Surface-mode lifetime and the terahertz transmission of subwavelength hole arrays

We measure the enhanced transmission of Terahertz radiation through a metal film perforated with arrays of subwavelength holes of varying hole size. By measuring transmission spectra in the time domain and comparing our experimental results to a rigorous modal-matching model, we are able to assess the relative contributions of resonant and nonresonant transmission channels. We see that the contribution of the resonant transmission becomes more important with decreasing hole size because the lifetime of the surface mode mediating the transmission is increased with reducing hole size. Using low-temperature measurements to control the nonradiative loss levels in our system, we show that losses limit the lifetime of the surface mode, thereby limiting the resonant transmission intensity for the smallest holes.

Figure 1

(Color online) Transmission of a pulse through a hole array. The holes are perforated in a gold film, supported on a substrate of silicon. Time-domain transmission spectra (of the type shown either side of the sample) are measured using a collimated, 1 cm diameter beam of THz radiation. (1) The incident vacuum region, (2) hole-array layer, and (3) dielectric substrate are indicated.

Figure 2

(Color online) Calculated transmission spectra through a $100\mu \text{m}$ pitch hole array in a thin conducting film shown (a) in the frequency domain and (b) in the time domain. In the time domain, regions of nonresonant transmission (A) and surface-mode-mediated transmission (B) are indicated. The time-domain traces are scaled to facilitate comparison between the pulse amplitudes, scaling factors $f$ are indicated; the plotted field is $E_{\text{trans}}/f$ for each trace. (c) Extension of the same time-domain traces shown in (b) to 200 picoseconds. The increase in the lifetime of the resonant modes with decreasing hole size can be clearly seen.

Figure 3

(Color online) Transmission spectra through hole arrays with hole sizes varying from 25 to $85\mu \text{m}$ (a) Experimental frequency-domain transmission spectra (b) Experimental time-domain spectra. Scaling factors $\left(f\right)$ are indicated, such that the plotted field is $E_{\text{trans}}/f$.

Figure 4

(Color online) (a) Spectra through the hole arrays, calculated using the modal matching model, with the incorporation of loss in the silicon layer (b). Calculated time-domain spectra, taken from the IFFT of the calculated spectra. Scaling factors $\left(f\right)$ are indicated, such that the plotted field is $E_{\text{trans}}/f$.

Figure 5

(Color online) The frequency dependent permittivity of our Silicon substrate, shown on a log scale. The imaginary component is shown at both 292 and 4.2 K.

Figure 6

(Color online) (a) Time-domain spectra through the $55\mu \text{m}$ holes at 292 and at 4.2 K Electric field amplitudes are scaled to the same peak level. (b) Fitting a Lorentzian form to the resonant component of the data with the surface mode lifetimes indicated. (c) Transmission intensity spectra of the $55\mu \text{m}$ holes at 292 and 4.2 K; the 4.2 K spectrum is scaled to match the peak transmission intensity of the 292 K spectrum in order to compare resonance mode widths.