Figure 1

(Color online) (a) A schematic drawing of a metal film with a periodic array of elliptical holes. The incident light beam is normal to the film surface, i.e., the $ac$ electric field $\mathbf{E}$ is parallel to the film plane, while the wave vector is normal to it (i.e., $\mathbf{k}\Vert y$). (b) An elliptical hole in a unit cell when the main semiaxes $a$ and $c$ are inclined with respect to the lattice axes $x$ and $z$ by an angle ${\alpha }_0$.Reuse & Permissions

Figure 2

(Color online) The ratio of polarizations of the transmitted light as a function of the aspect ratio $a∕c$ of the holes for different $\lambda$. For the values of $\lambda$ from $\sim 900\mathrm{nm}\text{to}\sim 700\mathrm{nm}$ the curves are close enough to the square law $y=x^2$ (left-hand dashed curve), while already for $\lambda =550\mathrm{nm}$ and $\lambda =500\mathrm{nm}$ (shown by dotted lines) the polarization ratio is essentially different from this law.Reuse & Permissions

Figure 3

(Color online) Transmission spectrum through an elliptical nanohole array for the $p$- and $s$-linear light polarizations. The $p$ polarization is parallel to the [0,1] direction, while $s$ is parallel to the [1,0] direction. (a) $\mathrm{Im}{\epsilon }_{xx}^{\left(e\right)}$ (${\mathbf{E}}_{\mathbf{0}}\Vert x$, $p$ polarization) and $\mathrm{Im}{\epsilon }_{zz}^{\left(e\right)}$ (${\mathbf{E}}_{\mathbf{0}}\Vert z$, $s$ polarization) vs $\omega ∕{\omega }_p$. (b) $\mathrm{Re}{\epsilon }_{xx}^{\left(e\right)}$ and $\mathrm{Re}{\epsilon }_{zz}^{\left(e\right)}$ vs $\omega ∕{\omega }_p$. In both polarizations there is a SP resonance peak at $\omega ={\omega }_{\mathit{sp}x}$ and $\omega ={\omega }_{\mathit{sp}z}$ (shown by the arrow), respectively. When ${\mathbf{E}}_{\mathbf{0}}\Vert z$, the resonance shifts for larger values $({\omega }_{\mathit{sp}z}>{\omega }_{\mathit{sp}x})$ and its amplitude reduces drastically. (c) Transmission coefficient $T$ vs frequency $\omega$, for different polarizations $\mathbf{E}\Vert x$ and $\mathbf{E}\Vert z$. The analytical results obtained using dilute and MG approximations are indicated by the dashed curves. The (connected by lines) filled and open symbols denote the results obtained numerically (Ref. 23) for a square array of holes in the shape of elliptical cylinders. Inset to (a): a unit cell with the elliptic hole and coordinate axes. The following sizes of the semiaxes were used: $a=0.1d$, $c=0.3d$, where $d$ is the size of the unit cell. The film thickness is $h=100\mathrm{nm}$.Reuse & Permissions

Figure 4

(Color online) The similar to Fig. 3c drawings, but vs wavelength $\lambda$. The peak at $\lambda \sim 600–700\mathrm{nm}$ corresponds to $E_0\Vert x$ (i.e., $p$) polarization (shown in Fig. 2 of Ref. 5), while the peak at $\lambda \sim 400\mathrm{nm}$ corresponds to $E_0\Vert x$ polarization (not shown in Fig. 2 of Ref. 5). Filled and open circles show results obtained for the case of elliptical holes (see left-hand inset), while filled and open squares show results obtained for the case of rectangular holes (see right-hand inset). Insets: cross sections of the unit cell with the elliptical hole (left-hand side) and with the rectangular hole (right-hand side) used in our calculations. The elliptical hole’s semiaxes are $a=0.1d$ and $c=0.3d$. The rectangular hole’s sites are $l_x=2\times 0.1d$, $l_z=2\times 0.3d$, so that the aspect ratio of both geometries is the same $a∕c=l_x∕l_z=0.33$. $d$ is the size of the unit cell. The film thickness is $h=100\mathrm{nm}$. ${\omega }_p=3\bullet {10}^{15}\mathrm{rad}∕\mathrm{s}$.Reuse & Permissions