  The Josephson plasma resonance (JPR) provides a sensitive probe of vortex
states in layered superconductors. We demonstrate that in the case of weak
damping in the liquid phase, broadening of the JPR line is caused mainly by
random Josephson coupling arising from the density fluctuations of pancake
vortices. In this case the JPR line has the universal shape, which is
determined only by parameters of the superconductors and temperature. This
mechanism gives a natural explanation for the experimentally observed
asymmetric lineshape. The tail at high frequencies arises due to mixing of the
propagating plasma modes by random Josephson coupling, while the tail at small
frequencies is caused by the localized plasma modes originating from a rare
fluctuation suppression of the Josephson coupling in large areas.
