Negative group velocity of surface plasmons on thin metallic films

By tailoring the dispersion curve of surface plasmons (SPs) of a thin metallic film surrounded by dielectric half-spaces, it is shown that the group velocity of the symmetric mode is always positive, while the group velocity of the anti-symmetric mode can be negative. Consequently, the forward and backward propagation of SPs, in which the energy flow is respectively parallel or antiparallel to the wave vector, can be realized. The physical origin of the intriguing backward SPs is given. Furthermore, schemes for the negative refraction and imaging of SPs are proposed by incorporating two plasmon modes with group velocities of opposite signs