We investigate the nonlocal optical conductivity of Fermi surface nesting materials which support charge density waves or spin density waves. The nonlocal optical conductivity contains information of correlations in electron fluids which could not be accessed by standard optical probes. Half metal emerges from doping a charge density wave and similarly spin-valley half metal emerges from doping a spin density wave. Based on the parabolic band approximation, we find the Drude peak is shifted to higher frequency and splits into two peaks in the nonlocal optical conductivity. We attribute this to the two Fermi velocities in the half-metal or spin-valley half metal states.