Metamaterial span for 2D objects


#1

Continuing the discussion from All dielectric photonic crystals: plot of near field in reflection E and H…:

Regarding the question of how to set the metamaterial span of a graphene metamaterial which is specified using the 2D conductivity model, since the 2D graphene sheet has infinitesimal thickness, I would set the metamaterial span setting of the S-parameter analysis group to 0. If the graphene is on top of a substrate with a certain thickness, then I would use the thickness of the substrate.


#2

Thank you for your reply.

If the graphene is on top of a substrate with a semi-infinite thickness, then how much the metamaterial span setting of the S-parameter analysis group I should set?

Addition, if I stimulated a metamaterial with double graphene layers which are specified using the 2D conductivity model, and the gap size between the graphene double layers is defined as d. How much the metamaterial span setting of the S-parameter analysis group I should set?


#3

If the substrate is semi-infinite, then the metamaterial span can be set to 0 since the substrate is not considered to be part of the metamaterial. The metamaterial span setting is used to calculate the phase compensation for the phase accumulated in the background material between the source and monitors which is discussed on the parameter extraction page here:
https://kb.lumerical.com/en/index.html?metamaterials_s_parameters.html

The phase accumulation distances are illustrated here:

For example, the distance travelled in the background medium between the source and transmission monitor is the distance between the source and monitor minus the span of the metamaterial. Since the span of the metamaterial is very small compared to the wavelength of light even when using multiple layers of graphene, you can use a metamaterial span setting of 0.

For multiple layers of graphene, the “conductivity scaling” factor of the surface conductivity graphene material in the material database can be set to match the number of layers. This is discussed in the paragraph below figure 1 on this page:
https://kb.lumerical.com/en/index.html?other_application_graphene_simulation_tips.html