Abstract

We analyze the intensity of a Laguerre–Gaussian correlated Schell-model (LGCSM) beam focused by a thin lens near the focal region, and it is found that a controllable optical cage can be formed through varying the initial spatial coherence width. Furthermore, we carry out experimental measurement of the intensity of a focused LGCSM beam, and we observe that the optical cage is indeed formed in experiment. Our results will be useful for trapping particles or atoms.

© 2014 Optical Society of America

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2014 (3)

2013 (9)

2012 (4)

2011 (3)

2010 (3)

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

Y. Zhang, B. Ding, and T. Suyama, Phys. Rev. A 81, 023831 (2010).
[CrossRef]

P. Xu, X. He, J. Wang, and M. Zhan, Opt. Lett. 35, 2164 (2010).
[CrossRef]

2009 (1)

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

2007 (3)

2006 (1)

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

2005 (1)

Y. Cai and S. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

2002 (2)

1993 (1)

A. Belendez, L. Carretero, and A. Fimia, Opt. Commun. 98, 236 (1993).
[CrossRef]

1984 (1)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

1975 (1)

Arinaga, S.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Belendez, A.

A. Belendez, L. Carretero, and A. Fimia, Opt. Commun. 98, 236 (1993).
[CrossRef]

Cai, Y.

Cang, J.

J. Cang, P. Xiu, and X. Liu, Opt. Laser Technol. 54, 35 (2013).
[CrossRef]

Carretero, L.

A. Belendez, L. Carretero, and A. Fimia, Opt. Commun. 98, 236 (1993).
[CrossRef]

Chen, R.

Chen, Y.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Davidson, F. M.

Ding, B.

Y. Zhang, B. Ding, and T. Suyama, Phys. Rev. A 81, 023831 (2010).
[CrossRef]

Dong, Y.

Y. Dong, F. Wang, C. Zhao, and Y. Cai, Phys. Rev. A 86, 013840 (2012).
[CrossRef]

Du, S.

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

Eyyuboglu, H. T.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Fimia, A.

A. Belendez, L. Carretero, and A. Fimia, Opt. Commun. 98, 236 (1993).
[CrossRef]

Fischer, D. G.

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

Gbur, G.

Gori, F.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
[CrossRef]

Gu, Y.

He, S.

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

He, X.

Kato, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Kermisch, D.

Kitagawa, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Korotkova, O.

Lajunen, H.

Liang, C.

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, Opt. Lett. 39, 769 (2014).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

Lin, Q.

Liu, L.

Liu, X.

Mei, Z.

Mima, K.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Miyanaga, N.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Nakatsuka, M.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Peschel, U.

Qu, J.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

Ricklin, J. C.

Saastamoinen, T.

Sahin, S.

Sanchez, V. R.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

Santarsiero, M.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
[CrossRef]

Schchepakina, E.

Shchepakina, E.

Shen, Y.

Shirai, T.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

Suyama, T.

Y. Zhang, B. Ding, and T. Suyama, Phys. Rev. A 81, 023831 (2010).
[CrossRef]

Tong, Z.

Van Dijk, T.

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

Visser, T. D.

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

Wang, F.

Wang, J.

Wolf, E.

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Wu, G.

Xiu, P.

J. Cang, P. Xiu, and X. Liu, Opt. Laser Technol. 54, 35 (2013).
[CrossRef]

Xu, P.

Yamanaka, C.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

Yuan, Y.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, Opt. Lett. 38, 1814 (2013).
[CrossRef]

Zhan, M.

Zhang, Y.

Y. Zhang, B. Ding, and T. Suyama, Phys. Rev. A 81, 023831 (2010).
[CrossRef]

Zhao, C.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).
[CrossRef]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, Phys. Rev. A 86, 013840 (2012).
[CrossRef]

C. Zhao and Y. Cai, Opt. Lett. 36, 2251 (2011).
[CrossRef]

Zhu, S.

Appl. Phys. Lett. (1)

Y. Cai and S. He, Appl. Phys. Lett. 89, 041117 (2006).
[CrossRef]

J. Opt. A (1)

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, J. Opt. A 11, 085706 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, Opt. Commun. 305, 57 (2013).
[CrossRef]

A. Belendez, L. Carretero, and A. Fimia, Opt. Commun. 98, 236 (1993).
[CrossRef]

Opt. Express (3)

Opt. Laser Technol. (2)

J. Cang, P. Xiu, and X. Liu, Opt. Laser Technol. 54, 35 (2013).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, Opt. Laser Technol. 50, 14 (2013).
[CrossRef]

Opt. Lett. (14)

Phys. Rev. A (3)

Y. Dong, F. Wang, C. Zhao, and Y. Cai, Phys. Rev. A 86, 013840 (2012).
[CrossRef]

Y. Zhang, B. Ding, and T. Suyama, Phys. Rev. A 81, 023831 (2010).
[CrossRef]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, Phys. Rev. A 89, 013801 (2014).
[CrossRef]

Phys. Rev. E (1)

Y. Cai and S. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984).
[CrossRef]

T. Van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

Other (2)

L. Mandel and E. Wolf, eds., Optical Coherence and Quantum Optics (Cambridge, 1995).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (6)

Fig. 1.
Fig. 1.

Normalized intensity distribution of a LGCSM beam focused by a thin lens near the focal region in the ρxz plane with ρy=0 for different values of the initial coherence width δ0.

Fig. 2.
Fig. 2.

Experimental setup for generating a controllable optical cage by focusing a LGCSM beam and measuring its intensity. BE, beam expander; SLM, spatial light modulator; CA, circular aperture; L1, L2, L3, thin lenses; RGGD, rotating ground-glass disk; GAF, Gaussian amplitude filter; BPA, beam profile analyzer; PC1, PC2, personal computers.

Fig. 3.
Fig. 3.

Experimental results of the square of the modulus of the generated LGCSM beam of n=1 with different values of δ0 just before the GAF. The solid curve is a result of the theoretical fit.

Fig. 4.
Fig. 4.

Experimental results of (a) the intensity distribution of the generated LGCSM beam of n=1 near the focal region in the ρxz plane and (b) the transverse intensity distribution at several propagation distances with δ0=0.2mm.

Fig. 5.
Fig. 5.

Experimental results of (a) the intensity distribution of the generated LGCSM beam of n=1 near the focal region in the ρxz plane and (b) the transverse intensity distribution at several propagation distances with δ0=0.5mm.

Fig. 6.
Fig. 6.

Experimental results of (a) the intensity distribution of the generated LGCSM beam of n=1 near the focal region in the ρxz plane and (b) the transverse intensity distribution at several propagation distances with δ0=2mm.

Equations (11)

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J(r1,r2)=exp[r12+r224σ02(r1r2)22δ02]Ln0[(r1r2)22δ02],
J(ρ1,ρ2)=1(λB)2exp[ikD2B(ρ12ρ22)]×J(r1,r2)exp[ikA2B(r12r22)]×exp[ikB(r1·ρ1r2·ρ2)]d2r1d2r2,
(ABCD)=(1z01)(101/f1)(1f01)=(1z/ff1/f0).
rs=r1+r22,Δr=r1r2.
J(ρ1,ρ2)=1(λB)2exp[ikD2B(ρ12ρ22)]×P*(rs+Δr2)P(rsΔr2)g(Δr)×exp[ikB((rs+Δr2)·ρ1(rsΔr2)·ρ2)]d2Δrd2rs,
P*(rs+Δr2)=exp[(14σ02ikA2B)(rs+Δr2)2],
P(rsΔr2)=exp[(14σ02ikA2B)(rsΔr2)2],
g(Δr)=exp[Δr22δ02]Ln0[Δr22δ02].
P*(rs+Δr2)=1(λB)2P˜*(u1λB)exp(ikB(rs+Δr2)·u1)d2u1,
P(rsΔr2)=1(λB)2P˜(u2λB)exp(ikB(rsΔr2)·u2)d2u2.
J(ρ1,ρ2)=2n1(kB)2σ*2(B)σ2(B)δ02n+2×[(σ*2(B)+σ2(B)+2δ02)]n1exp[ikD2B(ρ12ρ22)]×exp[(k2B)2(σ*2(B)ρ12+σ2(B)ρ22)]×exp[(k2B)2(σ*2(B)ρ1+σ2(B)ρ2)2(σ*2(B)+σ2(B)+2δ02)]×Ln0[(k2B)2(σ*2(B)ρ1+σ2(B)ρ2)2(σ*2(B)+σ2(B)+2δ02)],

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