Finite Conductance Governs the Resonance Transmission of Thin Metal Slits at Microwave Frequencies

Fabry-Perot–like resonant transmission of microwave radiation through a single subwavelength slit in a thick aluminum plate is quantified for a range of slit widths. Surprisingly, and in contrast to previous studies [e.g., Y. Takakura, Phys. Rev. Lett. 86, 5601 (2001)], the resonant frequency exhibits a maximum as a function of slit width, decreasing as the slit width is reduced to less than 2% of the incident wavelength. This result accords with a new model based on coupled surface plasmon theory taking into account the finite conductivity, and hence permittivity, of the metal. This is contrary to a common assumption that metals can be treated as infinitely conducting in this regime.

Figure 1

Resonant transmission of a $250\mu \mathrm{m}$ slit. Inset: the slit labeled with dimensions and polarization of incident microwaves.

Figure 2

(a) Mode 2: Experimental data, slit widths $20–990\mu \mathrm{m}$ (points), resonant frequency corrected by $-0.019\pm 0.005\mathrm{GHz}$ due to finite beam spot size, width corrected by $-10\pm 4\mu \mathrm{m}$ due to plate bowing and surface roughness. HFSS [12] modeling (solid line) and Takakura prediction (dashed line). Inset: frequency against inverse slit length squared for slit width of $80\mu \mathrm{m}$ (points), linear fit (solid line), frequency at intercept $\sim 15.05\mathrm{GHz}$. (b) Mode 9: Experimental data for slit widths $24–994\mu \mathrm{m}$ (points), resonant frequency corrected by $-0.035\pm 0.008\mathrm{GHz}$, width corrected by $-13\pm 3\mu \mathrm{m}$, HFSS modeling (solid line) and Takakura prediction (dashed line).

Figure 3

Mode shifts from the simple Fabry-Perot model, as given by Takakura predictions and the data for a $500\mu \mathrm{m}$ slit.