Transmission of Light through a Single Rectangular Hole

We show that a single rectangular hole in a metallic film exhibits transmission resonances that appear near the cutoff wavelength of the hole waveguide. For light polarized with the electric field pointing along the hole’s short axis, it is shown that the normalized-to-area transmittance at resonance is proportional to the ratio between the long and short sides, and to the dielectric constant inside the hole. Importantly, this resonant transmission process is accompanied by a huge enhancement of the electric field at both entrance and exit interfaces of the hole.

Figure 1

Diagram of a single rectangular hole of sides $a_x$ and $a_y$ perforated on a metal film of thickness $h$. The structure is illuminated by a $p$-polarized plane wave with its angle of incidence with respect to the normal being $\theta$.

Figure 2

Normalized-to-area transmittance ($T$) versus wavelength (in units of the cutoff wavelength, ${\lambda }_c=2a_y$), for a normal incident plane wave impinging on a rectangular hole, for different ratios $a_y/a_x$. Metal thickness is $h=a_y/3$. For comparison, the inset shows $T$ versus wavelength for a single square (black line) and circular (red line) holes.

Figure 3

$T$ for a normal incident plane wave versus wavelength for a rectangular hole with $a_y/a_x=10$ and different values of $ϵ$ inside the hole. Metal thickness is $h=a_y/3$. Dashed and dotted lines show the behavior of Eqs. (5, 6), respectively. Inset: enhancement of the $E$-field intensity obtained for the previous cases; black curve renders Eq. (7).

Figure 4

Enhancement of the $E$-field amplitude with respect to the incident one, for a rectangular hole with $a_y/a_x=3$ and $h=a_y/3$ at two different planes: cut through the center of the rectangle ($y=0$, top panel; wave impinging from the bottom) and entrance surface ($z=0^{-}$, bottom panel). In both cases, the $E$-field amplitude is evaluated at the resonant wavelength.