Calculation of phase of reflected spectra from metasurface

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1. What device are you trying to simulate? Include diagrams if available.
I want to calculate the phase of the reflected light from the metasurface. The configuration of my device is shown in Figure below. The idea is to extract the phase change induced by the metasurface when we change the height of the silicon grating from silicon mirror as shown in attached Figure below. I am refering to Figure 2A and B of the attached paper.

2019_Science_Temporal color mixing and dynamic beam shaping with silicon metasurface.pdf (1.2 MB) 2019_Science_Temporal color mixing and dynamic beam shaping with silicon metasurface_supplementary.pdf (606.2 KB)

2. What results are you trying to obtain? Be as specific as possible.

More specific I want to reproduce the Fig S2 of the supplementary material (attached below).

Somehow I can reproduce the reflection spectra as see attached image (Fig S1 of supplementary) but I can also to some extend being able to reproduce Fig S2a i.e. phase contour plot for width 90 nm. But for width 140 nm something weird happening to my plot.

Pls note: I need the phase induced by metasurface only, thus I substracted the propagation phase and for that I wrote script attached here.

3. Description of the problem or issue.

I can reproduce the phase contour plot for silicon slab width 90 nm but for width 140 nm the contour plot does not match. See attached

fig below.

4. Lumerical product and software version.
FDTD 2020

5. Please attach your simulation files, including any logs.
phase_.lsf (399 Bytes) Si grating_2D.fsp (313.3 KB)

If all other parameters gave reasonable result, but only one is suspicious, I guess it may have two reasons:

1: the paper actually used other value of the width than 140nm. This could happen when there were a lot of results, and when they inserted the image, a wrong one was chosen; or file name was labelled with wrong parameter.

2: In the special case of 140nm, the phase is more sensitive than any other values, which is possible. As you know the phase is calculated as atan(imag(Ex)/real(Ex)). At certain wavelengths it might have stronger resonance and need much longer simulation time or autoshutoffmin. However since we use one template for the simulation so it is not known if the simulation terminates properly to lead reasonable result. Or it may be due to PML or other issues that leads to not accurate result.

While attaching the override mesh with the Si_slab, I would suggest to use two override meshes: one is attaching with the slab, but only override its y mesh; the other will not move but only override the x mesh throughout the x span of simulation. I would use larger xspan for the 2nd override mesh than the simulation span, and make sure it has integer number of cells.

Since we have no information from the paper, you may spend some time to make sure the reflection and transmission are correct when you do the sweep.

As a tip, please always use larger monitor span than period to pick up correct field information.