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 file monitor_data.hdf5 using tidy3d.web.download_results(). The recommended approach is to load the data file into the corresponding Simulation object that was used for the run using Simulation.load_results(). The Simulation object stores a list of all included monitors as Simulation.monitors, and the data can be queried using Simulation.data(). Loading the results in this way also allows you to use our in-built visualization functions. The specifics of running a simulation and loading and analyzing data is fully covered in our walkthrough example.

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). In the online user interface, we provide an estimate of the billed amount a simulation would incur, but the final value is determined by timing the actual run. If you notice a significant difference between the estimate and the final value, please let us know!

What are the units used in the simulation?¶

We assume the following physical units:

• 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 td.constants.C_0 has a unit of μm/s.

For example:

freq_Hz = td.constants.C_0 / wavelength_um
wavelength_um = td.constants.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.

How do I add PML absorbing boundaries to my simulation?¶

Upon initializing a simulation, the user can provide an optional argument pml_layers, an array of three elements defining the PML boundaries along x, y, and z. The easiest way to define PML is to use e.g. pml_layers=(None, None, 'standard') to define PML in the z-direction only (in x and y, the default periodic boundaries will be used). It is also possible to customize the PML further as explained in the documentation and below.

Tidy3D uses a complex frequency-shifted formulation of the perfectly-matched layers (CPML), for which it is more natural to define the thickness as number of layers rather than as physical size. We provide two pre-set PML profiles, 'standard' (default) and 'stable'. The standard profile has 12 layers by default and should be sufficient in many situations. In the case of a diverging simulation, or when the fields do not appear to be fully absorbed in the PML, the user can increase the number of layers in the 'standard' profile, or try the 'stable' profile, which requires more layers (default is 40) but should generally work better.

NB: The PML layers extend beyond the simulation domain. This makes it easier not to worry about PMLs intruding into parts of your simulation where you don’t want them to be. The one thing to keep in mind, however, is that structures that span the full simulation should also extend into the PML. So when defining such structures, it is best to extend them well beyond the simulation size. You could even use td.inf, a shortcut for a very large value, for dimensions that span the full domain. Below is an example of a right and a wrong way to make a dielectric slab.

import tidy3d as td
import matplotlib.pyplot as plt

sim_size = [4., 4., 3.]
pml_layers = [15, 15, 15]

# Correct way: extend slab beyond simulation domain
slab_right = td.Box(
center=[0, 0, 0],
size=[td.inf, td.inf, .5],
material=td.Medium(epsilon=5))

sim_right = td.Simulation(
size=sim_size,
resolution=20,
structures=[slab_right],
pml_layers=pml_layers)

# Wrong: use simulation domain size when using PML
slab_wrong = td.Box(
center=[0, 0, 0],
size=[sim_size[0], sim_size[1], .5],
material=td.Medium(epsilon=5))

sim_wrong = td.Simulation(
size=sim_size,
resolution=20,
structures=[slab_wrong],
pml_layers=pml_layers)

fig, ax = plt.subplots(1, 2, figsize=(11, 4))
sim_right.viz_eps_2D(normal='y', ax=ax[0])
sim_wrong.viz_eps_2D(normal='y', ax=ax[1])
ax[0].set_title('Right: extend through PML')
ax[1].set_title('Wrong: use simulation domain size')
plt.show()


Notice that the simulation size in y is defined as 4 micron on initialization, but the full simulation domain with the PML layers is 5.5 micron. A large number of PML layers can thus lead to a significant increase of computation time in some cases.

Why is a simulation diverging?¶

Sometimes, a simulation is numerically unstable and can result in divergence. The two things that can be tuned to avoid that are the thickness of the PML layers and the Courant stability factor, each of which are defined upon initializing a simulation. If materials with frequency-independent permittivity smaller than one are included in the simulation, the Courant factor must be set to a value lower than the lowest refractive index. In the case of dispersive materials, understanding the reason for the instability is a matter of trial and error. Some things to try include:

• Remove dispersive materials extending into the PML.

• Increase the number of PML layers.

• Decrease the value of the Courant stability factor. Note that this leads to an inversely proportional increase in the simulation time.

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 include the value of the refractive index dispersion $$\mathrm{d}n/\mathrm{d}\lambda$$ in units of 1/micron when defining the Medium. 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.