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We are trying to recreate the results in the Berini paper [1], so it is important to use the same material properties.  We will create a new silver material, rather than using the standard silver definitions included with MODE. the permittivity of Ag given in the reference paper is -19+0.53j.

 

The screenshot below shows the plasmon waveguide and the mode solver region.

 

Notice the shaded green and blue regions. The blue shaded section is a result of the fact that the x min boundary condition of the simulation region has been set to symmetric. In other words, we have put a magnetic wall (perfect magnetic conductor) at x = 0. Similarly, the green shaded region indicates that the y min boundary condition is anti-symmetric. This indicates that we have put an electric wall (perfect electric conductor) at y = 0. See Symmetric and anti-symmetric BCs for more information about choosing symmetric and anti-symmetric boundary conditions.

 

Table 1 of the reference shows that the fields from the ssb0 posses this symmetry. The boundary conditions will need to be changed if you are interested in finding modes which have fields with different symmetry. You can find all of the modes that the waveguide supports if you set all of the boundary conditions to metal. Note that the time to find modes and memory required to find modes will increase if all the boundary conditions are metal. This is because the mode solver can use shortcuts to find the fields in the shaded region if your simulation posseses symmetry/anti-symmetry about one axis.

 

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The orange lines in the screenshot above show the mesh used in the mode calculation. Notice that the mesh is finer at the edges of the structure. This is because we expect the fields to be concentrated near the edges of the waveguide. Increasing the mesh here, will increase the rate of convergence of the effective index, loss and field profiles as you reduce the size of the mesh.

 

Finally, notice that we use metal boundary conditions instead of PML boundary conditions. The reasons for this are described in the Starting with metal boundary conditions page.

 

Find and plot mode SSb0

 

To find the SSb0 mode, we overrode the default "search near n" settings in the analysis window. This is because plasmon modes often exhibit a higher effective index than would be predicted by the maximum effective index estimate. In this case, we set the mode solver to search near an effective index of 2.5, which is slightly above the guess for the maximum effective index. We knew the effective index from the reference. If you set this number to 5 then you will find the same modes, but it will take the mode solver a bit longer to find the modes.

 

The following figures show the field components of the SSb0 mode. The phase of the mode automatically determined from MODE differs from the Berini figures by 180 degrees.  This phase difference can be correct in the plasmon_plot.lsf script.

 

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It is important to notice that most of the field energy is confined to the corners of the waveguide.  The following figures show the electric field intensity over the entire waveguide area (left figure), then zoomed in near the waveguide corner (right figure).

 

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Effective index as a function of waveguide thickness

 

The plots below show the results of a sweep calculating the ssb0 mode effective index as a function of waveguide thickness, from 50nm-200nm. The effective index increased from about 2.18 to 2.63.  These results are in very good agreement with Figure 2A and 2B from the reference paper [1].  

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