Main pageTutorial:FDTD & GPU Yee's algorithm Sources Materials Boundary conditions Near-to far field Application notes | ## Application note: Transmission diffraction gratingAs an example of extensive use of Near-to-Far Field (NFFF) transformation we dicuss modeling of a diffractive optical element performance. Scattering from diffraction gratings and similar periodic structures can be evaluated analytically to some extent (e.g. for ideal gratings). However, for analysis of different defects, like shape of a single groove, roughness or faults in periodicity, we need to use some numerical technique. FDTD is one of the options, however as the grating is periodic it is very suitable also for RCWA (the best option) or FEM. ## Transmission through single aperture
If we consider where
As a result we obtain a far field radiation pattern as shown below on the right image (analytical result is in the left image). Both images are in logarithmic scale for intensity false color plot. Only a single lobe is calculated (i.e. a quarter of the whole pattern that is four times repeated in 0-360 degrees due to the fact that aperture is square). We can clearly see the diffraction pattern and we can compare it with analytical result. Comparison can be even better done on single profile across the direction of diffraction pattern as shown below. Note the effect of limited angular resolution of the calculation which can be one of reasons of small differences (besides limited NFFF integration area and other numerical errors). ## Transmission through a grating
The whole pattern as simulated for grating spacing to wavelength ratio of approx 10:1 and finite size of 13x13 holes is shown below, both in normal and logarithmic scale (note that in contrast to aperture simulation results now the θ axis is the horizontal one). Analytically this can be written for diffraction angles θ (in the y direction)
as_{2}where a are grating hole spacing in x,y direction and _{2}N and _{1}N
are number of holes in these directions; the rest of symbols is same as in aperture equation._{2}Even if it would be in principle possible to calculate the same images also using FDTD, the number of far field points with the same resolution would be around million which is already significantly slow in present version of GSvit. Therefore we had compared result only on a single profile in x direction again, similarily to how the aperture intensity graphs were obtained. Results are show below (x axis is in degrees) To setup calculation similar to those shown in this example you can try this XSvit example and related files .(c) Petr Klapetek, 2013 |