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