Dielectric smoothing/averaging

[sp94]

Accuracy of FDFD and PWEM solutions can be improved by dielectric averaging

Resources

• https://empossible.net/wp-content/uploads/2019/08/Lecture-4f-FDFD-Extras.pdf
• Paper discussing subpixel averaging in MEEP http://ab-initio.mit.edu/~oskooi/papers/Oskooi10.pdf

[sp94]

Could signed distance functions be a fast way to implement this smoothing?

Such as in this example for blurred rectangles

[kabume]

A simple example can be used:

for m=1:Nx # grid length of x-axis
    for n=1:Ny # grid length of y-axis
        index=(n-1)*Nx+m
        # flag function: Determine whether the lattice is medium or air, if medium return 1, else return 0
        flag1 = flag((m-1)*deltax, (n-1)*deltay)
        flag2 = flag((m-1)*deltax, (n)*deltay)
        flag3 = flag((m)*deltax, (n-1)*deltay)
        flag4 = flag((m)*deltax, (n)*deltay)
        eps[index] = 1 + (flag1 + flag2 +flag3 +flag4) / 4 * (eps0[index] - 1)
    end
end