Learning Forum

[allenduh]

Hi Lumerical support

I am Yi-Shiou Duh from Stanford university. I am running a FDTD simulation

-- with 100 micron propagation

-- on a gentle absorbed medium. imag(index) = 5 * 10^-6

-- Plane wave (periodic BC) with no structure at all

Problem:

Transmission should be T = 0.995 with 100 micron propagation length.

However, I encounter an over attenuation. Following is the Transmission - mesh order (accuracy) plot.

Coarse mesh can lead to errors in energy flow at long ranges. 

You can see from the attached figure (transmission vs. mesh order at 600nm) that the mesh plays a crucial role and could be the reason for the discrepancy. The simulation is run with a simple plane wave simulation (100 um simulation size) and swept over mesh accuracy.

[Taylor Robertson]

I wouldn't be surprised that the mesh discretization, may effect the accuracy in the case of small attenuation. And you may be correct that some dispersion means that the pulse hasn't completely propagated through the medium before the sim is terminated. The best way to converge this in FDTD would be to reduce the dimensionality to 1D. Essentially 1D, using 1 mesh cell and periodic BC in both transverse directions X,Y. Then use a mesh override for dz, and reduce the mesh step in the propagation direction dz. I suspect that you will continue to see convergence as you reduce the mesh step in the propagation direction. You may not be able to converge on the exact value, but at least this should give you an estimate on the error you would expect. It looks to me like the Transmission is still converging at mesh accuracy 8.

A better approach to simulating such effects would be to use analytic methods like STACKRT. I looked at this problem using the following code snippet and these are the results are obtained.
n = [1 + 1i*5e-6];

d = 100e-6;

lam = linspace(400e-9,800e-9,10);

f = c/lam;

RT = stackrt(n,d,f);