# How to calculate the transmission characteristics of a coupler with symmetry

Member Posts: 7

Hi, I want to calculate the transmission characteristics (transmission of the through/drop port) of the coupler shown in the attached figure by calculating only half of the coupler structure since the coupler is symmetric with respect to the x = 0 axis. Is it possible to deduct the transmission characteristics of port 5 and 6 by the S parameters of port 1-4? Thank you!

• Posts: 1,652Ansys Employee
edited January 7

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

Sure you can simulate half the device, since it is symmetric. If at the ports there is only one fundamental mode, things can be much easier: from ports 1,2 to ports 3,4, you get the s parameters, and it is lossy, so you only need to double the loss will give you the transmission at ports 5 and 6. You could use transfer matrix or scattering matrix to get the exact results, since you know the s parameters at each port. You will need to flip signs for the second part. The details are up to you to develop. More modes would also work if you use more s parameters.

You could use the "s parameter utility" to get more helpful info: S-parameter matrix sweep utility

Ring resonator getting started - Final parameter extraction

Ring resonator getting started - Design and initial simulation

I think you will need to spend more time than the simulation to develop a math model for this.

• Posts: 30Member

Thank you so much for your reply! I guess I am still a little bit confused about the parameters that can be extracted from the port expansion tab. For example, if I were to calculate the transmission of one specific mode of port 4 with the excitation only at port1, would that be T_in or T_out from port expansion of port 4? Or would that be abs(S)^2 of from port expansion of port 4?

• Posts: 1,652Ansys Employee

abs(S)^2 is originated from S parameters.

But I am not sure where T_in and T_out are from. The regular port gives

and a Chinese post Ansys Insight: 关于mode expansion监视器的使用和结果分析

• Posts: 30Member

Like this one shows.

• Posts: 30Member

And what does S exactly stand for in this "modal expansions" tab. The website you provided does not include the information of S.

• Posts: 1,652Ansys Employee

I am sorry that I do not know which example you are referring for the T_in, T_out. We have used the above T_forward and T_backward for long time.

S parameter is used to describe mode amplitude reflection/transmission (field) coefficients. It is originally from microwave network analyzer. You can find some textbook to get some details. It is similar to Fresnel coefficients in traditional optics. Since this is fundamental concept, Lumerical does not provide any background.

• Posts: 30Member

It is not only of the examples provided in your database, I was referring to the results I got from my own simulation file. Based on the definition of S parameters, abs(S41)^2 should give me the transmission of port 4 if there is only excitation from port 1 which should correspond or the exact same value of either T_forward or T_in in this figure. But these two do not match.