Learning Forum

[takuya.sobue]

I can't understand the calculations in below script which is a part of "calc_scanspot_image.lsf".

I understand (ESS, EPS) is farfield E components of (Eφ, Eθ) in the simulation on S polarized plane wave.
However, I don't understand the meaning of next step. Why inverse rotation matrix of input angle φi is multiplied to  (ESS, EPS) and (ESP, EPP) ? Does it mean polarization compensation caused by angle φi? I don't understand physical meaning of (ExS_FF, EyS_FF) and (ExP_FF, EyP_FF) . are they global coordinates  value of E=(Ex, Ey, Ez)?
Also, I don't understand next step. I don't understand physical meaning of (Exx_FF, Exy_FF, Eyx_FF, Eyy_FF) .
Please let me know.

Best regards

[anna.wirth-singh]

Hi Takuya,

Thanks for the question – I can clarify the meaning of the subscripts. I think there may be some confusion there.

The fields ESS, EPS, ESP, and EPP are part of an S-matrix. You can think of the S matrix as a black box that represents the inputs and outputs from a simulation. This article is for a different application, but it explains how an S matrix is defined and used: Metamaterial S parameter extraction – Ansys Optics

In this case, the S matrix records the far-field information for various input and output polarizations. The subscripts (S and P) refer to the polarization state of the input (first letter of the subscript) and output (second letter). So, for example, ESP corresponds to the far-field data for S polarization input and P polarization output. The data itself is in the far-field units ux and uy (see this page for more on unit conventions): Understanding direction unit vector coordinates in far field projections – Ansys Optics

This matrix was created in the example’s other script, build_S_matrix_sram.lsf:

# arguments are ux_in, uy_in, polarization_in (S,P), ux_out, uy_out, polarization_out (S,P)

S = matrix(length(ux0),length(uy0),2,length(ux0),length(uy0),2);

 

I believe the multiplication operations that you are asking about are to convert the S matrix results from S and P polarization definition to X and Y polarization.

So, for example ExS_FF , ExP_FF, EyS_FF, and EyP_FF is the first step where the input light (corresponding to the first letter of the subscript) has been converted from S,P polarization to X,Y polarization units. Secondly, Exx_FF, Exy_FF, Eyx_FF, and Eyy _FF do the final step of converting the output light (second letter) to X and Y polarization.

Does this help to clarify the issue?

 

Best,

Anna