Abstract

We report on the singular shaping of light using closed-loop subwavelength slits whose shape is homeomorphic to the circle. Various sets of optical phase singularities can be generated depending on the given closed path whose geometry tailors the spin-orbit interaction for the light that passes through the curved slit. Here three families of closed-loop curves are considered—polygons, hypocycloids, and epicycloids.

© 2013 Optical Society of America

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References

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  1. G. Biener, A. Niv, V. Kleiner, and E. Hasman, Opt. Lett. 27, 1875 (2002).
    [CrossRef]
  2. P. F. Chimento, N. V. Kuzmin, J. Bosman, P. F. A. Alkemade, G. W. ’t Hooft, and E. R. Eliel, Opt. Express 19, 24219 (2011).
    [CrossRef]
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    [CrossRef]
  4. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
  5. V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, Opt. Lett. 33, 89 (2008).

2012 (1)

2011 (1)

2008 (1)

2002 (1)

1997 (1)

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

’t Hooft, G. W.

Alkemade, P. F. A.

Biener, G.

Bosman, J.

Chimento, P. F.

Denisenko, V. G.

Desyatnikov, A. S.

Eliel, E. R.

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).

Hasman, E.

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).

Kivshar, Y. S.

Kleiner, V.

Krolikowski, W.

Kuzmin, N. V.

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).

Minovich, A.

Niv, A.

Soskin, M. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, Opt. Lett. 33, 89 (2008).

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

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).

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Figures (4)

Fig. 1.
Fig. 1.

First row: slit aperture for polygons with mp=3 (triangle), 4 (square), and 5 (pentagon). Second and third rows: Fraunhofer diffraction intensity and phase patterns in the reciprocal coordinate system, here displayed in the range 0.1(ξ,η)0.1. Fourth row: azimuthal dependence of the phase along the closed contours that appear as dashed curves on phase plots.

Fig. 2.
Fig. 2.

Same as Fig. 1 for hypocycloids with mh=3 (deltoid), 4 (astroid), and 5.

Fig. 3.
Fig. 3.

Same as Fig. 1 for epicycloids with me=0 (circle), 1 (cardiod), and 2. Bottom row: phase profiles refers to elliptical path indicated by black-dashed ellipse on corresponding upper rows.

Fig. 4.
Fig. 4.

Comparative analysis of higher-order structures with mi=8 and i=(h,p,e). Bottom row: see text for details. Coordinate ranges are similar to those of Fig. 1.

Equations (5)

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x(θ)=mh1mhcosθ+1mhcos[(mh1)θ],y(θ)=mh1mhsinθ1mhsin[(mh1)θ],
x(θ)=me+1me+2cosθ1me+2cos[(me+1)θ],y(θ)=me+1me+2sinθ1me+2sin[(me+1)θ],
h=σ(2mh)
e=σ(2+me)
Eσ(ξ,η)t(x,y)ei2πRλ(ξx+ηy)dxdy,

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