A DNG material. Metamaterials are materials made up of periodic structures whose macroscopic behavior can be controlled through the material's design. A double negative (DNG) material is one whose permittivity and permeability both exhibit dispersion, so that at particular frequencies both of these, and thus the index of refraction, can be negative.

(a) Model a slab of Drude material in 2D with dispersive permittivity only per wavelength and make the slab 100 grid cells thick. Launch a sinusoidal wave at the slab with a wavelength of 1 cm ( f = 30 GHz) and observe the wave phase behavior in the slab.

(b) Derive the ADE method for a DNG material. Start with the µ version of equation (10.77) and write an auxiliary equation for the magnetization current M related to H. Then, include M in the update equation for H.

(c) Now, repeat (a) but make the slab a DNG material in 2D whose permittivity and permeability µ both exhibit Drude behavior, both with the same relaxation time and resonant frequency as in part (a). Comment on the results.