Abstract

We derive the general expression for the orbital angular momentum (OAM) flux of an astigmatic partially coherent beam carrying twist phase [i.e., twisted anisotropic Gaussian–Schell model (TAGSM) beam] propagating through an astigmatic ABCD optical system with loss or gain. The evolution properties of the OAM flux of a TAGSM beam in a Gaussian cavity or propagating through a cylindrical thin lens are illustrated numerically with the help of the derived formula. It is found that we can modulate the OAM of a partially coherent beam by varying the parameters of the cavity or the orientation angle of the cylindrical thin lens, which will be useful in some applications, such as free-space optical communications and particle trapping.

© 2014 Optical Society of America

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2013 (2)

2012 (6)

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, Appl. Phys. B 109, 345 (2012).
[CrossRef]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Y. Yang, M. Mazilu, and K. Dholakia, Opt. Lett. 37, 4949 (2012).

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, Opt. Lett. 37, 184 (2012).
[CrossRef]

Z. Tong and O. Korotkova, Opt. Lett. 37, 2595 (2012).
[CrossRef]

2011 (1)

2010 (1)

2009 (4)

Y. Cai, Q. Lin, and O. Korotkova, Opt. Express 17, 2450 (2009).

C. Zhao, Y. Cai, and O. Korotkova, Opt. Express 17, 21472 (2009).
[CrossRef]

W. Chen, J. W. Haus, and Q. Zhan, Opt. Express 17, 17829 (2009).
[CrossRef]

J. Li and B. Lu, J. Opt. A 11, 045710 (2009).
[CrossRef]

2008 (1)

2007 (2)

2006 (2)

Y. Cai and L. Hu, Opt. Lett. 31, 685 (2006).
[CrossRef]

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

2003 (2)

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

D. Grier, Nature 424, 810 (2003).
[CrossRef]

2002 (3)

2001 (2)

J. Serna and J. M. Movilla, Opt. Lett. 26, 405 (2001).
[CrossRef]

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

1999 (1)

L. Allen, M. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

1998 (2)

C. Palma, G. Cardone, and G. Cincotti, IEEE J. Quantum Electron. 34, 1082 (1998).
[CrossRef]

R. Simon and N. Mukunda, J. Opt. Soc. Am. A 15, 2373 (1998).
[CrossRef]

1996 (1)

P. De Santis, A. Mascello, C. Palma, and M. R. Perrone, IEEE J. Quantum Electron. 32, 802 (1996).
[CrossRef]

1994 (2)

A. T. Friberg, E. Tervonen, and J. Turunen, J. Opt. Soc. Am. A 11, 1818 (1994).
[CrossRef]

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

1993 (1)

1992 (1)

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

1985 (1)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef]

1984 (1)

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Allen, L.

L. Allen, M. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

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

Ambrosini, D.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

Arlt, J.

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Attard, A. E.

Babiker, M.

L. Allen, M. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

Bagini, V.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

Baykal, Y.

Beijersbergen, M. W.

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

Bryant, P.

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Cai, Y.

Cardone, G.

C. Palma, G. Cardone, and G. Cincotti, IEEE J. Quantum Electron. 34, 1082 (1998).
[CrossRef]

Chen, W.

Cincotti, G.

C. Palma, G. Cardone, and G. Cincotti, IEEE J. Quantum Electron. 34, 1082 (1998).
[CrossRef]

De Santis, P.

P. De Santis, A. Mascello, C. Palma, and M. R. Perrone, IEEE J. Quantum Electron. 32, 802 (1996).
[CrossRef]

Dholakia, K.

Y. Yang, M. Mazilu, and K. Dholakia, Opt. Lett. 37, 4949 (2012).

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Dong, Y.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, Appl. Phys. B 109, 345 (2012).
[CrossRef]

Eyyuboglu, H. T.

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Friberg, A. T.

Gbur, G.

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

Ge, D.

Gori, F.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

Grier, D.

D. Grier, Nature 424, 810 (2003).
[CrossRef]

Han, Y.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Haus, J. W.

He, S.

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

Hu, L.

Huang, H.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Korotkova, O.

Kumar, A.

Li, J.

J. Li and B. Lu, J. Opt. A 11, 045710 (2009).
[CrossRef]

Lin, Q.

Liu, L.

Liu, X.

Lu, B.

J. Li and B. Lu, J. Opt. A 11, 045710 (2009).
[CrossRef]

MacDonald, M.

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Mascello, A.

P. De Santis, A. Mascello, C. Palma, and M. R. Perrone, IEEE J. Quantum Electron. 32, 802 (1996).
[CrossRef]

Mazilu, M.

Movilla, J. M.

Mukunda, N.

Padgett, M.

L. Allen, M. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

Palma, C.

C. Palma, G. Cardone, and G. Cincotti, IEEE J. Quantum Electron. 34, 1082 (1998).
[CrossRef]

P. De Santis, A. Mascello, C. Palma, and M. R. Perrone, IEEE J. Quantum Electron. 32, 802 (1996).
[CrossRef]

Paterson, L.

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Perrone, M. R.

P. De Santis, A. Mascello, C. Palma, and M. R. Perrone, IEEE J. Quantum Electron. 32, 802 (1996).
[CrossRef]

Peschel, U.

Prabhakar, S.

Reddy, S. G.

Ren, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Santarsiero, M.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

Serna, J.

Shen, Y.

Sibbett, W.

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Simon, R.

Singh, R. P.

Spreeuw, R. J. C.

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

Sudarshan, E. C. G.

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef]

Tervonen, E.

Tong, Z.

Tur, M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Turunen, J.

Visser, T. D.

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

Wang, F.

Wang, J.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Wang, Y.

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, Appl. Phys. B 109, 345 (2012).
[CrossRef]

Willner, A. E.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Woerdman, J. P.

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

Yan, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yang, Y.

Yao, M.

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Zhan, Q.

Zhang, Y.

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, Appl. Phys. B 109, 345 (2012).
[CrossRef]

Zhao, C.

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, Appl. Phys. B 109, 345 (2012).
[CrossRef]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

C. Zhao, Y. Cai, and O. Korotkova, Opt. Express 17, 21472 (2009).
[CrossRef]

Zhu, S.

Appl. Opt. (1)

Appl. Phys. B (1)

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, Appl. Phys. B 109, 345 (2012).
[CrossRef]

Appl. Phys. Lett. (2)

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

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

IEEE J. Quantum Electron. (2)

P. De Santis, A. Mascello, C. Palma, and M. R. Perrone, IEEE J. Quantum Electron. 32, 802 (1996).
[CrossRef]

C. Palma, G. Cardone, and G. Cincotti, IEEE J. Quantum Electron. 34, 1082 (1998).
[CrossRef]

J. Mod. Opt. (1)

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

J. Opt. A (1)

J. Li and B. Lu, J. Opt. A 11, 045710 (2009).
[CrossRef]

J. Opt. Soc. Am. A (5)

Nat. Photonics (1)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Nature (1)

D. Grier, Nature 424, 810 (2003).
[CrossRef]

Opt. Commun. (1)

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

Opt. Express (5)

Opt. Lett. (11)

Phys. Rev. A (2)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef]

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

Prog. Opt. (1)

L. Allen, M. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

Science (1)

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Normalized OAM flux of a TAGSM beam in a Gaussian cavity versus N for different values of cavity parameters g and ε.

Fig. 2.
Fig. 2.

Schematic of a cylindrical thin lens, which is located in the source plane.

Fig. 3.
Fig. 3.

Normalized OAM flux of a TAGSM beam propagating through a cylindrical thin lens versus the orientation angle φ.

Equations (20)

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

W(r1,r2)=G0exp[14r1T(σI2)1r114r2T(σI2)1r2]×exp[12(r1r2)T(σg2)1(r1r2)]×exp[ik2(r1r2)T(R1+μJ)(r1+r2)],
(σI2)1=(σI112σI122σI122σI222),(σg2)1=(σg112σg122σg122σg222),R1=(R111R121R211R221).
J=(0110).
J¯z=Ic(xvyu),
xv=1Ixvh(x,y,u,v)dxdydudv,
yu=1Iyuh(x,y,u,v)dxdydudv.
J¯z=(I02c){Tr[(R1σI2σI2R1)J]2μTr(σI2)},
W(r˜)=G0exp[ik2r˜TM01r˜],
M01=(R1i2k(σI2)1ik(σg2)1ik(σg2)1+μJik(σg2)1+μJTR1i2k(σI2)1ik(σg2)1).
W(ρ˜)=k24π2[det(B¯)]1/2W(r˜)dr˜×exp[ik2(r˜TB¯1A¯r˜2r˜TB¯1ρ˜+ρ˜TD¯B¯1ρ˜)],
A¯=(A0I0IA*),B¯=(B0I0IB*),C¯=(C0I0IC*),D¯=(D0I0ID*),
W(ρ˜)=G1exp[ik2ρ˜TM11ρ˜],
G1=G0[det(A¯+B¯M01)]1/2,
M11=(C¯+D¯M01)(A¯+B¯M01)1.
M11=(m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44),=(R11i2k(σI12)1ik(σg12)1ik(σg12)1+μ1Jik(σg12)1+μ1JTR11i2k(σI12)1ik(σg12)1),
(σI12)1=(ik(m11+m33+2m13)ik(m12+m34+m14+m32)ik(m12+m34+m14+m32)ik(m22+m44+2m24)),(σg12)1=(ikm13ik(m14+m32)/2ik(m14+m32)/2ikm24),R11=12(m11m33m12m34m12m34m22m44),μ1=(m14m32)/2.
J¯z1=I1f12cf2,
f1=2i(m11m32+m24m32m14m22m14m24)+2i(m11m34m14m33m22m34m24m34+m32m44)+2im12(m24m13m33+m44)+2im13(m14+m32+m34),f2=k(m122+m142m11m222m13m222m11m24)+k(m3224m13m24m22m332m24m33)+k(m342m11m442m13m44m33m44+2m32m34)+2km14(m32+m34)+2km12(m14+m32+m34),I1=2πG1/a1b1,a1=k2(m12+m14+m32+m34)2.b1=k2(m11+2m13+m33)(m22+2m24+m44).
(ABCD)=(ILI(2Riλπε2)I(12LRiλLπε2)I)N.
A=D=I,B=0I,C=(cos2φ/fsin2φ/2fsin2φ/2fsin2φ/f),

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