Abstract

The superposition of noncoaxial light beams containing screw wave-front dislocations is shown to create light patterns with a richer vortex content than that given by the arithmetic of the topological charges of the individual beams. We report the experimental observation of this phenomenon.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [CrossRef]
  2. A. Ashkin, Opt. Photon. News 10(5), 41 (1999); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
    [CrossRef]
  3. G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
    [CrossRef]
  4. D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
    [CrossRef]
  5. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef]
  6. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
    [CrossRef]
  7. M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
    [CrossRef] [PubMed]
  8. I. Freund, Opt. Commun. 159, 99 (1999).
    [CrossRef]
  9. B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
    [CrossRef]
  10. G. Molina-Terriza, L. Torner, and D. V. Petrov, Opt. Lett. 24, 899 (1999).
    [CrossRef]
  11. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
    [CrossRef]
  12. K. Burnett, M. Edwards, and C. W. Clark, Phys. Today 52(12), 37 (1999).
    [CrossRef]

1999

A. Ashkin, Opt. Photon. News 10(5), 41 (1999); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
[CrossRef]

I. Freund, Opt. Commun. 159, 99 (1999).
[CrossRef]

G. Molina-Terriza, L. Torner, and D. V. Petrov, Opt. Lett. 24, 899 (1999).
[CrossRef]

K. Burnett, M. Edwards, and C. W. Clark, Phys. Today 52(12), 37 (1999).
[CrossRef]

1997

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
[CrossRef]

1994

B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
[CrossRef]

1993

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

1992

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

1991

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

1974

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Ashkin, A.

A. Ashkin, Opt. Photon. News 10(5), 41 (1999); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
[CrossRef]

Battipede, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Brambilla, M.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

Burnett, K.

K. Burnett, M. Edwards, and C. W. Clark, Phys. Today 52(12), 37 (1999).
[CrossRef]

Clark, C. W.

K. Burnett, M. Edwards, and C. W. Clark, Phys. Today 52(12), 37 (1999).
[CrossRef]

Edwards, M.

K. Burnett, M. Edwards, and C. W. Clark, Phys. Today 52(12), 37 (1999).
[CrossRef]

Freund, I.

I. Freund, Opt. Commun. 159, 99 (1999).
[CrossRef]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (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, 4064 (1997).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Indebetouw, G.

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

Law, C. T.

Lugiato, L. A.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

Luther-Davies, B.

B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
[CrossRef]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Molina-Terriza, G.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Penna, V.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

Petrov, D. V.

Powles, R.

B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
[CrossRef]

Prati, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

Rozas, D.

Rubinstein-Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Swartzlander, G. A.

Tamm, C.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

Tikhonenko, V.

B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
[CrossRef]

Torner, L.

Vasnetsov, M. V.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Weiss, C. O.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

White, A. G.

J. Mod. Opt.

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

I. Freund, Opt. Commun. 159, 99 (1999).
[CrossRef]

Opt. Lett.

Opt. Photon. News

A. Ashkin, Opt. Photon. News 10(5), 41 (1999); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
[CrossRef]

Opt. Quantum Electron.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Phys. Rev. A

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A 43, 5090 (1991); N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, Phys. Rev. A 54, 2369 (1996).
[CrossRef] [PubMed]

Phys. Today

K. Burnett, M. Edwards, and C. W. Clark, Phys. Today 52(12), 37 (1999).
[CrossRef]

Proc. R. Soc. London Ser. A

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[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.


Figures (4)

Fig. 1
Fig. 1

Calculated locations of all the single-charge vortices that are present in the superposition S as a function of the separation between the axes of the individual beams x0. Filled circles, positive vortices, such as those nested on the individual beams; open circles, negative vortices. (a), (b) B=1, ϕ=0; (c), (d) B=0.6, ϕ=π/2.

Fig. 2
Fig. 2

Light pattern generated by the numerical superposition of two identical Gaussian beams with a charge 3 vortex nested in the center of each beam, for different separations between the beam axes: (a) x0=0.1, (b) x0=0.4, (c) x0=0.8, (d) x0=1.75. The plus and minus signs stand for the charge of the existing vortices. The symbols are to help the eye but do not necessarily indicate the exact locations of the vortices.

Fig. 3
Fig. 3

Experimental setup: L1, lens 1; BS3, BS4, beam splitters; M1, mirror 1. See text for other definitions.

Fig. 4
Fig. 4

(a), (c), (e) Observed light distribution and (b), (d), (f) interferograms produced by the superposition of two equal Gaussian beams with a single-charge vortex nested in the center of each beam. Axial separations between the beams: (a), (b) x03.6 mm, (c), (d) x02 mm, (e), (f) x00.1 mm. Waist of the input beams, 1 mm.

Equations (3)

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

Sx,y=X1+i sgnm1Y1m1F1X1,Y1+X2+i sgnm2Y2m2F2X2,Y2,
Sx,y=x-x0+iyexp-x-x02-y2+A2x+x0+iyexp-x+x02-y2,
x/x0=tanh2xx0.

Metrics