2.14 Remarks

There is one general remark concerning lossy dielectrics that should be made at this point. When solving Maxwell equations within lossy dielectrics, we multiply certain terms by a loss scaling factor sf₁:

sf₁ = 1-0.5*σ*Δt / ε

and we divide certain terms by a loss scaling factor sf₂:

sf₂ = 1+0.5*σ*Δt / ε

The terms sf₁ and sf₂ are responsible for attenuation of the fields. Thus for losses to be effectively considered by the FDTD implementation with standard 4 byte floating point arithmetics, losses are taken into account by the FDTD model only if the following condition is obeyed:

sf₃ = 0.5*σ*Δt / ε > 1*10^-7

Materials where sf₃ < 1*10^-7 are treated as lossless ones.

In the above relation, σ is conductivity in [S/m], ε is real permittivity in [F/m] and Δt is FDTD time step (which can be checked in Simulation Info window).

The users interested in modelling very small losses have the following options:

Option 1 – recommended

Scale the problem by increasing σ so that relation (3) is obeyed. Note that small losses practically do not change the EM field patterns and dissipated power patterns scale linearly with medium conductivity. Thus if with σ₂=100σ₁ one obtains dissipated power density P₂, then with σ₁ dissipated power density at the same point may be safely assumed as P₁ = 0.01 P₂.

Option 2

Try to apply coarser discretisation in space, causing larger value of FDTD time step Δt.

The dual conditions apply to magnetic losses.