Dear Lumerical staff,
I’m having some difficulties understanding the ring modulator model and how to set up the parameters in for the primitive ring modulator element in the library.

first, the “measurement type” under “standard” has a choice between “effective index” and “absorption and phase”. here the effective index appears to be complex. does this mean that the imaginary part of it should be the amplitude loss due to absorption?

is this the absolution index change or index change divided by the nominal effective index (value given as “effective index” under “waveguide”)?

if the absorption loss is included in the “effective index”, then the “loss” under “waveguide” should be loss other than absorption?

the “digital filter” part is the most confusing to me. when I choose “disable” for “time variant digital filter”, I get an eye diagrams to seemingly show the dynamic behavior of the modulator. when this is set to “update” of “interpolate”, the eye is totally square looking. why is that? does the eye diagram in “disable” really represents the dynamic of the modulator?

The ring modulator element can be seen as made of several sub-elements:

The couplers are defined by their coupling coefficients, the waveguides (composing the ring) are defined by loss, effective index, group index, dispersion and length, and the modulation is defined either by the effective index vs modulation or absorption & phase vs modulation, and the fill factor.

The modulation is applied on top of the waveguide, on a length ratio defined by the fill factor. So the measurement in the element are the variation of effective index caused by the modulation (real part, dn, will cause a phase shift and the imaginary part, dk, will add some absorption/loss) or the additional phase shift and loss caused by the modulation.

The loss defined under waveguide can include all sources of loss (absorption, propagation, etc.). The effective index of the waveguide will only be real so no absorption loss is included. Any loss should be in the loss parameter of the waveguide.

In the time domain, the element transfer function is implemented as a time varying digital filter. You can find some information about how the filter is calculated (depending on the “time variant digital filter” setting) in this white paper.
The effect of the setting are also shown in the Optical Ring Modulator KB page.

Maybe I’m not understanding. When you answered the first part of my question you said that the effective index change has real part which results in phase change, and imaginary part which accounts for absorption/loss, in the second part of your answer, however, you said the effective index is real, so the absorption loss need to be added to the “loss” parameter. This seems contradictory?

If I understand the last part of your answer correctly, the “time varying digital filter” is to emulate the transient response of the modulator. Then why choosing “disable” seems to give you the transient response while other choices don’t?

I actually have a new question, which has to do how the modulation amplitude is calculated. I believe the resonance wavelength change of the ring divided by wavelength should equal to effective index change (due to modulation) divided by effective index. Or delta lambda over lambda = delta neff over neff. However, the model appears to give me delta lambda over lambda = delta neff over ngroup, where ngroup is the group index. Any comment on this? This is an important question, because the ring modulator’s modulation efficiency is a very important parameter to get right.

In the Ring Modulator element, there are 2 different settings:

Waveguide properties (under the “Waveguide” category)

Modulation properties (under “Standard”)

In the waveguide properties, you set the global properties of the waveguide (effective index, group, index, etc.). There, the effective index will only have the real part as there is a specific field for the loss.

In the modulation properties, you specify how the waveguide properties are affected by the modulation. As I mentioned, this can be defined as an effective index vs modulation, or absorption & phase vs modulation.

If “effective index” is selected, the measurement is a table of 3 columns, with the real part and imaginary part of the effective index variation vs modulation.

I think it is slightly different: the digital filter is to emulate the transient response of the modulator. I believe the time varying digital filter is there to emulate the dynamics of the resonator. I’m not totally familiar with the implementation of the model, so I will ask my colleagues to look at this discussion.

In the model, we consider the effective index as frequency dependent, so the element properties depend on the group index.

The resonance wavelength follows the equation: 2*pi*r*neff = m*lambda0
where m is an integer. When voltage applied to the modulator, the effective index of the ring changed by the amount delta_nerf and the equation becomes: 2*pi*r*(neff+delta_neff) = n*lambda1
while you can think of lambda1 as lambda1 = lambda0 + delta_lambda however, since the ring’s circumference is in much larger magnitude than lambda, the integer numbers ain’t the same. Hence delta_lambda/lambda doesn’t directly translate to delta_neff/neff (m!=n). It is not equal todelta_neff/ng either.

For the “time variant digital filter”, by selecting the update option the modulator will update the filter coefficient as function of time – this option is accurate but requires constant updating of filter coefficients. By selecting the interpolate option the modulator will pre-calculate the filter coefficients for a set of pre-defined input voltage values (v1, v2,…vN) at the beginning of the simulation, and it will interpolate coefficient values during the simulation – the accuracy of the interpolation depends on the number of pre-defined input voltage values and it does not require constant updating of the filter coefficients. With the time variant update of the filter coefficients, the transient effect is less.

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