Convergence time

[Sridarshini Thirumaran]

Can anyone help me out in calculating the simulation step size for a layout with ring resonators? Is there any formula for it?

[Damian Marek]

There is an absolute maximum for the time step size, but no formula for directly calculating what minimum is the correct choice. The default choice of OptiFDTD is the aforementioned maximum. This at least guarantees a stable simulation.

I think your issue might be the number of time steps and not the individual time step size. Resonators and cavities trap light within them and it takes time for the light to leak out (Q-factor). This means that you will need to check to see if the energy in the resonator has had time to leave. You can do this by using an observation point placed inside the resonator or at on of the ports. You should see the electric field decaying with something similar to an exponential envelope. Check to see if the electric field has diminished to an appropriately small value by the end of the simulation.

[Scott Newman]

As a side note you will also want to ensure that you are running a high enough resolution spatially. While the default in the software and for most people is 10 points per smallest wavelength in the material, this is only for characterizing the source. If your features such as the waveguides of your resonator are less than your wavelength (a typical condition in integrated devices where refractive indices are high) you need to ensure you are running a sufficiently high resolution to characterize the spatial layout. While 10 points per smallest feature is a good rule of thumb you should keep an eye on this and run convergence testing. One way of checking is to use the refractive index viewers in Designer as these are based off the grid and not the drawn specifications.

[Paulo Lourenco]

Hi guys,

I apologize for jumping into this topic but maybe you can clarify my doubts about convergence time and time steps, together with time step size. In an usual simulation (let’s say a 2D silicon waveguide in air simulation), if we keep all options to “auto” at the Simulation Parameters window, we find that the EM energy almost reaches (see Note: please) the end of simulation. Is this to prevent the interference of the reflected wave? If so, shouldn’t APML be able to cancel out all reflections?

As Scott and Damian mentioned, if there are resonant features or cavities we should increase our spatial resolution. For a higher spatial resolution shouldn’t we also increase the number of time steps or is it better to keep it “auto”? I mentioned this because whenever I increase simulation time steps, field amplitudes vary…

Note: I am attaching an image of what I mean by “… EM energy almost reaches…”.

Thank you in advance.

Best regards.

[Scott Newman]

Hello Paulo,

The auto setting for the number of time steps or “Run for…” setting is it is the number of time steps required to get from one corner of the simulation domain to the opposite corner if it were traveling through the highest refractive index material in the design. it is not meant to reduce the reflections as you are correct this is the role of the PML that is defined at that boundary.

As with any auto setting it is merely a good starting point to get the simulation running. This is one of the reasons we almost always recommend placing an observation point where you are going to be extracting information and looking at the time domain information to ensure that the power has fully propagated through the structure (for CW – reach steady state and for pulse – power decays to zero).

Scott

[Paulo Lourenco]

Hi Scott,

Thanks a lot for your explanation. I am clarified now as far as this case is concerned though, I have one other question 🙂 if I may: – Does this mean that if I want to analyze reflection I should increase the number of time steps to insure that EM field goes forth and back (may put another obervation point before the input field to check reflected field arrival)?

Best regards.

[Scott Newman]

Hi Paulo,

Precisely, to do the kind of simulation you are now discussing I would use an observation point either just before or just after the input field and monitor the time domain data. This will allow you to see when the signal initially passes the point and then have a result for each “pass” as it reflects, such would be the case in a Fabry-Perot cavity.

Scott

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