The plasmon-forbidden deep sub-wavelength transmission with the TE polarization.

As is well-known, the sub-wavelength transmissions and field enhancement are related to the surface plasmon excitation. Here we demonstrate that in two-layer metallic gratings the deep sub-wavelength transmissions is supported with the TE polarization where the surface plasmon mode is forbidden. The new mechanism to the sub-wavelength transmission is discovered to be completely different from the findings in the literatures. we propose a simple resonance condition to classify the resonance types which are responsible for those sub-wavelength transmissions and confirm with numerical simulations. To give a complete explanation of underlying physics, we inspect the near-field phenomenon within the grating slits.