Surface plasmon polaritons in optical lattices with -symmetry and -antisymmetry

Rafi Ud Din; Amin Ur Rashid; Hazrat Ali; Xiaodong Zeng; Ghaus Ur Rehman

doi:10.1140/epjp/s13360-022-02468-2

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2024 Impact factor 2.9

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2022) 137: 243
https://doi.org/10.1140/epjp/s13360-022-02468-2

Regular Article

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

Rafi Ud Din¹, Amin Ur Rashid¹, Hazrat Ali², Xiaodong Zeng³ and Ghaus Ur Rehman⁴

¹ Department of Applied Physical and Material Sciences, University of Swat, Swat, Pakistan
² Abbottabad University of Science and Technology, Havelian, Pakistan
³ Department of Physics, Shanghai University, Shanghai, China
⁴ Department of Mathematics and Statistics, University of Swat, Swat, Pakistan

Received: 7 September 2021
Accepted: 10 February 2022
Published online: 18 February 2022

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 ( $P T$ ${\mathcal {P}}{\mathcal {T}}$ )-symmetric/ $P T$ ${\mathcal {P}}{\mathcal {T}}$ -antisymmetric modulation on its permittivity $ε$ $\varepsilon$ in two dimensions. With proper coupling of the applied fields, we present the conditions imposed on the rubidium atoms that lead to $P T$ ${\mathcal {P}}{\mathcal {T}}$ -symmetric/ $P T$ ${\mathcal {P}}{\mathcal {T}}$ -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.