Enhanced Transmission through Periodic Arrays of Subwavelength Holes: The Role of Localized Waveguide Resonances

By using the rigid full-vectorial three-dimensional finite-difference time-domain method, we show that the enhanced transmission through a metallic film with a periodic array of subwavelength holes results from two different resonances: (i) localized waveguide resonances where each air hole can be considered as a section of metallic waveguide with both ends open to free space, forming a low-quality-factor resonator, and (ii) well-recognized surface plasmon resonances due to the periodicity. These two different resonances can be characterized from electromagnetic band structures in the structured metal film. In addition, we show that the shape effect in the enhanced transmission through the Au film with subwavelength holes is attributed to the localized waveguide resonance.

Figure 1

The schematic of a perfect conductor film with a square array of rectangular air holes.

Figure 2

(a) The normalized transmission through a PEC film with a square array of rectangular holes of size $0.9a\times 0.2a$ ($a$ is an arbitrary length unit) for different lattice constants: $d=1.0a$ (solid line), $1.1a$ (dashed line), and $1.2a$ (dotted line). The thickness of the film is $0.2a$. (b) The band structure for the case of the lattice constant $d=1.0a$. The odd (even) mode is denoted by the line marked with points (triangles). The white area is the region in the light cone.

Figure 3

The mean value of the normalized transmission for the sample with different square cell size: $(5a{)}^2$, $(7a{)}^2$, $(9a{)}^2$, and $(11a{)}^2$. For the comparison, the normalized transmission for the case of the periodic array of holes (the lattice constant $d=1.0a$) is denoted by the solid line. The ratio of the hole area to the cell area in the case of random distributed holes is equal to that in the case of the periodic array. The inset shows an example of 25 randomly distributed holes in a $5a\times 5a$ cell.

Figure 4

The normalized transmission through the Au films with periodic aperture arrays for the different lattice constant $d=425,450,475\mathrm{nm}$. The Au film is on a glass substrate ($ϵ=2.117$), the dimension of the hole is fixed at ($225\times 75{\mathrm{nm}}^2$), and the thickness of the films is 200 nm. The up (down) horizontal axis is labeled as the wavelength (frequency), where $a$ is 425 nm.