## How do I run a simulation and access the results?#

Submitting and monitoring jobs, and donwloading the results, is all done through our web API. After a successful run, all data for all monitors can be downloaded in a single .hdf5 file using tidy3d.web.webapi.load(), and the raw data can be loaded into a SimulationData object.

From the SimulationData object, one can grab and plot the data for each monitor with square bracket indexing, inspect the original Simulation object, and view the log from the solver run. For more details, see this tutorial.

## How is using Tidy3D billed?#

The Tidy3D client that is used for designing simulations and analyzing the results is free and open source. We only bill the run time of the solver on our server, taking only the compute time into account (as opposed to overhead e.g. during uploading). When a task is uploaded to our servers, we will print the maximum incurred cost in Flex units. This cost is also displayed in the online interface for that task. This value is determined by the cost associated with simulating the entire time stepping specified. If early shutoff is detected and the simulation completes before the full time stepping period, this cost will be pro-rated. For more questions or to purchase Flex units, please contact us at support@flexcompute.com.

## What are the units used in the simulation?#

We generally assume the following physical units in component definitions:

• Length: micron (μm, 10-6 meters)

• Time: Second (s)

• Frequency: Hertz (Hz)

• Electric conductivity: Siemens per micron (S/μm)

Thus, the user should be careful, for example to use the speed of light in μm/s when converting between wavelength and frequency. The built-in speed of light C_0 has a unit of μm/s.

For example:

wavelength_um = 1.55
freq_Hz = td.C_0 / wavelength_um
wavelength_um = td.C_0 / freq_Hz


Currently, only linear evolution is supported, and so the output fields have an arbitrary normalization proportional to the amplitude of the current sources, which is also in arbitrary units. In the API Reference, the units are explicitly stated where applicable.

Output quantities are also returned in physical units, with the same base units as above. For time-domain outputs as well as frequency-domain outputs when the source spectrum is normalized out (default), the following units are used:

• Electric field: Volt per micron (V/μm)

• Magnetic field: Ampere per micron (A/μm)

• Flux: Watt (W)

• Poynting vector: Watt per micron squared (W/μm2)

• Modal amplitude: Sqare root of watt (W1/2)

If the source normalization is not applied, the electric field, magnetic field, and modal amplitudes are divided by Hz, while the flux and Poynting vector are divided by Hz2.

## How are results normalized?#

In many cases, Tidy3D simulations can be run and well-normalized results can be obtained without normalizing/empty runs. This is because care is taken internally to normalize the injected power, as well as the output results, in a meaningful way. To understand this, there are two separate normalizations that happen, outlined below. Both of those are discussed with respect to frequency-domain results, as those are the most commonly used.

### Source spectrum normalization#

Every source has a spectrum associated to its particular time dependence that is imprinted on the fields injected in the simulation. Usually, this is somewhat arbitrary and it is most convenient for it to be taken out of the frequency-domain results. By default, after a run, Tidy3D normalizes all frequency-domain results by the spectrum of the first source in the list of sources in the simulation. This choice can be modified using the Simulation.normalize_index attribute, or normalization can be turned off by setting that to None. Results can even be renoramlized after the simulation run using SimulationData.renormalize(). If multiple sources are used, but they all have the same time dependence, the default normalization is still meaningful. However, if different sources have a different time dependence, then it may not be possible to obtain well-normalized results without a normalizing run.

This type of normalization is applied directly to the frequency-domain results. The custom pulse amplitude and phase defined in SourceTime.amplitude and SourceTime.phase, respectively, are not normalized out. This gives the user control over a (complex) prefactor that can be applied to scale any source. Additionally, the power injected by each type of source may have some special normalization, as outlined below.

### Source power normalization#

Source power normalization is applied depending on the source type. In the cases where normalization is applied, the actual injected power may differ slightly from what is described below due to finite grid effects. The normalization should become exact with sufficiently high resolution. That said, in most cases the error is negligible even at default resolution.

The injected power values described below assume that the source spectrum normalization has also been applied.

• PointDipole: Normalization is such that the power injected by the source in a homogeneous material of refractive index $$n$$ at frequency $$\omega = 2\pi f$$ is given by

$\frac{\omega^2}{12\pi}\frac{\mu_0 n}{c}.$
• UniformCurrentSource: No extra normalization applied.

• CustomFieldSource: No extra normalization applied.

• ModeSource, PlaneWave, GaussianBeam, AstigmaticGaussianBeam: Normalized to inject 1W power at every frequency. If supplied SourceTime.num_freqs is 1, this normalization is only exact at the central frequency of the associated SourceTime pulse, but should still be very close to 1W at nearby frequencies too. Increasing num_freqs can be used to make sure the normalization works well for a broadband source.

The correct usage for a PlaneWave source is to span the whole simulation domain for a simulation with periodic (or Bloch) boundaries, in which case the normalization of this technically infinite source is equivalent to 1W per unit cell. For the other sources which have a finite extent, the normalization is correct provided that the source profile decays by the boundaries of the source plane. Verifying that this is the case is always advised, as otherwise results may be spurious beyond just the normalization (numerical artifacts will be present at the source boundary).

• TFSFSource: Normalized to inject 1W/μm2 in the direction of the source injection axis. This is convenient for computing scattering and absorption cross sections without the need for additional normalization. Note that for angled incidence, a factor of $$1/\cos(\theta)$$ needs to be applied to convert to the power carried by the plane wave in the propagation direction, which is at an angle $$\theta$$ with respect to the injection axis. Note also that when the source spans the entire simulation domain with periodic or Bloch boundaries, the conversion between the normalization of a TFSFSource and a PlaneWave is just the area of the simulation domain in the plane normal to the injection axis.

## Why is a simulation diverging?#

Sometimes, a simulation is numerically unstable and can result in divergence. All known cases where this may happen are related to PML boundaries and/or dispersive media. Below is a checklist of things to consider.

• For dispersive materials with $$\epsilon_{\infty} < 1$$, decrease the value of the Courant stability factor to below $$\sqrt{\epsilon_{\infty}}$$.

• Move PML boundaries further away from structure interfaces inside the simulation domain, or from sources that may be injecting evanescent waves, like PointDipole, UniformCurrentSource, or CustomFieldSource.

• Make sure structures are translationally invariant into the PML, or if not possible, use Absorber boundaries.

• Remove dispersive materials extending into the PML, or if not possible, use Absorber boundaries.

• If using our fitter to fit your own material data, make sure you are using the plugins.StableDispersionFitter.

• If none of the above work, try using StablePML or Absorber boundaries anyway (note: these may introduce more reflections than in usual simulations with regular PML).

## How do I include material dispersion?#

Dispersive materials are supported in Tidy3D and we provide an extensive material library with pre-defined materials. Standard dispersive material models can also be defined. If you need help inputting a custom material, let us know!

It is important to keep in mind that dispersive materials are inevitably slower to simulate than their dispersion-less counterparts, with complexity increasing with the number of poles included in the dispersion model. For simulations with a narrow range of frequencies of interest, it may sometimes be faster to define the material through its real and imaginary refractive index at the center frequency. This can be done by defining directly a value for the real part of the relative permittivity $$\mathrm{Re}(\epsilon_r)$$ and electric conductivity $$\sigma$$ of a Medium, or through a real part $$n$$ and imaginary part $$k$$. The relationship between the two equivalent models is

\begin{align}\begin{aligned}&\mathrm{Re}(\epsilon_r) = n^2 - k^2\\&\mathrm{Im}(\epsilon_r) = 2nk\\&\sigma = 2 \pi f \epsilon_0 \mathrm{Im}(\epsilon_r)\end{aligned}\end{align}

In the case of (almost) lossless dielectrics, the dispersion could be negligible in a broad frequency window, but generally, it is importat to keep in mind that such a material definition is best suited for single-frequency results.

For lossless, weakly dispersive materials, the best way to incorporate the dispersion without doing complicated fits and without slowing the simulation down significantly is to provide the value of the refractive index dispersion $$\mathrm{d}n/\mathrm{d}\lambda$$ in Sellmeier.from_dispersion(). The value is assumed to be at the central frequency or wavelength (whichever is provided), and a one-pole model for the material is generated. These values are for example readily available from the refractive index database.

## Why did my simulation finish early?#

By default, Tidy3D checks periodically the total field intensity left in the simulation, and compares that to the maximum total field intensity recorded at previous times. If it is found that the ratio of these two values is smaller than 10-5, the simulation is terminated as the fields remaining in the simulation are deemed negligible. The shutoff value can be controlled using the Simulation.shutoff parameter, or completely turned off by setting it to zero. In most cases, the default behavior ensures that results are correct, while avoiding unnecessarily long run times. The Flex Unit cost of the simulation is also proportionally scaled down when early termination is encountered.

## Should I make sure that fields have fully decayed by the end of the simulation?#

Conversely to early termination, you may sometimes get a warning that the fields remaining in the simulation at the end of the run have not decayed down to the pre-defined shutoff value. This should usually be avoided (that is to say, Simulation.run_time should be increased), but there are some cases in which it may be inevitable. The important thing to understand is that in such simulations, frequency-domain results cannot always be trusted. The frequency-domain response obtained in the FDTD simulation only accurately represents the continuous-wave response of the system if the fields at the beginning and at the end of the time stepping are (very close to) zero. That said, there could be non-negligible fields in the simulation yet the data recorded in a given monitor can still be accurate, if the leftover fields will no longer be passing through the monitor volume. From the point of view of that monitor, fields have already fully decayed. However, there is no way to automatically check this. The accuracy of frequency-domain monitors when fields have not fully decayed is also discussed in one of our FDTD 101 videos.

The main use case in which you may want to ignore this warning is when you have high-Q modes in your simulation that would require an extremely long run time to decay. In that case, you can use the the ResonanceFinder plugin to analyze the modes, as well as field monitors with apodization to capture the modal profiles. The only thing to note is that the normalization of these modal profiles would be arbitrary, and would depend on the exact run time and apodization definition. An example of such a use case is presented in our high-Q photonic crystal cavity case study.

## Why can I not change Tidy3D instances after they are created?#

You may notice in Tidy3D versions 1.5 and above that it is no longer possible to modify instances of Tidy3D components after they are created. Making Tidy3D components immutable like this was an intentional design decision intended to make Tidy3D safer and more performant.

For example, Tidy3D contains several “validators” on input data. If models are mutated, we can’t always guarantee that the resulting instance will still satisfy our validations and the simulation may be invalid.

Furthermore, making the objects immutable allows us to cache the results of many expensive operations. For example, we can now compute and store the simulation grid once, without needing to worry about the value becoming stale at a later time, which significantly speeds up plotting and other operations.

If you have a Tidy3D component that you want to recreate with a new set of parameters, instead of obj.param1 = param1_new, you can call obj_new = obj.copy(update=dict(param1=param1_new)). Note that you may also pass more key value pairs to the dictionary in update. Also, note you can use a convenience method obj_new = obj.updated_copy(param1=param1_new), which is just a shortcut to the obj.copy() call above.