Josephson Plasma Excitation and Vortex Oscillation Mode in Josephson Vortes State

The Josephson plasma resonance has been investigated in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ single crystals in parallel magnetic fields to the $ab$-plane. We found two resonance modes; one appears at higher frequency in high fields above the plasma frequency ${\omega }_p$ at zero field and absolute zero, and the other lies below ${\omega }_p$ and is observed only in magnetic fields without considerable field dependence. Two resonance lines were also found in numerical simulations in a single junction model with randomness of the critical current. The higher frequency mode is attributed to the Josephson plasma mode modified by the periodic structure of Josephson vortices, while the lower frequency mode is interpreted as oscillations of Josephson vortices.