Abstract

The propagation of an Airy beam with a spiral phase is studied. The centroid position and spread of the beam are investigated analytically for different topological charges. Study shows that the centroid position of the Airy beam with a spiral phase keeps moving during propagation. The motion with positive topological charge is in the direction opposite to that with negative topological charge. The speed of the motion of the centroid position is proportional to the topological charge and the normalized distance. From the variation of the second moment of the beam, we can also see that the beam spread is speeded up by the spiral phase during propagation. The speed of the beam spread is proportional to the square of the topological charge.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2012

R. Chen, L. Zhong, Q. Wu, and K. Chew, Opt. Laser Technol. 44, 2015 (2012).
[CrossRef]

2011

X. Chu, C. Qiao, and X. Feng, Appl. Phys. B 105, 909 (2011).
[CrossRef]

X. Chu, Opt. Lett. 36, 2701 (2011).
[CrossRef]

2010

2009

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C-1 (2009).

2008

P. Saari, Opt. Express 16, 10303 (2008).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

2007

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

1987

1979

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

Asorey, M.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Baumgartl, J.

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C-1 (2009).

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chen, R.

R. Chen, L. Zhong, Q. Wu, and K. Chew, Opt. Laser Technol. 44, 2015 (2012).
[CrossRef]

Chew, K.

R. Chen, L. Zhong, Q. Wu, and K. Chew, Opt. Laser Technol. 44, 2015 (2012).
[CrossRef]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

Chu, X.

X. Chu, C. Qiao, and X. Feng, Appl. Phys. B 105, 909 (2011).
[CrossRef]

X. Chu, Opt. Lett. 36, 2701 (2011).
[CrossRef]

Cizmar, T.

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C-1 (2009).

Dai, H. T.

Dholakia, K.

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C-1 (2009).

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I.

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

Ellenbogen, T.

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Facchi, P.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Feng, X.

X. Chu, C. Qiao, and X. Feng, Appl. Phys. B 105, 909 (2011).
[CrossRef]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Gbur, G.

Gu, Y.

Hanson, S. G.

Liu, Y. J.

Luo, D.

Man’ko, V. I.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Marmo, G.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Mazilu, M.

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C-1 (2009).

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Pascazio, S.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Qiao, C.

X. Chu, C. Qiao, and X. Feng, Appl. Phys. B 105, 909 (2011).
[CrossRef]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Saari, P.

Siviloglou, G. A.

Sudarshan, E. C. G.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Sun, X. W.

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Wu, Q.

R. Chen, L. Zhong, Q. Wu, and K. Chew, Opt. Laser Technol. 44, 2015 (2012).
[CrossRef]

Yura, H. T.

Zhong, L.

R. Chen, L. Zhong, Q. Wu, and K. Chew, Opt. Laser Technol. 44, 2015 (2012).
[CrossRef]

Am. J. Phys.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Appl. Phys. B

X. Chu, C. Qiao, and X. Feng, Appl. Phys. B 105, 909 (2011).
[CrossRef]

Appl. Phys. Lett.

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Opt. Express

Opt. Laser Technol.

R. Chen, L. Zhong, Q. Wu, and K. Chew, Opt. Laser Technol. 44, 2015 (2012).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, Phys. Rev. A 77, 042115 (2008).
[CrossRef]

Phys. Rev. Lett.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Proc. SPIE

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C-1 (2009).

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Figures (6)

Fig. 1.
Fig. 1.

Normalized intensity distribution of the vortex Airy beam calculated from Eq. (1) with a=0.2m, w0=0.1m, and xd=yd=0, where the transverse scale denotes the times of w0.

Fig. 2.
Fig. 2.

Variation of the centroid position xc, yc of the Airy beam with a spiral phase.

Fig. 3.
Fig. 3.

Variation of the slope of the curve xc-ξ with a where m=1.

Fig. 4.
Fig. 4.

Second moment of the Airy beam with a spiral phase where the quantity of the moment denotes the times of w0.

Fig. 5.
Fig. 5.

Second central moment of the Airy beam with a spiral phase where the quantity of the moment denotes the times of w0.

Fig. 6.
Fig. 6.

Intensity distribution of the beam with a=0.1 and ξ=1 where the transverse scale denotes the times of w0.

Equations (17)

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

u0(x0,y0)=[(x0xd)+i(y0yd)]mA(x0,y0),
A(x0,y0)=exp[aw0(x0+y0)]Ai(x0w0)Ai(y0w0).
u0(x0,y0)=[(x0xd)+i(y0yd)]m[(x0xd)2+(y0yd)2]m/2A(x0,y0).
xj1yj2=1Pxj1yj2I(x,y,z)dxdy,
P=I(x,y,z)dxdy=w028πaexp(4a33).
I(x,y,z)=(k2πz)2H(p2,q2)exp[ikz(xp2+yq2)]dp2dq2,
H(p2,q2,z)=W0(p1,q1)exp[ikz(p1p2+q1q2)]dp1dq1,
W0(p1,q1)=u0(p1+p22,q1+q22)u0*(p1p22,q1q22).
δ(n)(s)=(2π)1(ix)nexp(isx)dx,n=0,1,2,
f(x)δ(n)(x)dx=(1)nf(n)(0)n=0,1,2,
xj1yj2=ij1+j2P(kz)j1j2j1+j2p2j1q2j2[H(p2,q2)]p2=q2=0.
x=xm=0mξw08πaexp(4a3/3)q1p12+q12N,
FN=Fexp[2a(x+y)]Ai2(x)Ai2(y)dxdy.
xm=0=(a214a)w0,
x2=x2m=0+8πaexp(4a3/3)×[m2ξ2(q1p12+q12)2N2mξp1q1p12+q12N]w02,
x2m=0=w0216a2(3+8a3+16a6+4aξ2).
μ2=(xxc)2=x2xc2.

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