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This section mainly deals with simulating the the artificial "atoms" such as wire pairs and split rings of metal that can be used to create unusual effective bulk properties, such as a negative refractive index, and we will discuss the details of effective parameter extraction. For an example of creating bulk electric and magnetic media, please see the bulk metamaterials example.





See also

S Parameter extraction

Effective bulk properties

Effective parameters - Smith

Low frequency simulations


Simulation setup tips

To ensure your metamaterial simulations are setup in the most efficient manner, consider applying some of the following techniques to your simulations.  These tips are most important for devices that operate at low frequencies (relative to optical frequencies).


Perfect metal approximation

For 3D objects at low frequencies, where metals behave in an 'ideal' fashion (100% reflection, 0% absorption), use the Perfect Electrical Conductor (PEC) material model, rather than Sampled 3D data, Conductive 3D or other material models. The PEC model is the most numerically efficient option since it does not require as fine of a simulation mesh.

If your device operates at a frequency where the metal is not ideal (i.e. in visible range), then the PEC model should not be used.  


Thin layers

Some metamaterials have extremely thin layers compared to wavelength. It is possible to represent a thin layer using a 2D rectangle or 2D polygon object and specifying the material using a conductive material model.


If using a 3D object to represent the thin layer, for accurate simulation results it's important to to have at least a couple of mesh cells to resolve the thickness of the layer.  When the layer is very thin, this requires an extremely small mesh, which significantly increases the total memory and time requirements of the simulation.  In such cases, it is possible to use a much thicker layer in your simulations. For example, if the layer is actually 1/1000 of a wavelength thick, setup your simulation with a layer thickness of 1/10 or 1/50.  This allows you to use a much larger mesh size, without a significant loss of accuracy.


Check the default settings for low frequency simulations

The default settings in FDTD are setup for optical frequencies. If you are working at much lower frequencies, some defaults will not be correct.  In particular, check the following settings:

Units - In the Settings menu. You may want to change the units settings. For example, from THz to GHz.  

Simulation time - The default value of 1000fs will not be long enough for low frequency simulations. The time must be sufficient for the fields to decay back to zero after the source pulse.

Mesh size - In most cases, the mesh size will default to reasonable values, even for very low frequency simulations. However, in some cases (such as copying a mesh override region from a different simulation file), it is possible to end up with a mesh size that is unreasonably large or small.  


Use periodic (or Bloch) boundary conditions

Most metamaterials are periodic, which means you only need to simulate ONE unit cell.  Use periodic (if the source is at normal incidence) or Bloch (if the source is at an angle) boundary conditions.  There is no reason to simulate multiple periods of the device when using periodic or bloch boundary conditions.  If you re-run the simulation with two unit cells, you will end up with exactly the same answer, but it will take at least twice as long to run!

Quantities of interest

It is possible to directly measure many quantities of interest from an FDTD simulation of a metamaterial device, including

field enhancement throughout the structure

transmission and reflection spectrum

scattering and absorption cross sections

circular dichroism


In addition, the effective material properties are often of interest.  Parameter extraction is possible, but requires additional post-processing of the simulation results.  See the following page for more information on calculating:

S parameters

effective material parameters: refractive index, impedance, permittivity and permeability

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