Effect of film thickness and dielectric environment on optical transmission through subwavelength holes

Abstract

We present a detailed theoretical study for the spectral position of transmission resonances appearing in isolated subwavelength apertures in metallic films. We provide analytical expressions for the resonant wavelength as a function of the film thickness and the dielectrics surrounding (and filling) the system that are valid for hole shapes supporting large-cutoff wavelengths and for both isolated and periodically arranged holes. Our results are quantitatively valid in the microwave and terahertz regimes, but they also have qualitative validity in the optical regime. Our results show that for unfilled holes, in the limiting case when the hole is in a very thin film (metal thickness much smaller than the wavelength), the transmission resonance is controlled by a length scale related to the vanishing of the effective admittance of vacuum, as seen from the hole. On the contrary, for metal thicknesses larger than half the wavelength, the transmission resonance is controlled by the cutoff of the fundamental waveguide mode inside the hole. When thin films and high-index dielectrics are combined, the spectral location of the maximum transmission can be strongly redshifted compared to the cutoff wavelength of the apertures, and transmission intensity is substantially enhanced.

Theory of absorption-induced transparency

“…In this case, the mechanism behind is the hybridization between SPPs and localized resonances, 6,18 which occurs near the cutoff wavelength. 8,19 As n A ≈ 1.2 in the wavelength range from 500 to 600 nm, the localized resonance is expected near n A λ o c ≈ 515 nm, thus overlapping with the SPP. The second change is, in agreement with the experimental finding, 12 the appearance of the AIT peak at λ ∼ 720 nm.…”

Terahertz gas sensor based on absorption-induced transparency

“…However, good convergence is attained only by considering the less decaying transversal electric mode, TE 0,1 for subwavelength rectangular holes (the fundamental waveguide mode). Within this ''minimal model'', results can be worked out analytically [9]. The in-plane electric field component of the TE 0,1 mode is defined as: within the intervalr jj 2 ½Àa y =2; a y =2  ½Àa x =2; a x =2 and zero otherwise, where q y = p/a y is the only component of its parallel wave-vector, being the corresponding propagation constant q z ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi e II g 2 À q 2 y q , with g = 2p/k(e II = e hole ).…”

“…Metallic films drilled by holes may feature EOT in many situations; when the holes are either isolated, randomly distributed, periodically arranged, etc. The local dielectric environment is also important [8,9]. Depending on the value of the geometrical parameters, the number of holes and their arrangements and the presence of nearby resonant systems (like molecules), the optical transmittance may present resonances due to different mechanisms.…”

Second-harmonic generation from metallic arrays of rectangular holes

“…In Fig. 8(a), the SHG peak is due to a localized resonance [67][68][69] excited at the FH wavelength [for an example, see the inset of Fig. 8(a), which represents the FH transmission spectrum at AR 2].…”