Abstract

We have broken the symmetry of nongeneric singularities in Laguerre–Gauss fields by diffracting them through apertures. Conservation of topological charge strength was observed after the aperture. We theoretically and experimentally study this effect using Laguerre–Gauss fields diffracted by the square and triangular apertures.

© 2019 Optical Society of America

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References

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  5. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
    [Crossref]
  6. M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
    [Crossref]
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    [Crossref]
  8. X.-L. Ge, B.-Y. Wang, and C.-S. Guo, “Evolution of phase singularities of vortex beams propagating in atmospheric turbulence,” J. Opt. Soc. Am. A 32, 837–842 (2015).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (1)

A. Ambuj, E. Walla, S. Andaloro, S. Nomoto, R. Vyas, and S. Singh, “Symmetry in the diffraction of beams carrying orbital angular momentum,” Phys. Rev. A 99, 013846 (2019).
[Crossref]

2017 (1)

2016 (1)

2015 (2)

X.-L. Ge, B.-Y. Wang, and C.-S. Guo, “Evolution of phase singularities of vortex beams propagating in atmospheric turbulence,” J. Opt. Soc. Am. A 32, 837–842 (2015).
[Crossref]

M. Bahl and P. Senthilkumaran, “Energy circulations in singular beams diffracted through an isosceles right triangular aperture,” Phys. Rev. A 92, 013831 (2015).
[Crossref]

2014 (1)

2013 (1)

2012 (1)

2011 (1)

2010 (2)

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

2008 (1)

2007 (1)

2005 (1)

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

2004 (1)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
[Crossref]

1999 (1)

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).
[Crossref]

1997 (1)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[Crossref]

1970 (1)

Alencar, M. A. R. C.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Ambuj, A.

A. Ambuj, E. Walla, S. Andaloro, S. Nomoto, R. Vyas, and S. Singh, “Symmetry in the diffraction of beams carrying orbital angular momentum,” Phys. Rev. A 99, 013846 (2019).
[Crossref]

Andaloro, S.

A. Ambuj, E. Walla, S. Andaloro, S. Nomoto, R. Vyas, and S. Singh, “Symmetry in the diffraction of beams carrying orbital angular momentum,” Phys. Rev. A 99, 013846 (2019).
[Crossref]

Bahl, M.

M. Bahl and P. Senthilkumaran, “Energy circulations in singular beams diffracted through an isosceles right triangular aperture,” Phys. Rev. A 92, 013831 (2015).
[Crossref]

Beijersbergen, M. W.

G. P. Karman, M. W. Beijersbergen, A. van Duijl, and J. P. Woerdman, “Creation and annihilation of phase singularities in a focal field,” Opt. Lett. 22, 1503–1505 (1997).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
[Crossref]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[Crossref]

Borghi, R.

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Collins, S. A.

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

Dennis, M. R.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009), pp. 293–363.

Fonseca, E. J. S.

Freund, I.

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).
[Crossref]

Gåsvik, K. J.

K. J. Gåsvik, Optical Metrology (Wiley, 2003).

Gbur, G.

Gbur, G. J.

G. J. Gbur, Singular Optics (CRC Press, 2016).

Ge, X.-L.

Guo, C.-S.

Hickmann, J. M.

Jack, B.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

Jesus-Silva, A. J.

Karman, G. P.

Kartashov, Y. V.

King, R. P.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

Mesquita, P. H. F.

Nomoto, S.

A. Ambuj, E. Walla, S. Andaloro, S. Nomoto, R. Vyas, and S. Singh, “Symmetry in the diffraction of beams carrying orbital angular momentum,” Phys. Rev. A 99, 013846 (2019).
[Crossref]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[Crossref]

O’Holleran, K.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009), pp. 293–363.

Padgett, M. J.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009), pp. 293–363.

Roux, F. S.

Senthilkumaran, P.

M. Bahl and P. Senthilkumaran, “Energy circulations in singular beams diffracted through an isosceles right triangular aperture,” Phys. Rev. A 92, 013831 (2015).
[Crossref]

Silva, J. G.

Singh, S.

A. Ambuj, E. Walla, S. Andaloro, S. Nomoto, R. Vyas, and S. Singh, “Symmetry in the diffraction of beams carrying orbital angular momentum,” Phys. Rev. A 99, 013846 (2019).
[Crossref]

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Stahl, C.

Torner, L.

Tyson, R. K.

van Duijl, A.

Vyas, R.

A. Ambuj, E. Walla, S. Andaloro, S. Nomoto, R. Vyas, and S. Singh, “Symmetry in the diffraction of beams carrying orbital angular momentum,” Phys. Rev. A 99, 013846 (2019).
[Crossref]

Vysloukh, V. A.

Walla, E.

A. Ambuj, E. Walla, S. Andaloro, S. Nomoto, R. Vyas, and S. Singh, “Symmetry in the diffraction of beams carrying orbital angular momentum,” Phys. Rev. A 99, 013846 (2019).
[Crossref]

Wang, B.-Y.

Woerdman, J. P.

G. P. Karman, M. W. Beijersbergen, A. van Duijl, and J. P. Woerdman, “Creation and annihilation of phase singularities in a focal field,” Opt. Lett. 22, 1503–1505 (1997).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

J. Opt. A (1)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nat. Phys. (1)

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[Crossref]

New J. Phys. (1)

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

Opt. Commun. (1)

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (3)

A. Ambuj, E. Walla, S. Andaloro, S. Nomoto, R. Vyas, and S. Singh, “Symmetry in the diffraction of beams carrying orbital angular momentum,” Phys. Rev. A 99, 013846 (2019).
[Crossref]

M. Bahl and P. Senthilkumaran, “Energy circulations in singular beams diffracted through an isosceles right triangular aperture,” Phys. Rev. A 92, 013831 (2015).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Phys. Rev. Lett. (1)

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Proc. R. Soc. London A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[Crossref]

Other (3)

G. J. Gbur, Singular Optics (CRC Press, 2016).

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009), pp. 293–363.

K. J. Gåsvik, Optical Metrology (Wiley, 2003).

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Figures (4)

Fig. 1.
Fig. 1. Geometry of the system. The light beam E0 after crossing the aperture Ω diffracts through an ABCD system producing the final field E.
Fig. 2.
Fig. 2. Geometry of the edge of an equilateral triangular aperture of side length l. y1 and y2 represent the line functions along the indicated edges.
Fig. 3.
Fig. 3. Plots of the amplitude and phase of the exact theoretical (left) and experimental results (right) for the Fraunhofer diffraction patterns of LG beams after crossing apertures, showing the breaking and scrambling of vortexes through diffraction by triangular and square apertures. All windows are 0.36  mm×0.36  mm.
Fig. 4.
Fig. 4. Experimental setup for measuring the beam’s phase and topological charge strength SE˜m.

Equations (11)

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

E˜m(x,y,z)=ik2πBΩEm(x0,y0,0)exp{(ik2B)×[D(x2+y2)2xx02yy0+A(x02+y02)]}dx0dy0,
Em(x0,y0,0)=(x0±iy0)|m|exp(x02+y022w02),
E˜m(x,y,z)=ik2πB(ikB)|m|exp[(ikD2B)(x2+y2)](x±iy)|m|ΩE0(x0,y0,0)exp{(ik2B)×[2xx02yy0+A(x02+y02)]}dx0dy0,
E˜m(kT,θ,z)=E1(kT,θ,z)E2(kT,θ,z),
E1(kT,θ,z)=ik2πBexp[(ik2B)DkT2]exp(imθ),
E2(kT,θ,z)=[(Bik)(kT±ikTθ)]|m|Ωexp(x02+y022w02)×exp{(ik2B)[2x0kTcosθ2y0kTsinθ+A(x02+y02)]}dx0dy0.
SE˜m=limkT12π02πdθRe[(i)θE˜m(kT,θ,z)E˜m(kT,θ,z)].
limkTE2(kT,θ,z)=(BikkT)mΩexp(x02+y022w02)×exp[(ikB)(x0kTcosθ+y0kTsinθ)]dx0dy0.
E˜0(x,y)=l36l33y1y2exp[i(xx0+yy0)]dy0dx0,
E˜0(x,y)=1iyl34exp[i(yl4+xl312)]sinc[(y33+x)l34π]1iyl34exp[i(yl4+xl312)]sinc[(y33+x)l34π],
E˜m(x,y)=(x±iy)|m|E˜0(x,y).

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