Trapped Electromagnetic Modes and Scaling in the Transmittance of Perforated Metal Films

We describe measurements and simulations of the enhanced transmittance by subwavelength hole arrays in silver films. The array period and hole size are systematically varied to give peak transmittances at wavelengths spanning a factor of 14. The spectra coincide when scaled using the array geometry and substrate refractive index alone, thus showing no significant dependence on the dielectric function of the metal. We argue that the spectra can be explained by interference of diffractive and resonant scattering. The resonant contribution comes from electromagnetic modes trapped in the film vicinity.

Figure 1

Transmittance vs wavelength for 9 different hole arrays. The open area fractions are 0.44 for the top 3 curves, 0.25 for the middle 3, and 0.11 for the bottom 3. The colors indicate the period: blue has $D_g=4\mu \mathrm{m}$, green $6\mu \mathrm{m}$, and red $8\mu \mathrm{m}$. The number above each set of curves is the open area fraction $f$.

Figure 2

Transmittance vs scaling variable, ${\lambda }_s=\lambda /(n_d{D}_g)$, for five arrays with the same open area fraction, $f=0.25$. The upper panel shows the data for two arrays made on a fused silica substrate ($n_d=1.4$) with $D_g=1\mu \mathrm{m}$ (blue curve) and $D_g=2\mu \mathrm{m}$ (red curve). The lower panel shows the data for three arrays on ZnSe ($n_d=2.4$). Variations in $D_g$ and $n_d$ yield a variation of $\lambda$ by a factor of 14.

Figure 3

Comparison of numerical results (black curves) with the experiment (red curves) for three arrays with $D_g=4\mu \mathrm{m}$.

Figure 4

The sum of the calculated transmittance and reflectance (left panels) near ${\lambda }_s=1$. The Ohmic losses in the metal produced by the trapped modes correspond to dips in these curves for ${\lambda }_s>1$. The red dashed lines show the positions of the corresponding transmittance peaks. A redshift effect is clearly visible. The right panels show the energy density of the corresponding trapped mode in the plane of the metal-dielectric interface as a function of $x/D_g$ (horizontal) and $y/D_g$ (vertical). The color code varies from dark brown (zero) to bright yellow (maximum) on a linear scale.