The Grating Accelerator

In optics, a reflective grating is a conducting surface with a ripple. The typical use of such a grating involves an incident electromagnetic wave with wave vector k in the x-z plane, and interference effects lead to a discrete set of reflected waves also with wave vectors in the x-z plane. Consider, instead, an incident plane electromagnetic wave with wave vector in the y-z plane and polarization in the x direction: We show that for small ripples, this leads to a reflected wave plus two surface waves that are attenuated exponentially with z. For certain values of the grating wavelength and the optical wavelength, the component of the phase velocity of the surface waves is the speed of light c. In this case, a charged particle moving with v_x ~ c could extract energy from the wave, which is the principle of the "grating accelerator".