Once you have calculated the optical modes using the FDE solver, there is no straightforward way to overlap a vector plot of your electric field on top of the mode profile in MODE Solutions. However, you can do this using some other tool such as Matlab. To do this, you will have to first condition the Efield data and send it to Matlab. Then in Matlab you can use the “hold on” command to plot a contour plot and a vector plot together. Take a look at this KB page to see how you can condition your data to be exported to Matlab (MATLAB - Lumerical integrations). The example also shows what command you need to use in Matlab to create a vector plot.
In MODE Solutions, your Efield data will be on a 2D plane so you will need to modify the script on this page a little. I have created an example script to show how you can do this using Matlab for the pin MZI example in KB (pin MZI). To check this, download the MODE project file from the example, and run the script file [[save_Efield_data.lsf]]. Then in Matlab use the following lines of command to create the desired plot:
contourf(xmesh*1e6,zmesh*1e6,sqrt(real(Ex2).^2+real(Ez2).^2),20); % contour plot
quiver(xmesh*1e6,zmesh*1e6,real(Ex2),real(Ez2)); % vector plot
The resulting plot will look as follows. Note that I have disabled the lines in the contour plot and have used the “jet” colormap.