# Definition of Length in Ring Modulator INTERCONNECT Example

Hello,

I’m trying to simulate the fifth step of the Ring Modulator Example which is in INTERCONNECT. But I’m confused about how the length of the ring is partitioned between the arms/waveguides.
(https://support.lumerical.com/hc/en-us/articles/360042322794-Ring-modulator#h_5605dd75-5ae3-4d01-8489-4bab5cc619da)

For example in the ring resonator, given in the link below, the overall length of the ring (2pir) is divided in two for both arms, so that the arms have equal length. Also, note that this ring has a smaller radius than the modulator example.
(https://support.lumerical.com/hc/en-us/articles/360042323794-Ring-resonator-using-INTERCONNECT-primitive-elements)

But in the modulator example, the length is not equally divided.

I noticed that the Passive_Bent and the Active_Bent_0V waveguides’ lengths add up to the total length of the ring which is 10pi2 um.

1- Why isn’t the length of these waveguide’s equal and half the total length of the ring?

2- What part of the ring does the Active_Bent_modulated waveguide define? (This shouldn’t be a racetrack structure; as far as I know, this a perfect ring modulator since all of the preceding calculations in FDTD, MODE, CHARGE assumed a perfect ring.)

3- Is there a specific reason why the Active_Bent_Modulated and the Active_Bent_0V waveguides are equal in length?

4- Let’s say I want to simulate a ring modulator with radius R how should I define it for INTERCONNECT? (I had no issues with the other solvers since they had direct radius definitions.)

Thank you.

Hey!

1. It isn’t really necessary that the two branches are equal in length, although that would correctly represent the real resonator, computationally the effect is identical. This of course only in the case of basic resonators with no consideration of effects like counter propagating modes.

2. Although the waveguide coupler is simulated as an arch (pi/2 in angle between the two ring ports), the phase term of the coupler is not saved, hence the ring needs to have the full length modelled as waveguides 2\pi r . Active_Bent_modulated waveguide defines the section of the ring that is being electrically modulated, its calculated as k\cdot(2 \pi r), wher k is the modulation fraction (length proportion of the ring that is being modulated).

3. Yes. The model for the active waveguide saves only the change of refractive index (dneff) based on the applied voltage, hence you need to include the same waveguide with no modulation (that will induce the baseline effects).

4. The file was created so that you can modify this easily in the parameters of the model. In Interconnect, just make sure to not select anything, then in the properties view go to Validation, where you will find the variables you can edit, as shown in the image below (note however that you should also run again the simulations in Mode to account for the different bending radius in the waveguides).

I hope this helps.

Juan