# Polarisation rotation due to Metasurface-more questions

**2**

This is a continuation of my previous discussion.

https://forum.ansys.com/discussion/comment/143024#Comment_143024

(1) Polarisation state mean, as we know in FDTD plane wave source , we need to define the amplitude and phase difference for two orthogonal plane wave source for elliptical light. So i am looking for this that how to get amplitude and phase difference for each mode (at +45, -45 and 0 deg diffraction order) from polarisation ellipse analysis group?

(2) Yes i want to use polarisation state of all the modes so that i can verify the reciprocity, right? and i should get the linear light back. so that means i need six plane wave , 2 plane wave for each mode. can i use all six plane wave in the simulation?

Do you mean two plane source , with 0 deg and 90 pol input, a and b amplitude input, and phase difference which we can calculate from polarisation ellipse?

## Comments

1,692Ansys EmployeeThank you for creating this new post. This is a good practice as the forum is intended to have one-question-one-answer policy, and it is easier for later reference.

A1: in the analysis group, it has ratio r=b/a and phase difference, thus, you will have 1+(b/a)*exp(i*phase) information.

A2: When there is higher diffraction order, I am not sure how does the reciprocity can work: for a single-pair of plane wave, it is easy to have relative phase. When more then two are involved, it might be challenge. for example, you now have 3 pair of elliptical sources, and each pair works perfectly. However, what is the phase difference between them? This may need more thorough anaysis.

are you sure the +1 order can create the diffraction to the previous +1,0 and -1 order? similarly for the -1 order.

a+b*exp(i*phase) is a general description of a polarization state.

14MemberI think from polarisation ellipse analysis group, one can get the phase difference and ratio information for each mode. SO in my case i have 3 modes , so i know each mode's corresponding pol state (i.e. phase difference and ratio and all). here n is mode order.

I am not sure using 6 plane wave source is good or not? 2 plane corresponds to each mode.

14MemberCan we use one mode at a time? i mean 2 plane wave source at a time for specific mode and then second and third? in this way how can we add up the results?

1,692Ansys EmployeeYou can definitely try. But if they create other higher orders then it may not be reciprocal. There is still the same issue: how to you combine the results without knowing their relative phase differences? in each pair you have the phase difference. but you do not have the relative phase between pairs.

14MemberYes, True. In that case, what should I do then? How can I take care of this problem?

1,692Ansys EmployeeAs I mentioned in my first reply, it is more theoretical issue other than simulation. You may try to output the original phases of all the elliptical polarization states, eg, you have a*exp(i*phasea)+ib*exp(i*phaseb) ~1+i(b/a)*exp(i*phase_diff) for all three pairs. This will need you to modify the script.

14MemberHI ,

Thanks.

So from polarisation ellipse we can calculate the phase at each mode, so now if we minus the phase at two modes will it be phase difference between two modes?

1,692Ansys EmployeeIt depends what phase you are referring. As mentioned previously, If you can get a*exp(i*phasea)+ib*exp(i*phaseb) for each mode then you may probably get the phase difference for different modes. However if you only get 1+i(b/a)*exp(i*phase_diff) which is the direct output from the analysis group then it would be a problem. This is why I suggest that you get the original data from the analysis group and then process them accordingly.

14MemberHI, thanks.

I am referering the phase i am getting from here. this is from pol ellipse analysis group.

What do you mean by "you get the original data from the analysis group and then process them accordingly"?

1,692Ansys EmployeeThis phase difference is between the two polarized light that compose the elliptical. However you have 3 pairs, how do you define their difference? eg,

1: exp(i*phase1)*(1+(b1/a1)exp(i*phase_diff1))

2: exp(i*phase2)*(1+(b2/a2)exp(i*phase_diff2))

3: exp(i*phase3)*(1+(b3/a3)exp(i*phase_diff3))

Wouldn't you need those phase1,phase2 and phase3?

Please read the script and see how to extract them.

I believe this is a more theoretical question, other than simulation.

14MemberHi,

Yes i am able to extract the phase of each mode and polarisation of all 3 pairs using polarisation ellipse. So now i have six plane wave , 2 plane wave for each mode and phase difference i got from polarization ellipse. That part is all clear.

But the problem is phase difference between the modes.

I am aware that it is necessary to know the phase between the modes now. For that reason, I have been asking your thoughts. Any way in lumericals for this?

1,692Ansys EmployeeI missed one bracket, it should be like this

1: exp(i*phase1)*(1+(b1/a1)exp(i*phase_diff1))

2: exp(i*phase2)*(1+(b2/a2)exp(i*phase_diff2))

3: exp(i*phase3)*(1+(b3/a3)exp(i*phase_diff3))

So you will need to get phase1, phase2 and phase3 at the same time, and set the sources accordingly. eg,

mode 1 : sources with amplitudes a1 and b1, phases are phase 1 and phase 1+phase_diff1;

mode 2 : sources with amplitudes a2 and b2, phases are phase 2and phase 2+phase_diff2;

mode 3 : sources with amplitudes a3 and b3, phases are phase 3 and phase 3+phase_diff3;

This will completely recover all the original decomposed elliptical modes.

####################### side notes.

However, I am not sure if this will be reciprocal: for example, the a1 and b1 will not only create the beam diffracted into the original incident beam in the first simulation (with reduced transmission), they will also creates other diffraction orders. It is up to you to do the analysis.

I just give you some suggestions:

suppose in the first simulation, the incident source has amplitude 1v/m. It creates mode1 (a1,b1), mode2 (a2,b2) and mode3 (a3,b3) with their phases, and their transmission <1, eg {ai,bi}<1; or T1+T2+T3<1, Ti is the transmission of each mode. In the reciprocity, you want to get a beam of 1v/m with the three decoupled modes as incidence.

then in the second simulations, you use {ai,bi} as inputs. for example {a1,b1}, it has 0th order, and higher orders. One of the higher order goes to the original beam in the first simulation. However its transmission is smaller than 1, for example it is T4, then sqrt(T4)*{a1,b1} is not that part in the original beam that creates this {a1,b1}. Maybe this is difficult to describe. You may draw a picture, and see how do you recover the original incident beam of amplitude 1v/m.

As long as you have the phases and amplitudes, the simulation issue is resolved. As for how to construct the simulations to the reciprocity, it is totally a theoretical matter, and is out of the forum scope. If you do not agree, you can simply ignore the above side notes.

14MemberHello, thanks for the nice explanation.

I was wondering, as you said in one of your previous responses, that I need to modify the script. Could you please let me know where exactly I should start modifying the script from.

1,692Ansys EmployeeYou only need to add one output of the amplitude and the phase of the polarization. Since you know the ratio and phase difference, you can get the amplitude and phase of the other polarization. Please read through the script file and find what is it.

14MemberHi,

Yes i know the polarisation state of each mode. But the problem is how exactly add the phase difference between the modes. Morover its different for all the pairs. So even if i keep phase difference according to mode 1 and 2 , it will not be correct for mode 3.

Meaning of this? : You only need to add one output of the amplitude and the phase of the polarization.

1,692Ansys Employeewhat I mean is, please output the original data of the two linearly polarized components that constitute the elliptical polarization, for each mode. then for each mode, you have

a1*exp(j*phase_a1)+b1*exp(j*phase_b1)

you do not need to have

1+(b1/a1)*exp(j*phase_diff)

right? the later is a simplified result of the former for the same physics: elliptical polarization. and It just illustrates the exact expression in the textbook. But it is not necessarily the only expression for the same physics.

That's what I mentioned before: this is a more theoretical issue than simulation issue. The previously reply with phase 1, phase2 and phase2 are the original phases of each mode. you do not need to add additional phase difference among them, as long as you get them. Just use the original, raw data.

14MemberHI， Thanks for kind support.

From the script i noticed that phase difference is from this step:

Now, to calculate the phase for s and p component separately, i introduced Gtheta and Gphi here as follows:

But the difference between them is not the same as in phase difference calculated from here:

I think it should be the same? Am I approaching it correctly?

1,692Ansys EmployeePlease note that Gtheta and Gphi are field quantities, not angles. Calculating their phase difference is a little subtle, as you can see from the above screenshot.

You do not need to re-calculate them, just use Gtheta and Gphi as two sources: each has its abs() and phase angle().

If you do not think it carefully about how to excite the device with decomposed fields, you may suffer difficulties to get what expected. Please discuss with your colleagues or supervisor, as there are more theoretical issues. we are here to help you for simulation only.