Multi-Slit Diffraction of Evanescent Electromagnetic Waves

The well-known Fraunhofer multi-slit diffraction is described as the multi-slit interference modulated by the single-slit diffraction, namely the multiplication between the single-slit diffraction factor and the multi-slit interference factor. By considering the simplified argument we show that the multi-slit diffraction of evanescent waves which are in the near-field region also has the interference and diffraction effects, and that this two-fold effect can be expressed as the convolution of the diffraction factor and the interference factor. Our conclusion could be helpful to understand the contribution of evanescent waves to the optical responses of sub-wavelength structures such as slits and grooves.