Abstract

A new method that allows simultaneous frequency doubling and dynamic shaping of a Gaussian beam into a variety of light patterns is introduced. The novel technique is based on the controllable generation of multiple-vortex patterns in seeded schemes. Applications include the generation of dynamic patterns of frequency-doubled, coherent optical tweezers.

© 2001 Optical Society of America

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References

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  1. O. Bryngdahl, J. Opt. Soc. Am. 64, 1092 (1974).
  2. I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
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    [CrossRef]
  9. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
    [CrossRef]
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    [CrossRef]
  11. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
    [CrossRef]
  12. D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
    [CrossRef]
  13. D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
    [CrossRef]
  14. G. Molina-Terriza and L. Torner, J. Opt. Soc. Am. B 17, 1197 (2000).
    [CrossRef]
  15. I. Freund, Opt. Commun. 159, 99 (1999).
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  17. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
    [CrossRef]
  18. P. C. Mogensen and J. Glckstad, Opt. Commun. 175, 75 (2000).
    [CrossRef]

2000 (3)

I. Freund, Opt. Commun. 181, 19 (2000).
[CrossRef]

P. C. Mogensen and J. Glckstad, Opt. Commun. 175, 75 (2000).
[CrossRef]

G. Molina-Terriza and L. Torner, J. Opt. Soc. Am. B 17, 1197 (2000).
[CrossRef]

1999 (5)

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
[CrossRef]

E. G. Churin, Opt. Lett. 24, 620 (1999).
[CrossRef]

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

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

A. Ashkin, Opt. Photon News 10(5), 41 (1999).
[CrossRef]

1998 (2)

D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
[CrossRef]

I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
[CrossRef]

1997 (2)

E. Abramochkin and V. Volostnikov, Opt. Commun. 141, 59 (1997).
[CrossRef]

M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).

1996 (2)

E. Abramochkin and V. Volostnikov, Opt. Commun. 125, 302 (1996).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

1993 (2)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

1992 (1)

1974 (1)

Abramochkin, E.

E. Abramochkin and V. Volostnikov, Opt. Commun. 141, 59 (1997).
[CrossRef]

E. Abramochkin and V. Volostnikov, Opt. Commun. 125, 302 (1996).
[CrossRef]

Allen, L.

M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Ashkin, A.

A. Ashkin, Opt. Photon News 10(5), 41 (1999).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Bryngdahl, O.

Churin, E. G.

Dholakia, K.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Freund, I.

I. Freund, Opt. Commun. 181, 19 (2000).
[CrossRef]

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

Glckstad, J.

P. C. Mogensen and J. Glckstad, Opt. Commun. 175, 75 (2000).
[CrossRef]

Gur, I.

I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
[CrossRef]

Haist, T.

Heckenberg, N. R.

McDuff, R.

Mendlovic, D.

I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
[CrossRef]

Mogensen, P. C.

P. C. Mogensen and J. Glckstad, Opt. Commun. 175, 75 (2000).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza and L. Torner, J. Opt. Soc. Am. B 17, 1197 (2000).
[CrossRef]

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

Padgett, M.

M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).

Padgett, M. J.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Petrov, D. V.

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
[CrossRef]

Reicherter, M.

Simpson, N. B.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Smith, C. P.

Soskin, M. S.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Tiziani, H. J.

Torner, L.

G. Molina-Terriza and L. Torner, J. Opt. Soc. Am. B 17, 1197 (2000).
[CrossRef]

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
[CrossRef]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Vasnetsov, M. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Volostnikov, V.

E. Abramochkin and V. Volostnikov, Opt. Commun. 141, 59 (1997).
[CrossRef]

E. Abramochkin and V. Volostnikov, Opt. Commun. 125, 302 (1996).
[CrossRef]

Wagemann, E. U.

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (9)

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

I. Freund, Opt. Commun. 181, 19 (2000).
[CrossRef]

P. C. Mogensen and J. Glckstad, Opt. Commun. 175, 75 (2000).
[CrossRef]

I. Gur and D. Mendlovic, Opt. Commun. 145, 237 (1998).
[CrossRef]

E. Abramochkin and V. Volostnikov, Opt. Commun. 125, 302 (1996).
[CrossRef]

E. Abramochkin and V. Volostnikov, Opt. Commun. 141, 59 (1997).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

Opt. Lett. (3)

Opt. Photon News (1)

A. Ashkin, Opt. Photon News 10(5), 41 (1999).
[CrossRef]

Phys. Rev. A (1)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Phys. Rev. E (1)

D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
[CrossRef]

Phys. World (1)

M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).

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Figures (4)

Fig. 1
Fig. 1

Marginal curves separating regions with different vortex content, and hence intensity pattern, of the output SH beam as a function of amplitude and width of the input SH seed beam. The diagrammatic labels indicate the vortex pattern predicted in each region. Conditions: crystal length ξ=1; amplitude and width of the pump beam, A0,1=0.1, w1=2, respectively; input topological charges m1,m2=1,-2. Mismatch: solid curves, β=0; dotted curves, β=3; the vertical lines are identical for both values of β. Triangles, input conditions of the simulations shown in Fig.  3, below.

Fig. 2
Fig. 2

Analogous to Fig.  1 but for input topological charges of the pump and seed beams m1,m2=2,-4. Solid curves, ξ=1; dotted curves, ξ=1.5; the vertical line located at w2=2 is identical for both values of ξ. A0,1=0.1, w1=2, and β=0. Triangles, input conditions of the simulations shown in Fig.  4.

Fig. 3
Fig. 3

Representative examples of the patterns of SH light that are numerically obtained when the amplitude of the input SH seed is changed. The simulations correspond to the triangles of Fig.  1. (a) A0,2=0.005, (b) A0,2=0.01, (c) A0,2=0.05, (d) A0,2=0.1.

Fig. 4
Fig. 4

Analogous to Fig.  3 but for the conditions indicated by the triangles of Fig.  2. (a) A0,2=0.001, (b) A0,2=0.02, (c) A0,2=0.04, (d) A0,2=0.1.

Equations (7)

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

ia1ξ-α122a1+a1*a2exp-iβξ=0,
ia2ξ-α222a2+a12expiβξ=0,
a2x,y,ξ=A0,2rw2m211+iξsm2+1×exp-r2w221+iξsexpim2ϕ+iA0,12rw12m1fξv;βv1+iξv2m1+1×exp-2r2w121+iξvexpi2m1ϕ,
fξv;βv=0ξvexpiβvζ1+iζdζ,
A0,2A0,12z0v=κ2m11+ξv2/4κ4m1+1/21+ξv2m1+1/2fξv;βv,
w1=w22,
w1w2=2ξ.

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