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Transmitting sub-wavelength information to the far-zone is of great interest for various electromagnetics and optics applications, e.g., for overcoming the diffraction limit in imaging or enabling multiple-input/multiple-output operation in closely spaced antennas. The common phenomenon in these applications is the conversion of evanescent to propagating waves. In this paper, we rigorously analyze and study evanescent-to-propagating wave conversion based on sub-wavelength metallic strip gratings. A theory is provided, which fully captures all diffracted fields and clearly highlights this conversion phenomenon. The Green's function of the strip gratings is constructed by introducing the spectral impulse response. This method solves the problem of the aperiodic excitation of the periodic grating and along the way provides insight and clear explanation of the evanescent-to-propagating wave conversion that takes place. All proposed results are validated against full-wave electromagnetic simulations. The theory is used to highlight and explain “extraordinary” transmission through a sub-wavelength metal strip grating when excited by a current source. Finally, an interesting application is presented where a nonradiating arrangement of sources is made to radiate by converting and diffracting its reactive near-field spectrum into the propagating regime using a simple metal strip grating.