# Farfield electric field vs Angle plots for periodic systems

#1

Hi,
Using the grating order transmission monitor, we can plot the far-field Electric field as a function of angle for periodic structures (normal incidence with periodic or bloch boundary conditions with BFAST or nomal plane wave source). eg: https://kb.lumerical.com/en/diffractive_optics_gratings_order_transmission.html. There is always an angle spread for any diffraction lobe. Even the 0th order transmission has some spread in angle space. Ideally, a periodic system shouldnt have any spread but realistic systems which are finite do have a spread. The width ( in angle space) of the lobe decreases if the size of the periodic unit cell is increased but it is independent of the mesh size used with in the periodic cell. Also the angle spread increase as the beam going away from 0degrees which may or maynot increase as a function of wavelength.

I was curious if the way FDTD works has some physical significance. Is there a way to extract just the angle of the diffraction order as a function of wavelength without showing any angle spread.

Thank you

Far field extraction with Bloch Boundary Conditions
#2

You can use the “grating order transmission” analysis group which is shown here to get the reflected and transmitted grating angles and the amount of power into each grating order direction.
However, you are injecting light at an angle with broadband sources. If you are not using the BFAST method, light is being injected at different angles for each wavelength. The BFAST method allows you to inject broadband light at a single fixed angle over all wavelengths so I would recommend using that. More information about BFAST can be found here:
https://www.lumerical.com/support/video/bfast.html

#3

Hi@konslekk

Thank you for your reply. I did use the BFAST source and the problem still persists. Consider a simple case of sub-wavelength periodic array of scatters under normal incidence. When you plot the farfield E = f(angle, wavelength), there is a finite width in angle space for every diffraction lobe (from 0th order to higher order) Ideally, periodic structures shouldn’t have any width in angle space. The diffraction lobe should be a point (representing the direction) in angle space but it in wavelength space it will have a FWHM etc.I hope I was able to clarufy my question further.

Thank you

#4

but feel free to continue discussion in this post should you have further questions.

Thanks

#5

Dear @bkhanaliloo,

Thank you so much for clearing this up. Dy default, the far-field projections assumes 10 grating periods and doesnt show the projection of an infinitely periodic strucutre. I hadnt realized this was the case.

Sorry for the confusing style of the question and I appreciate your patience and time in figuring this out.

Thank you.

#6

#7

Dear @bkhanaliloo,

Could you take alook at my structure to get the proper results?
I have tried but I coudn’t find where’s my mistake. Would you help me?
My file: cone.fsp (272.8 KB)