## Photonics

Topics related to Lumerical and more

#### How to get farfield projection for periodic structure?

• fdtdisgreat
Subscriber

Hi,

According to this page, using farfield3D on a single unit cell of a periodic structure will result in significant diffraction artifacts. It states that, if the structure is infinitely periodic, then 'Grating Projection' functions should be used. However, it is not clear to me which grating functions one should use to get a 2D field intensity profile for the far field. 'grating' only returns fraction of power in each beam, so cannot be used to get a 2D color plot of the field profile. Could you let me know which grating functions are equivalent to the 'farfield3D' function, which can be used to plot a 2D color map of the field intensity together with farfieldux and farfielduy? Or is the only option to include several periods within the FDTD region rather than just 1 and use the farfield3D function then? Thank you in advance.

• Greg Baethge
Ansys Employee

Thanks for your post. You're correct, far field projections is not meant for periodic structures, as it calculates the far field from a single period, so it is like having an aperture in front of the structure and it will show some diffraction. To avoid that, farfield2d and farfield3d have the option to emulate the periodicity: you can specify a number of periods and a type of illumination (top hat or Gaussian), as explained in the link you referred to.
Because only the dataset/monitor and the frequency vector is required, you have to specify all the parameters explicitly. It would be something like:
E2 = farfield3d("mname", 1, 150, 150, 1, 50,50);
ux = farfieldux("mname", 1, 150, 150);
uy = farfielduy("mname", 1, 150, 150);
image(ux, uy, E2, "","","","polar");
This would calculate the far field using 50 periods in x and in y, using Gaussian illumination, for the first frequency point.
As you noted, grating projection will give the grating orders' strength. Each grating order is more like a Dirac, since the grating projection assumes an infinite number of periods, so there's no width. Actually, if you increase the number of periods used in farfield2d and farfield3d, you will see the peaks getting narrower.

• fdtdisgreat
Subscriber
This answers my question fully, thank you so much for this reply!
• Greg Baethge
Ansys Employee
You're very welcome!
• haoyang
Subscriber
Hi Greg
In my understanding, the farfield3d command assumes that the projection radius is 1 meter. If I want to see the far-field projection result at 1mm, the command farfieldexact3d (https://support.lumerical.com/hc/en-us/articles/360034930733-farfieldexact3d-Script-command) might be better. However, I am wondering whether the farfieldexact3d could support periodic illumination. If not, do you have recommended way to simulate the far projection at 1 mm for a periodic structure?

Best Hao
• Greg Baethge
Ansys Employee

You're correct, farfieldexact3d won't be able to deal with the periodicity. To get the projection at 1mm, I think you could rescale the result at 1m as shown in this example. The example is not using a periodic structure, but the idea is the same. The result should be correct as long as the wavelength is still much smaller than the distance.
• haoyang
Subscriber
Hi Greg