# Simulating Coupling Region for a Ring Resonator

#1

Hi everyone. I’m trying to simulate the coupling region for a ring region so I can get an approximation of the value for the coupling coefficient. I’ve already have the asymmetric coupling script working properly and I’m currently in the process of sweeping for different radiuses and gap sizes in order to get the S-parameters matrix. I’ve attached the analysis script so you can take a look at it. It’s basically the default one that comes up with the asymmetric coupler FDTD file. I am not sure how to proceed and figure the coupling coefficient I need. Basically the whole simulation is run twice for two different cases when the light is being coupled in the ring and the other case of the light coupling from the ring to the waveguide. The results come in two set of matrixes, one which has all values equal to 0 and the other one with a graph showing 4 matrix elements plotted.

I’m not sure how to proceed to extract the S-Params from these. Can anyone help me out

#2

Hi @sti1g14
From the uploaded pictured, i noticed that you use simultaneously two sources. I would recommend you to run two simulations. Each simulation will use one source. As a result you will produce a 4x4 matrix. Also, i would like to mention that you should use your sources some μm away from the coupling point. I think that in your design you are very close to the coupling point.

#3

Hi. Thanks for the tip. I’m currently re-running it now. I’ve managed to understand the port mapping and how to figure which one of the matrix elements is the coupling coefficient and the coupling length. The problem is that there’s a series of values in each element of this matrix and I can’t figure how to get the value which I’m interested in. Here’s a picture of it:

#5

I’ve attached a copy of the new structure and the results window of the S-Params. The weird thing is that I’m getting only one matrix S12, which represents the transmission of the waveguide from port 1 to port 2, basically a straight waveguide, while all the other parameters are all 0 or close to 0. This tells me that there is no coupling at all in the structure. Can you please help me out with this?

#6

Hi @sti1g14
It is expecting that the coupling coefficient will be near zero. But it will not be equal to 0. For instance the value of the coupling coefficient will be approximately 0.016, it is random value. Also, the gap should from 100[nm] to 200[nm]. The transmission coefficient will be near 0.983.

#7

Hi @sti1g14
The coupling length at which power is completely transferred from one waveguide into the other waveguide is determined from the propagation constants of the supermodes. Lc: coupling length , Lx=cross over length
Please be careful the following example

k*=0.001431 because it is the point of the critical coupling.

Concerning which one of the matrix elements is the coupling coefficient. It is up to you. Most of the time s we select the value of 1550[nm] or near that.

#8

Hi,

Can you please clarify why this is the case? Is not the goal of the structure to couple light into the semi-ring structure? And why is the coupling coefficient so small?

Regards.

#9

Hi @sti1g14,

I just noticed you still needed some clarification about your issues, sorry for the delay.

A good way to get the full S matrix of your device, would be to used the “Port” objects, as shown in this ring resonator example. But in order to get the full matrix, you need to do a sweep using the S-parameter matrix sweep tool. Note that at the moment, the sweep tool cannot take into account the symmetries of the device, so you have to run a full sweep.
Alternatively, you can get the S-parameters using the mode source and mode expansion monitors and some scripting.

As @konslekk mentioned, the coupling efficiency depends on several factors, including the gap between the wavelength and the coupling length. You can do some analysis of the coupling between the waveguides using MODE Solutions, as shown in this example.