Superconductivity along the c axis of cuprate superconductor is mainta
ined by the Josephson coupling between the CuO2 layers. Combining the
Josephson current with the electromagnetic field, we have the Josephso
n plasma whose frequency appears in the range of 100 GHz and 1 Tera Hz
in cuprate superconductors. In the presence of the vortices, the effe
ctive Josephson coupling responsible for the plasma is weakened and th
e plasma frequency is reduced. This effect may explain the temperature
dependence of the plasma frequency observed in the mixed state of Bi2
Sr2CaCu2O8+delta. The interaction between the Josephson plasma and the
vortices is strong enough to excite the plasma by the vortex flow. Th
e excited plasma will decay by emitting the electromagnetic wave, sinc
e the plasma frequency is much smaller than the superconducting energy
gap and the plasma has no other decay process.