predictions.

© 2014 Optical Society of America

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2014

Y. V. Loiko, G. S. Sokolovskii, D. Carnegie, A. Turpin, J. Mompart, and E. U. Rafailov, Proc. SPIE 8960, 89601Q (2014).

H. Chen, S. Tripathi, and K. C. Toussaint, Opt. Lett. 39, 834 (2014).
[CrossRef]

2013

2012

J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, Opt. Lett. 37, 1463 (2012).
[CrossRef]

Y. V. Loiko, A. Turpin, T. K. Kalkandjiev, and J. Mompart, Opt. Lett. 37, 4197 (2012).
[CrossRef]

A. Hendriks, D. Naidoo, F. S. Roux, C. López-Mariscal, and A. Forbes, Proc. SPIE 8490, 849001 (2012).
[CrossRef]

C. Maher-McWilliams, P. Douglas, and P. F. Barker, Nat. Photonics 6, 386 (2012).
[CrossRef]

2011

2010

H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

K. Jahn and N. Bokor, Opt. Commun. 283, 4859 (2010).
[CrossRef]

V. Peet, J. Opt. 12, 095706 (2010).
[CrossRef]

V. Peet, Opt. Express 18, 19566 (2010).
[CrossRef]

S. Gras, D. G. Blair, and L. Ju, Phys. Rev. D 81, 042001 (2010).
[CrossRef]

2009

2008

2007

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

W. Wang, P. X. Wang, Y. K. Ho, Q. Kong, Y. Gu, and S. J. Wang, Rev. Sci. Instrum. 78, 093103 (2007).
[CrossRef]

2006

2004

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

2001

1999

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

1998

I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
[CrossRef]

1996

1980

R. E. Grojean, D. Feldman, and J. F. Roach, Rev. Sci. Instrum. 51, 375 (1980).
[CrossRef]

1978

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

Ait-Ameur, K.

Bagini, V.

Barker, P. F.

C. Maher-McWilliams, P. Douglas, and P. F. Barker, Nat. Photonics 6, 386 (2012).
[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 Pure Appl. Opt. 6, 289 (2004).
[CrossRef]

Blair, D. G.

S. Gras, D. G. Blair, and L. Ju, Phys. Rev. D 81, 042001 (2010).
[CrossRef]

Bokor, N.

K. Jahn and N. Bokor, Opt. Commun. 283, 4859 (2010).
[CrossRef]

Borghi, R.

Botha, L. R.

N. C. du Preez, A. Forbes, and L. R. Botha, Proc. SPIE 7131, 71311E (2009).

Bursukova, M.

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

Cai, Y.

Campos, J.

Carnegie, D.

Y. V. Loiko, G. S. Sokolovskii, D. Carnegie, A. Turpin, J. Mompart, and E. U. Rafailov, Proc. SPIE 8960, 89601Q (2014).

Carnegie, D. J.

Chen, H.

Cheng, W.

Clarkson, W. A.

Dan, Y.

Douglas, P.

C. Maher-McWilliams, P. Douglas, and P. F. Barker, Nat. Photonics 6, 386 (2012).
[CrossRef]

du Preez, N. C.

N. C. du Preez, A. Forbes, and L. R. Botha, Proc. SPIE 7131, 71311E (2009).

Eyyuboglu, H. T.

Feldman, D.

R. E. Grojean, D. Feldman, and J. F. Roach, Rev. Sci. Instrum. 51, 375 (1980).
[CrossRef]

Fernández, E.

Forbes, A.

S. Ngcobo, K. Ait-Ameur, I. Litvin, A. Hasnaoui, and A. Forbes, Opt. Express 21, 21113 (2013).
[CrossRef]

A. Hendriks, D. Naidoo, F. S. Roux, C. López-Mariscal, and A. Forbes, Proc. SPIE 8490, 849001 (2012).
[CrossRef]

N. C. du Preez, A. Forbes, and L. R. Botha, Proc. SPIE 7131, 71311E (2009).

I. A. Litvin and A. Forbes, Opt. Express 17, 15891 (2009).
[CrossRef]

A. Forbes, P. Mthunzi, M. McLaren, and T. Khanyile, in Optics in the Life Sciences, OSA Technical Digest (online) (Optical Society of America, 2013), paper JT2A.34.

Gori, F.

Gras, S.

S. Gras, D. G. Blair, and L. Ju, Phys. Rev. D 81, 042001 (2010).
[CrossRef]

Grojean, R. E.

R. E. Grojean, D. Feldman, and J. F. Roach, Rev. Sci. Instrum. 51, 375 (1980).
[CrossRef]

Gu, Y.

W. Wang, P. X. Wang, Y. K. Ho, Q. Kong, Y. Gu, and S. J. Wang, Rev. Sci. Instrum. 78, 093103 (2007).
[CrossRef]

Gur, I.

I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
[CrossRef]

Han, W.

Hasnaoui, A.

Hayes, J. R.

He, S.

Hendriks, A.

A. Hendriks, D. Naidoo, F. S. Roux, C. López-Mariscal, and A. Forbes, Proc. SPIE 8490, 849001 (2012).
[CrossRef]

Hnatovsky, C.

Ho, Y. K.

W. Wang, P. X. Wang, Y. K. Ho, Q. Kong, Y. Gu, and S. J. Wang, Rev. Sci. Instrum. 78, 093103 (2007).
[CrossRef]

Jahn, K.

K. Jahn and N. Bokor, Opt. Commun. 283, 4859 (2010).
[CrossRef]

Jeffrey, M. R.

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

Ju, L.

S. Gras, D. G. Blair, and L. Ju, Phys. Rev. D 81, 042001 (2010).
[CrossRef]

Kalkandjiev, T.

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

Kalkandjiev, T. K.

Khanyile, T.

A. Forbes, P. Mthunzi, M. McLaren, and T. Khanyile, in Optics in the Life Sciences, OSA Technical Digest (online) (Optical Society of America, 2013), paper JT2A.34.

Khapalyuk, A. P.

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

Kim, J. W.

Kong, Q.

W. Wang, P. X. Wang, Y. K. Ho, Q. Kong, Y. Gu, and S. J. Wang, Rev. Sci. Instrum. 78, 093103 (2007).
[CrossRef]

Krolikowski, W.

Litvin, I.

Litvin, I. A.

Liu, D.

Liu, Z.

H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Lizana, A.

Loiko, Y. V.

Loiko, Yu. V.

López-Mariscal, C.

A. Hendriks, D. Naidoo, F. S. Roux, C. López-Mariscal, and A. Forbes, Proc. SPIE 8490, 849001 (2012).
[CrossRef]

Lu, X.

Ma, H.

H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Ma, Y.

H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Mackenzie, J. I.

Maher-McWilliams, C.

C. Maher-McWilliams, P. Douglas, and P. F. Barker, Nat. Photonics 6, 386 (2012).
[CrossRef]

McLaren, M.

A. Forbes, P. Mthunzi, M. McLaren, and T. Khanyile, in Optics in the Life Sciences, OSA Technical Digest (online) (Optical Society of America, 2013), paper JT2A.34.

Mendlovic, D.

I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
[CrossRef]

Mompart, J.

Mthunzi, P.

A. Forbes, P. Mthunzi, M. McLaren, and T. Khanyile, in Optics in the Life Sciences, OSA Technical Digest (online) (Optical Society of America, 2013), paper JT2A.34.

Naidoo, D.

A. Hendriks, D. Naidoo, F. S. Roux, C. López-Mariscal, and A. Forbes, Proc. SPIE 8490, 849001 (2012).
[CrossRef]

Ngcobo, S.

Pacileo, A. M.

Peet, V.

Peinado, A.

Rafailov, E. U.

Roach, J. F.

R. E. Grojean, D. Feldman, and J. F. Roach, Rev. Sci. Instrum. 51, 375 (1980).
[CrossRef]

Roux, F. S.

A. Hendriks, D. Naidoo, F. S. Roux, C. López-Mariscal, and A. Forbes, Proc. SPIE 8490, 849001 (2012).
[CrossRef]

Santarsiero, M.

Shvedov, V.

Sokolovskii, G. S.

Y. V. Loiko, G. S. Sokolovskii, D. Carnegie, A. Turpin, J. Mompart, and E. U. Rafailov, Proc. SPIE 8960, 89601Q (2014).

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

Stepanov, M. A.

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

Toussaint, K. C.

Tovar, A. A.

Tripathi, S.

Turpin, A.

Wang, F.

Wang, P. X.

W. Wang, P. X. Wang, Y. K. Ho, Q. Kong, Y. Gu, and S. J. Wang, Rev. Sci. Instrum. 78, 093103 (2007).
[CrossRef]

Wang, S. J.

W. Wang, P. X. Wang, Y. K. Ho, Q. Kong, Y. Gu, and S. J. Wang, Rev. Sci. Instrum. 78, 093103 (2007).
[CrossRef]

Wang, W.

W. Wang, P. X. Wang, Y. K. Ho, Q. Kong, Y. Gu, and S. J. Wang, Rev. Sci. Instrum. 78, 093103 (2007).
[CrossRef]

Wang, X.

H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Xu, X.

H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Zhan, Q.

Zhang, B.

Zhao, C.

Zhou, P.

H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

Zhou, Z.

Adv. Opt. Photon.

J. Opt.

V. Peet, J. Opt. 12, 095706 (2010).
[CrossRef]

H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, J. Opt. 12, 045704 (2010).
[CrossRef]

J. Opt. A Pure Appl. Opt.

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

J. Opt. Soc. Am. A

Nat. Photonics

C. Maher-McWilliams, P. Douglas, and P. F. Barker, Nat. Photonics 6, 386 (2012).
[CrossRef]

Opt. Commun.

I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
[CrossRef]

K. Jahn and N. Bokor, Opt. Commun. 283, 4859 (2010).
[CrossRef]

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

Opt. Express

Opt. Lett.

Opt. Spectrosc.

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

Phys. Rev. D

S. Gras, D. G. Blair, and L. Ju, Phys. Rev. D 81, 042001 (2010).
[CrossRef]

Proc. SPIE

N. C. du Preez, A. Forbes, and L. R. Botha, Proc. SPIE 7131, 71311E (2009).

Y. V. Loiko, G. S. Sokolovskii, D. Carnegie, A. Turpin, J. Mompart, and E. U. Rafailov, Proc. SPIE 8960, 89601Q (2014).

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

A. Hendriks, D. Naidoo, F. S. Roux, C. López-Mariscal, and A. Forbes, Proc. SPIE 8490, 849001 (2012).
[CrossRef]

Prog. Opt.

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

Rev. Sci. Instrum.

R. E. Grojean, D. Feldman, and J. F. Roach, Rev. Sci. Instrum. 51, 375 (1980).
[CrossRef]

W. Wang, P. X. Wang, Y. K. Ho, Q. Kong, Y. Gu, and S. J. Wang, Rev. Sci. Instrum. 78, 093103 (2007).
[CrossRef]

Other

F. M. Dickey and S. C. Holswade, eds., Laser Beam Shaping: Theory and Techniques (Marcel Dekker, 2000).

A. Forbes, P. Mthunzi, M. McLaren, and T. Khanyile, in Optics in the Life Sciences, OSA Technical Digest (online) (Optical Society of America, 2013), paper JT2A.34.

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Figures (6)

Fig. 1.
Fig. 1.

Fundamental features of the CR phenomenon under conditions of ρ0R0/w01. (a) Bright and dark Poggendorff rings and field polarization distribution (yellow double arrows). (b) Intensity distribution in the zr plane showing the free space evolution of the CR beam.

Fig. 2.
Fig. 2.

Transverse intensity distributions at the focal plane ICP(ρ,Z=0) for an input Gaussian beam of circular polarization as given by Eqs. (1)–(3) for different values of the control parameter ρ0.

Fig. 3.
Fig. 3.

Cross-section of the intensity distribution along (a) the radial direction and (b) the beam propagation direction at the beam center for the original Gaussian beam (black-dashed line) and the super-Gaussian conical refraction (SGCR) beam obtained by adjusting ρ0=0.445 (red solid line). Black dots are the corresponding experimental measurements. (c) Intensity distribution in the zr plane showing the free space evolution of the SGCR beam. (d) Intensity distribution of the SGCR beam normalized to the beam area to help visualize the value of its confocal parameter b.

Fig. 4.
Fig. 4.

Transverse patterns along the beam propagation direction of the SGCR beam, i.e., for ρ0=0.445, calculated theoretically [see Eqs. (1)–(3)] for an input beam of transverse Gaussian profile. Insets are the cross-section of the intensity distribution along the horizontal direction.

Fig. 5.
Fig. 5.

Experimental setup. A diode laser coupled to a monomode fiber generates a Gaussian beam at 640 nm whose polarization is fixed to be circular by using the linear polarizer (LP) and the λ/4 waveplate. Then the beam is focused by means of a focusing lens (FL) along one of the optic axes of a KGd(WO4)2 biaxial crystal that transforms it into a super-Gaussian conical refraction beam. Experimental parameters f=200mm, l=2.4mm (R0=40.8μm).

Fig. 6.
Fig. 6.

Spatial evolution of the experimental transverse intensity patterns along the beam propagation direction for ρ0exp=0.44. Top insets represent the cross-section of the intensity distribution along the horizontal axis at the beam center.

Equations (4)

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

I(ρ,Z)=|BC|2+|BS|2,
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.

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