## Photonics

Topics related to Lumerical and more

#### Meaning of Paramaters in RCWA

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• xiaofei.xiao15
Subscriber

Hi,

RCWA has been introduced in Lumerical. I am trying to use it. however, I have some questions.

1. in the metalens example, we can get ax, ay, bx, by. what is their meaning? what is the difference between mode amplitudes and amplitude of E and H?
2. Do m and n in results refer to grating order? how to determine the number of order? it is numerically calculated or set?
3. In the FDTD simulation, the phase is extracted by calculating the amplitude of E several wavelength away (make sure it is uniform), however, in RCWA, I am not sure how far for ekx_f... can we use the same method in FDTD to get this phase?
4. Why they are called ax, bx, ekx_f, ekx_b, asx,bsx? what are they short for?
5. Are kx, ky wave vectors for each "mode"
6. thanks
• xiaofei.xiao15
Subscriber

in rcwa - export_phase_filed.lsf,

1. what is the meaning of the following sentence? why do we have *index_sub?  E_rcwa(:,:,:,:,i,:) =  pinch(pinch(Fields.E,5),5)*index_sub; #remove singletons in theta and phi
2. how to get this distance? dist = 0.151606*um; #Distance between source and first layer in FDTD model
3. why we set such wired value?  "z_min":-0.226606*um
• Guilin Sun
Ansys Employee

There are two script files for this example: https://optics.ansys.com/hc/en-us/articles/360042097313-Metalens

Next time please specify which script file you are referring.

A1: I am not sure where we mentioned the mode amplitude. I think it is the E amplitude. E anfd H are the mode fields.

A2: m and n are the grating diffraction orders. They are result, not input parameters

Q3 " in RCWA, I am not sure how far for ekx_f... can we use the same method in FDTD to get this phase?"

and since this is analytical solution, the result is on the surface, similar to Fresnel coefficients.

Amplitudes of E and H fields will be returned as `ekx_f`, `eky_f`, `ekz_f`, `ekx_b`, `eky_b`, and `ekz_b`

they are field amplitudes in k space for E and H.

Mode amplitudes will be returned as `asx`, `asy`, `bsx`, `bsy``apx`, `apy`, `bpx`, and `bpy`

Here s and p are the polarization. a and b means E and H (I do not know why), and xy components only.

I do not know where "kx, ky" is from in which file?

index_sub = getfdtdindex("SiO2 (Glass) - Palik",excitation.f,min(excitation.f),max(excitation.f)); is to get the refractive index of the material (SiO2 in this case).

Please note that Fields.E is a 6 dimension matrix, x,y,z,f,radius and Ex/Ey/Ez in the 6th dimension.

`dist = 0.151606*um; `#Distance between source and first layer in FDTD model

should be from FDTD simulation file. But I believe the FDTD simulation file has been modified as this distance is no loner this value.

Earnestly, I really do not know why it uses those strange values. If I did this example, I would use some values to match the mesh, or some integer numbers.

Subscriber

Hello Guilin Sun,

the question is regarding the sript file " rcwa-export_phase_field"could please explain how did you calculate the dist = 0.151606*um; you mentioned it is the distance between the source and the first layer in fdtd, i know the position of the first layer in this srcipt file  which comes out to be 0 but how do we determine the position of the excitaion ?? In order to calculate this dist we need to know two positions 1. positon of first layer which is zero 2. positon of the excitation (you have used plane wave source)?? I can not find the positon of source??

• Guilin Sun
Ansys Employee

I would suggest to have a new post next time since the forum will be clear for one question one answer.

The example distance is arbitrary I believe, and it is not a good practice to use so many significant digits for the distance. I did not find any particular reason to use this distance. the propagation phase is about 120 deg from source to the front surface.

You can set the excitation at any distance, but "better" to be closer to the front surface. You can use 0.1um for example.  You can compare the results using different distances.