The Grating Accelerator

where ky > 0 and kz > 0. Show that for small ripples (a d), this leads to a reflected wave as if a = 0, plus two surface waves that are attenuated exponentially with z. What is the relation between the grating wavelength d and the optical wavelength λ such that the x component of the phase velocity of the surface waves is the speed of light, c? In this case, a charged particle moving with vx ≈ c could extract energy from the wave, which is the principle of the proposed “grating accelerator” [1, 2, 3].