Compacted dimensions and singular plasmonic surfaces

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Science  17 Nov 2017:
Vol. 358, Issue 6365, pp. 915-917
DOI: 10.1126/science.aap7939


  • Fig. 1 A series of transformations compacts three dimensions into two dimensions.

    The infinite dimension along x in (A) is transformed into singular points in (D). (B) x = −∞ transforms into x′ = 0, x = +∞ to x′ = +∞. (C) x′ = 0 transforms to x″ = 1/a and x′ = +∞ to x″ = 0. The u axis lies out of the plane.

  • Fig. 2 Dispersion with respect to the hidden variable.

    (A) kx alone. (B) kx and ky for ku = 0.

  • Fig. 3 Profile of the grating and associated mode.

    (Left) Phase of a mode for kx = 10 at ky = ku = 0. (Right) Field amplitude on the surface of the grating.

  • Fig. 4 Merging the spectrum of graphene gratings into a continuum.

    (A) The transformation to a periodically doped grating. (C to E) Transmittance through gratings whose doping level approaches zero at the grating minimum, as given in (B).

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