  Josephson plasma resonance has been introduced recently as a powerful tool to
probe interlayer Josephson coupling in different regions of the vortex phase
diagram in layered superconductors. In the liquid phase, the high temperature
expansion with respect to the Josephson coupling connects the Josephson plasma
frequency with the phase correlation function. This function, in turn, is
directly related to the pair distribution function of the liquid. We develop a
recipe to extract the phase and density correlation functions from the
dependencies of the plasma resonance frequency $\omega_p({\bf B})$ and the $c$
axis conductivity $\sigma_c({\bf B}) $ on the {\it ab}-component of the
magnetic field at fixed {\it c} -component. Using Langevin dynamic simulations
of two-dimensional vortex arrays we calculate density and phase correlation
functions at different temperatures. Calculated phase correlations describe
very well the experimental angular dependence of the plasma resonance field. We
also 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 a universal shape, which is determined only by parameters of the
superconductors and temperature.
