Abstract

We analyze the evolution of the vortex and the asymmetrical parts of orbital angular momentum during its propagation through separable first-order optical systems. We find that the evolution of the vortex part depends on only parameters ax, ay, bx, and by of the ray transformation matrix and that isotropic systems with the same ratio b/a produce the same change of the vortex part of the orbital angular momentum. Finally, it is shown that, when light propagates through an optical fiber with a quadratic refractive-index profile, the vortex part of the orbital angular momentum cannot change its sign more than four times per period.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 163 (1997).
    [CrossRef]
  2. M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
    [CrossRef]
  3. A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 75, 127 (2002).
    [CrossRef]
  4. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, J. Opt. Soc. Am. A 20, 1635 (2003).
    [CrossRef]
  5. H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
    [CrossRef] [PubMed]
  6. J. Serna and J. M. Movilla, Opt. Lett. 26, 405 (2001).
    [CrossRef]
  7. M. J. Bastiaans, Opt. Commun. 25, 26 (1978).
    [CrossRef]
  8. M. J. Bastiaans and T. Alieva, Opt. Lett. 28, 2443 (2003).
    [CrossRef]
  9. M. J. Bastiaans, J. Opt. Soc. Am. A 17, 2475 (2000).
    [CrossRef]
  10. M. J. Bastiaans, J. Opt. Soc. Am. 69, 1710 (1979).
  11. M. J. Bastiaans, J. Opt. Soc. Am. A 3, 1227 (1986).
    [CrossRef]
  12. R. K. Luneberg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).
  13. K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979), Chap. 9.
    [CrossRef]
  14. A. W. Lohmann, J. Opt. Soc. Am. A 10, 2181 (1993).
    [CrossRef]
  15. G. P. Agrawal, A. K. Ghatak, and C. L. Metha, Opt. Commun. 12, 333 (1974).
    [CrossRef]
  16. D. Mendlovic and H. M. Ozaktas, J. Opt. Soc. Am. A 10, 1875 (1993).
    [CrossRef]

2003 (3)

2002 (1)

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 75, 127 (2002).
[CrossRef]

2001 (2)

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

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

2000 (1)

1997 (1)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 163 (1997).
[CrossRef]

1993 (2)

1986 (1)

1979 (1)

1978 (1)

M. J. Bastiaans, Opt. Commun. 25, 26 (1978).
[CrossRef]

1974 (1)

G. P. Agrawal, A. K. Ghatak, and C. L. Metha, Opt. Commun. 12, 333 (1974).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, A. K. Ghatak, and C. L. Metha, Opt. Commun. 12, 333 (1974).
[CrossRef]

Alieva, T.

Bastiaans, M. J.

Bekshaev, A. Ya.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, J. Opt. Soc. Am. A 20, 1635 (2003).
[CrossRef]

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 75, 127 (2002).
[CrossRef]

Denisenko, V. G.

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 75, 127 (2002).
[CrossRef]

Gbur, G.

Ghatak, A. K.

G. P. Agrawal, A. K. Ghatak, and C. L. Metha, Opt. Commun. 12, 333 (1974).
[CrossRef]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 163 (1997).
[CrossRef]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 163 (1997).
[CrossRef]

Lohmann, A. W.

Luneberg, R. K.

R. K. Luneberg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 163 (1997).
[CrossRef]

Mendlovic, D.

Metha, C. L.

G. P. Agrawal, A. K. Ghatak, and C. L. Metha, Opt. Commun. 12, 333 (1974).
[CrossRef]

Movilla, J. M.

Ozaktas, H. M.

Schouten, H. F.

Serna, J.

Soskin, M. S.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, J. Opt. Soc. Am. A 20, 1635 (2003).
[CrossRef]

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 75, 127 (2002).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 163 (1997).
[CrossRef]

Vasnetsov, M. V.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, J. Opt. Soc. Am. A 20, 1635 (2003).
[CrossRef]

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 75, 127 (2002).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 163 (1997).
[CrossRef]

Visser, T. D.

Wolf, E.

Wolf, K. B.

K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979), Chap. 9.
[CrossRef]

J. Opt. Soc. Am. (1)

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

JETP Lett. (1)

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, and M. S. Soskin, JETP Lett. 75, 127 (2002).
[CrossRef]

Opt. Commun. (2)

M. J. Bastiaans, Opt. Commun. 25, 26 (1978).
[CrossRef]

G. P. Agrawal, A. K. Ghatak, and C. L. Metha, Opt. Commun. 12, 333 (1974).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 163 (1997).
[CrossRef]

Prog. Opt. (1)

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

Other (2)

R. K. Luneberg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).

K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979), Chap. 9.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (14)

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

μpqrsE=----Wx,u;y,v×xpuqyrvsdxdudydv, p,q,r,s0.
Λa=Ec2×μ2000-μ0020μ1001+μ0110-2μ1010μ1100-μ0011μ2000+μ0020,
Λv=2Ec2×μ0020μ1001-μ2000μ0110+μ1010μ1100-μ0011μ2000+μ0020,
T=μ0020μ1001-μ2000μ0110+μ1010μ1100-μ0011.
μpqrsoutE=----Winx,u;y,v×axx+bxupcxx+dxuq×ayy+byvrcyy+dyvsdxdudydv=Ek=0p l=0q m=0r n=0spkqlrmsn×axp-kbxkcxldxq-layr-mbymcyndys-n×μp-k+l,q-l+k,r-m+n,s-n+m.
μpqrsoutFTx=μqprs-1qbxp-q, μpqrsoutFTy=μpqsr-1byr-s, μpqrsoutFTxy=μqpsr-1q+sbxp-qbyr-s,
Tx=μ0020μ0101+μ0200μ1010-μ0110μ1100+μ0011, Ty=-μ0002μ1010-μ2000μ0101+μ1001μ1100+μ0011, Txy=-μ0002μ0110+μ0200μ1001-μ0101μ1100-μ0011.
μ1001out=axcyμ1010+axdyμ1001+bxcyμ0110+bxdyμ0101, μ0110out=cxayμ1010+cxbyμ1001+dxayμ0110+dxbyμ0101
Λout=Ec2μ1001axdy-bycx-μ0110aydx-bxcy+μ0101bxdy-bydx+μ1010axcy-aycx.
Tout=axayT+aybxTx+axbyTy+bxbyTxy.
μ2000out+μ0020out=ax2μ2000+2axbxμ1100+bx2μ0200+ay2μ0020+2aybyμ0011+by2μ0002
Λvout=2Ec2a2T+abTx+Ty+b2Txya2μ2000+μ0020+2abμ1100+μ0011+b2μ0200+μ0002.
Tμ2000+μ0020=Tx+Ty2μ1100+μ0011=Txyμ0200+μ0002
Λvout=Λvp=2Ec2×T+pTx+Ty+p2Txyμ2000+μ0020+2pμ1100+μ0011+p2μ0200+μ0002,

Metrics