2.3    Metallic

Metallic is a lossy metal. For this medium type:

Mu = m_r [dimensionless] – relative magnetic permeability

and

Sigma = s [S/m] - electric conductivity

can be declared. Note that although the meaning of these two parameters is exactly the same as in the case of media with volumetric losses, declaring a particular medium as a metal with surface losses enforces an absolutely different approach to its modelling in the FDTD analysis. When considering lossy metals the skin depth is very small and in microwave frequency range it does not exceed several micrometres. If we wanted to model the wave evanescing exponentially in such material, it would require introducing a sub-micrometre cells, what will extremely prolong the simulation time. For that reason, in QuickWave we assume that even thin metal layer is non-transparent. Namely, QW‑Simulator will not calculate the fields inside this metal volume. Instead, it will apply special surface impedance boundary conditions along the metal surface to represent the frequency-dependent skin-effect (such approach allows for wideband modelling of skin effect). In this approach the losses are taken into account by assigning them to the tangential (to metal surface) magnetic field in the neighbouring dielectric cells.  To each of the tangential magnetic field components an RL ladder composed of a finite number (K) of cells is attached. With the number K increasing we can model accurately the skin effect in a wider band, but at the price of increasing computer time and memory. For that reason the decision regarding the K number is up to the user and it is made by declaring the bandwidth for rigorous consideration of frequency-dependent skin effect. There are three options in this manner: Narrow, Decade and Two-Decades, which correspond to the number K varying from 2 to 12, with appropriate change in wide band properties of the model. The central frequency for the band is taken as: in the case of sinusoidal excitation - frequency of the source; in the case of pulse excitation - central frequency of the band of post-processing; in the case of pulse excitation and no post-processing - 10 GHz.

Therefore this medium type should be used in the case of metals of finite, but very high conductivity. If the conductivity is low, it may cause increased computational errors or even algorithm instability. Details about the model and its implementation are discussed in references [32] [105] in User Guide 3D: Bibliography.

In case of metal objects, which dimensions with respect to wavelength cause that we deal with semi- or fully transparent objects, the lossy metal model is not adequate. In those cases it is recommended to use dielectric model (isotropic or anisotropic) to accurately model the wave penetration into this object. An example of such case is described based on Salisbury screen absorber scenario.