Surface plasmon polaritons in optical lattices with ${\mathcal {P}}{\mathcal {T}}$-symmetry and ${\mathcal {P}}{\mathcal {T}}$-antisymmetry

Abstract

We investigate the properties of surface plasmon polaritons (SPPs) at a geometrically flat interface between a metal and an optical lattice of driven cold rubidium atoms. The optical lattice is considered in the Gaussian density distribution, with a parity-time (${\mathcal {P}}{\mathcal {T}}$)-symmetric/ ${\mathcal {P}}{\mathcal {T}}$-antisymmetric modulation on its permittivity $\varepsilon$ in two dimensions. With proper coupling of the applied fields, we present the conditions imposed on the rubidium atoms that lead to ${\mathcal {P}}{\mathcal {T}}$-symmetric/ ${\mathcal {P}}{\mathcal {T}}$-antisymmetric dispersion of the SPPs. We find that at certain frequencies, the backscattering of SPPs into the far field is not only overcome, but the plasmonic modes are also greatly amplified, resulting in significantly improved lifetime and propagation distance for the modes. Moreover, the SPPs can be directionally excited by only varying the intensity of the driving fields. These fascinating results may be used in low-loss plasmonic routers and lasers.