In this example, we'll show how to recreate the results of H.-T. Chen et al. This meta material exhibits a negative index of refraction in the THz range.
The file negative_index_chen.fsp contains an example of the structure as described in Figure 1 from Chen' paper.
Metamaterial structure here is composed of gold patterning on a GaAs substrate. Gold can be represented using a plasma material model (with plasma resonance (ω) and collision frequency (vc)), and this can be expressed as a simple conductive model in the low frequency limit when ω << νc. In this limit, the material can be approximated using the PEC (perfect electrical conductor) material.
The physical thickness of the gold is 200 nm, but this would require a very small mesh size for dz. However, since the thickness of the material is much less than the wavelength of about 130-1200 um, the metal can be represented using 2D sheets which do not require a fine mesh in the z-direction.
For the GaAs substrate, a simple constant refractive index (dielectric) model was used. It may be possible to account for a free carrier model by adding a conductivity that depends on bias voltage.
In the file provided, the mesh override region uses a coarser mesh which gives initial results in a shorter simulation time. More accurate results can be obtained by specifying a finer mesh step size. The following results are achieved by changing the mesh step size in the x and y directions in the mesh override region to 1 nm.
When the simulation is finished, run negative_index_chen_analysis.lsf to produce the results.
The transmission as seen in Figure 3 from Chen. The peak and dip just above 1.4 THz in the spectrum is a Wood's anomaly due which occurs as the number of supported grating orders changes at this frequency.
The |E| field is similar to Figure 2a. Rerunning the simulation with a smaller mesh size would produce a higher resolution image.
The vector plot of the surface current density at resonance. Similar to figure 2b of the paper.
Once you have run the script to generate the vector plot, modify the plot properties as follows: