Investigation of fade-out mechanism of resonance modes in optical transmission using stacked metallic sub-wavelength slit arrays

We investigated the behavior of optical transmission modes in stacked systems composed of metallic sub-wavelength slit-array plates separated by air gaps using simulations based on the finite-difference time-domain method. In double- and triple-stacked structures without a lateral displacement between the plates, the Fabry-Perot-like waveguide resonance modes are classified according to whether the resonance frequencies depend strongly on the air-gap spacing. By introducing a lateral displacement of the plates for both double- and triple-stacked structures, we found that the modes of one category, which were barely affected by changes in the air-gap spacing without the displacement, vary their resonance frequencies considerably when the optical paths are extremely narrow within the air-gap regions and, then, rapidly but continuously attenuate through mixing with the modes of the other category. We demonstrate that this marked behavior results from a manifest distortion in the spatial distribution of the electromagnetic fields for the modes of the first category, induced by the boundary condition at the slit ends changing from open-open to open-closed. Although all resonance modes in the two-tier system disappear continuously through cooperative mode mixing, some modes remain in the three-tier system that vanishes independently and discontinuously as the optical paths become blocked. These findings are indispensable for practical applications and for gaining a deeper understanding of this type of metamaterial.