Yatpac - The Ultimate Open Source TLM Simulation Package

Plane wave impinging onto a lossy medium

1. Example description

In this example a plane wave impinging onto a lossy material is simulated. The plane wave excitation and the size of the simulation region are set in the same way as in the example Pane_wave_lossless.

We investigate the wave penetration into the lossy material of dielectric constant eps_r = 4.0 and conductivity 53 mS/m. The material is inserted outside the excitation region (the boundary condition is met from the plane wave at timestep 700).

2. TLM model

The different material properties for free-space and the dielectric are defined in the "C-Block" in the file I3D.PW_lossy. The description of the dielectric material in the I3D.file has been described in the example of the Plane wave propagating a lossless media. Therefore we briefly described here how to change the electric conductivity that we call sigma. The input parameter G for the I3D-file is calculated using: G = dl*sigma*Z_0 With dl is the discretization parameter (here 5e-3 m), sigma is the conductivity with unit S/m and Z_0 is the free space impedance of 377 Ohm. For our example we have an conductivity of 53 mS/m, what results in G = 0.1. Similar to the example mentioned above the material can also be implemented anisotropic.

3. Simulation Results

3.1 Electromagnetic Field Visualization

We display the simulation results similarly to the lossless case the observing that in this case the transmitted one is dumped. This can be seen on the screenshots form the visualization , Fig. 1-2-3-4.

Fig. 1: Plane wave before impinging onto the lossy dielectrics.

Fig. 2: Reflected and transmitted waves.

Fig. 3: The reflected and transmitted waves one timestep after splitting.

Fig. 4: The reflected and transmitted waves two timestep after splitting.

Fig. 5: The reflected and transmitted waves five timestep after splitting.

3.2 Computed Time-Domain Signals

Some additional remarks on the time signals are reported as we can see in Fig. 6 The yellow and the brown signals refer to the transmitted fields inside the lossy dielectric. This can be seen by the dumped amplitude of the electric field. The disturbed shape for the reflected signal is due to the stored and continuously reflected wave portions.

Fig. 6: Time distribution of the signals.