Abstract

We observe phase singularities in the superposed field of two Gaussian beams. It is seen that the formation of these singularities depends on the tilt between two Gaussian beams and the separation of their beam axes. By reversing the angle or the position of the beams, one can change the sign of the vortex. We have shown the formation of single as well as multiple vortices by changing the tilt angle and the position of two Gaussian beams. The experimental results are verified with theoretical analysis. We also observe that such a vortex structure can be formed through superposition of two backreflected Gaussian beams from any optical element with two flat surfaces, as illustrated through a beam splitter and a neutral density filter. This technique is very useful for generation of vortices with high-power lasers where one cannot use a spatial light modulator.

© 2013 Optical Society of America

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References

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  1. L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science EV, 1999), pp. 291–372.
  2. M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science EV, 2001), pp. 219–276.
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    [CrossRef]
  4. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [CrossRef]
  5. G. Molina-Terriza, J. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. K. J. Moh, X.-C. Yuan, W. C. Cheong, L. S. Zhang, J. Lin, B. P. S. Ahluwalia, and H. Wang, “High-power efficient multiple optical vortices in a single beam generated by a kinoform-type spiral phase plate,” Appl. Opt. 45, 1153–1161 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
    [CrossRef]
  13. N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Y. Zel’dovich, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).
  14. K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14, 3039–3044 (2006).
    [CrossRef]
  15. S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007).
    [CrossRef]
  16. S. Vyas and P. Senthilkumaran, “Vortex array generation by interference of spherical waves,” Appl. Opt. 46, 7862–7867 (2007).
    [CrossRef]
  17. D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
    [CrossRef]
  18. J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

2012

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

2011

2009

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
[CrossRef]

2008

2007

2006

2004

1998

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

1995

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef]

1993

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

1981

N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Y. Zel’dovich, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Ahluwalia, B. P. S.

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science EV, 1999), pp. 291–372.

Ando, T.

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science EV, 1999), pp. 291–372.

Baranova, N. B.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Y. Zel’dovich, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Barnett, S.

Beijersbergen, M.

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Cheong, W. C.

Courtial, J.

Dennis, M. R.

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

Franke-Arnold, S.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef]

Fukuchi, N.

Ghai, D. P.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
[CrossRef]

Gibson, G.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

Hara, T.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef]

Hershcovitz, O.

Inoue, T.

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Kumar, A.

Lin, J.

Lipson, S. G.

Mamaev, A. V.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Y. Zel’dovich, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Matsumoto, N.

Moed, S.

Moh, K. J.

Molina-Terriza, G.

G. Molina-Terriza, J. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

O’Brien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

O’Holleran, K.

Ohtake, Y.

Padgett, M.

Padgett, M. J.

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14, 3039–3044 (2006).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science EV, 1999), pp. 291–372.

Pas’ko, V.

Pilipetskii, N. F.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Y. Zel’dovich, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Rotschild, C.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef]

Senthilkumaran, P.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
[CrossRef]

S. Vyas and P. Senthilkumaran, “Vortex array generation by interference of spherical waves,” Appl. Opt. 46, 7862–7867 (2007).
[CrossRef]

S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007).
[CrossRef]

Shkukov, V. V.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Y. Zel’dovich, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Singh, R. P.

Sirohi, R. S.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
[CrossRef]

Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Soskin, M.

M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science EV, 2001), pp. 219–276.

Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Thompson, M. G.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

Torres, J.

G. Molina-Terriza, J. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

Vaity, P.

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

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Vasnetsov, M.

Vyas, S.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
[CrossRef]

S. Vyas and P. Senthilkumaran, “Vortex array generation by interference of spherical waves,” Appl. Opt. 46, 7862–7867 (2007).
[CrossRef]

S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007).
[CrossRef]

Wang, H.

Wang, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Woerdman, J. P.

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Yu, S.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Yuan, X.-C.

Zel’dovich, B. Y.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Y. Zel’dovich, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Zhang, L. S.

Zhu, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Zommer, S.

Appl. Opt.

J. Mod. Opt.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

J. Opt. Soc. Am. A

JETP Lett.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Y. Zel’dovich, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Nat. Phys.

G. Molina-Terriza, J. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

Opt. Commun.

M. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[CrossRef]

Science

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338, 363–366 (2012).
[CrossRef]

Other

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science EV, 1999), pp. 291–372.

M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier Science EV, 2001), pp. 219–276.

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup: BS1, BS2, BS3, and BS4, beam splitters; M1 and M2, mirrors; L, lens; CCD, camera. (a) Using Mach–Zehnder interferometer (MZI) and (b) Using beam splitter/NDF.

Fig. 2.
Fig. 2.

Experimental intensity profiles (first row) and corresponding interferograms (second row) of the vortex beam at different distance z. Inset shows magnified images.

Fig. 3.
Fig. 3.

Theoretical intensity profiles (first row) and corresponding interferograms (second row) of the vortex beam at different distance z.

Fig. 4.
Fig. 4.

Experimental (first and second column) and theoretical (third and fourth column) intensity profiles along with corresponding interferograms of the vortex beam at distance z=20cm.

Fig. 5.
Fig. 5.

Experimental (first and second column) and theoretical (third and fourth column) intensity profiles along with corresponding interferograms for the double charged vortex beam at distance z=40cm.

Fig. 6.
Fig. 6.

Experimental intensity profiles (first row) and corresponding interferograms (second row) for the vortex beam generated from beam splitter (first column) and NDF (second, third, and fourth columns).

Equations (7)

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

Etilt(xo,yo,0)=exp[xo2+(yo+d)2wo2]exp[ikxoθ],
Etilt(x,y,z)=ki2πzexp[ik2z(2z2+x2+y2)]++Etilt(xo,yo)exp[ik2z((xo2+yo2)2(xox+yoy))]dxodyo.
Etilt(x,y,z)=wwoexp[1w2((x+zθ)2+(y+d)2)]exp[iψ]exp[ikz+ik2R((x+zθ)2+(y+d)2)]exp[ik(xθ+zθ2/2)],
w=wo1+(zzr)2,R=z+zr2z,ψ=arctan(zzr).
Eg(x,y,z)=wwoexp[x2+y2w2]exp[iψ]exp[ikz+ik(x2+y2)2R].
E=Etilt(x,y,z,d,θ)+Etilt(x,y,z,d,θ)exp(iπ)=2iSin[k(xθ(1zR)+dyR)2iw2(xzθdy)]×Egexp[(ik2R1w2)(z2θ2+d2)]exp[ikzθ2/2].
E=2iSin[kθ(x+idθzry)]exp[(x2+y2)wo2]exp[d2wo2].

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