Backward waves in a grounded bilayer slab containing double-negative (DNG) and double-positive (DPS) metamaterials

TL;DR

This paper derives dispersion relations for guided modes in a grounded bilayer slab with DNG and DPS metamaterials, analyzing power flow, mode behavior, and the effects of thin coatings using numerical and FDTD methods.

Contribution

It provides new analytical dispersion relations and insights into mode power behavior, including the impact of thin DPS coatings on the guided modes in DNG slabs.

Findings

Existence of a turning point where mode power changes sign.

Dispersion relations reduce to known cases for single-layer DNG slabs.

Thin DPS coatings shift the turning point on the dispersion curve.

Abstract

Simple dispersion relations for the guided modes in a grounded DNG/DPS bilayer slab are given in terms of normalized parameters. Relations corresponding to the grounded single-layer DNG slab are refound as specific cases. Numerical examples are given showing dispersion curves of the lower order modes and the respective total normalized power carried on the propagation direction. Snapshots obtained by the finite-difference time-domain method are provided showing the electromagnetic field inside the grounded DNG/DPS bilayer slabs. Since an important characteristic of the guided modes in the slab containing a DNG layer is the existence of a turning point (TP) at which the power carried by each mode of order m>0 equals zero and changes the sign, we present implicit relations at the TP for the normalized parameters of the guided modes in the grounded DNG/DPS and DNG slabs. We show that a thin DPS layer coating on the grounded DNG slab produces a shift of the TP on the dispersion curve.