Lossy medium

We need a lossy medium to simulate accurately a thing absorbing Fe2O3 mask layer. It is likely that for b = σΔt /2ε → 1 we get at the left layer border Ex = 0 corresponding to perfect conductor condition.

delay it N b

In a conducting medium there is an induced current density in response to the E-field of the wave. The current density J = σE is linearly proportional to the electric field (Ohm's law). Maxwell equations are
    ε ∂t E = rot H - σE,
    ∂t H = - rot E
.
1D equations become
(Ex )zt+1 - (Ex )zt   =  –   (Hy )z+½t+½ - (Hy )z-½t+½  – σ (Ex )zt+1 + (Ex )zt
———————— ————————————   –––  ————————
Δt εz Δz εz 2
(Hy )z+½t+½ - (Hy )z+½t-½   =     (Ex )z+1t - (Ex )zt
———————————— – ————————
Δt Δz
or
    (Ex )zt+1 = - (a/εz (1 + b)) [(Hy )z+½t+½ - (Hy )z-½t+½] + (Ex )zt (1 - b)/(1 + b),
    (Hy )z+½t+½ = - a [(Ex )z+1t - (Ey )zt] + (Hy )z+½t+½
,
where a = Δt /Δz,   b = σΔt /2ε.


Electromagnetic wave simulation
updated 30 Mar 2014