  # Farfield Angular Projection [FDE]

Dear Community,

I have a question regarding farfield angular projection in MODE Solutions.

I’m simulation a simple waveguide (SiN 1um x 1um, buried in SiO2), and would like to extract the angular projection from it to air. I use FDE solver, chose the mode of interest (fundamental TE) and plot the farfield. It looks good in the plot, but when I try to export the data in .mat format, I cannot reproduce it afterwards: even when I just plot farfield1_angular_E2, there are two peaks instead of one.

My general goal is to extract the projection to define angles for 1/e^2 power or at FWHM.

Could you please suggest on how to do it properly?

Kind regards

Hello @jab
I have the same question. Did you figure out how to do it?

Hello @prova and @jab,

Sorry for missing this, @jab. The easiest way to do this would probably be to use Lumerical’s built-in script commands for farfield integration, like farfield3dintegrate (see the “Far field projections” tab on this page: Lumerical script commands).

For example, here is a script used to calculate the power within a cone with a given angle in the farfield:

farfield = getresult("FDE::data::mode1", "farfield");
E2 = pinch(farfield.E2);
ux = farfield.ux;
uy = farfield.uy;
halfangle = 0:90;
theta0 = 0;
phi0 = 0;
power_integral = farfield3dintegrate(E2, ux, uy, halfangle, theta0, phi0); # integrate over cones
total = farfield3dintegrate(E2, ux, uy); # integrate over entire hemisphere
results = power_integral/total; # fraction of far field power
plot(halfangle, results);


Here are the results of this script for the fundamental TE mode of your waveguide at a wavelength of 1550 nm @jab: I hope this helps. Let me know if you have any questions.

Hi @kjohnson,

Thanks for your response. The mode I am simulating is elliptical. In this case, how can I get the vertical and horizontal farfield data (E intensity) as a function of angle and get their corresponding FWHM or Half angle? This page demonstrates how to get data along different line traces of the far field projection (parameterized by phi):

The example from this page uses FDTD, but the techniques used will work for data from MODE as well. The data along the horizontal (uy = 0) line corresponds to phi = 0, and the vertical (ux = 0) line corresponds to phi = 90 degrees. You might find this page, which discusses how the ux/uy variables correspond to spherical coordinates, useful: