Vavilov-Cerenkov phenomenon in metal nanofilms

The Vavilov-Cerenkov phenomenon - light emission during the motion of a fast electron in a dense medium is observable in homogeneous media as well as in inhomogeneous media like photonic crystals. So long as a space (homogeneous or inhomogeneous) contains natural waves with phase velocities that are lower than the velocity of a flying through electron then a Cerenkov emission of light would appear. In nanofilms and nanowires made of silver, gold, copper there are so called surface plasmon polaritons, namely natural waves with a low phase velocity. These waves velocity could be by tens and hundreds times lower than the light velocity in vacuum. An electron with a velocity that is comparatively lower than a velocity of an electron that is able to emit in a uniform medium could emit Cerenkov light. Dispersion relations are calculated for the corresponding plasmons as well as the angles of emission of the plasmons of corresponding frequencies.