Figure 1

Impact of the different symmetries on the field scattered by two dielectric structures. The upper row shows the scattered intensity for a symmetric cylinder and the lower row for a pan-flute-like shape without any rotational, translational, or spatial inversion symmetry. The length and diameter of the cylinder are 200 nm. The pan flute is made of cylinders of different lengths and diameters; the longest one is 200 nm long and the total pan flute’s width is around 200 nm. In panels (a) and (c), the structures have $ϵ=2.25$, $\mu =1$, while in panels (b) and (d) we enforced duality symmetry by setting $ϵ=\mu ={ϵ}_{\mathrm{glass}}=2.25$. The incident field is a plane wave of well-defined helicity equal to 1, a momentum vector pointing to the positive $z$ axis, and a wavelength of 633 nm. Its electric field is $(\widehat{\mathbf{x}}+i\widehat{\mathbf{y}})/\sqrt{2}\exp (kz-\omega t)$. The left-half side of each subfigure corresponds to the scattered field with helicity equal to the incident plane wave ${\Lambda }_{+}$; the right half is for the opposite helicity ${\Lambda }_{-}$. The intensities of the two helicities ($\pm$) are computed as $|\mathbf{E}\pm i\mathbf{H}{|}^2$. In 13 (see Sec. 2.1), it is shown that $\mathbf{E}\pm i\mathbf{H}$ (with our choice of units) separates the two helicity components. The calculation plane is perpendicular to the $z$ axis and 20 nm away from the surface of the scatterers opposite to the one where the incident field comes from. The calculation area is $700\times 700\mathrm{nm}$. For color scaling purposes, the right-half side is multiplied by the factor in the upper right corner. The (lack of) cylindrical symmetry of the structures results in (non-)cylindrically symmetric field patterns, which is consistent with the geometry of each case. On the other hand, both scatterers behave identically with respect to the conservation of helicity, which is seen to depend exclusively on the electromagnetic properties of the material. The Supplemental Material [12] contains another simulation illustrating the fact that helicity preservation is independent of the angle of incidence of the plane wave.Reuse & Permissions