1d FDTD unstable with metal thin film

[zh168]

Hello,

I am writing a 1D FDTD to simulate a wave propagate into aluminium thin film. Unfortunately, whenever the wave hit the metal surface, the E-field progressively increases and becomes unstable.

Would anyone know what's the program and any solution for that?

Here below are the parameters that I am using:
wavelength: 1um
n_Al: 1.35 (measured)
k_Al: 9.58 (measured)
grid size: wavelength/50
time_step: grid size / (2*c)

Thanks!!!

 

[rrumpf]

While I can't be sure what your problem is, the phas velocity can exceed c under certain circumstances. This requires you to revised the stability condition to calculate a stable time step.

See Eq. (4.76) and surrounding discussion on page 103 of my dissertation.

http://etd.fcla.edu/CF/CFE0001159/Rumpf_Raymond_C_200608_PhD.pdf

Hope this helps!
Tip

 

[iyami]

Actually I think your problem is simply that your permittivity is negative
(epsilon = n^2 - k^2) at the given frequency.

FDTD is only stable for relative permittivity >= 1.0.

I think the best way to deal with your problem is to use one of the standard
models (Lorentz, Drude, Debye) for dispersive materials (a single pole is enough)
and fit the parameters and then implement it using recursive convolution or ADE.