Animations are often created from FDTD simulations to provide a more intuitive understanding of the physical phenomena being modeled. These animations can visualize the evolution of the field distribution over time, showing wave propagation, interactions, and other dynamic effects that static images cannot adequately depict. This can help researchers and engineers better understand the results of their simulations, identify anomalies, and develop or refine their models. Additionally, these animations can serve as effective educational and communication tools, making complex concepts more accessible to non-experts.

This tutorial demonstrates how to create animations in a waveguide taper simulation and display them directly in a Jupyter Notebook. We will show how to use Tidy3D convenience features to animate time-domain and frequency-domain fields.

We also provide a comprehensive list of other tutorials such as how to define boundary conditions, how to defining spatially-varying sources and structures, how to model dispersive materials, and how to visualize simulation setups and results.

If you are new to the finite-difference time-domain (FDTD) method, we highly recommend going through our FDTD101 tutorials.

Simulation Setup¶

For this demo, we simply simulate a linear waveguide taper. The simulation setup is directly borrowed from the waveguide size converter case study notebook.

To create a time-domain animation, we need to capture the frames at different time instances of the simulation. This can be done by using a FieldTimeMonitor. Usually, an FDTD simulation contains a large number of time steps and grid points. Recording the field at every time step and grid point will result in a large dataset. For the purpose of making time-domain animations, this is usually unnecessary. In this particular case, we will record one frame every 100 time steps, which is realized by setting interval=100 in the FieldTimeMonitor. Similarly, we set interval_space=(3,3,1) such that the field is recorded every 3 grid points. To further reduce dataset size, we will only be recording the z-component of the magnetic field.

To create a frequency-domain animation, we will include a FieldMonitor in the simulation to obtain the steady-state electromagnetic fields at the end of the simulation. Afterward, we will change the field phase using a convenience function to create the frequency-domain animation.

Now, we can define the simulation source and create the FDTD simulation object.

Visualize the simulation.

Submit the simulation.

Creating a Time-Domain Animation¶

Before creating the time-domain animation, we can inspect the field distribution at a few time instances.

To create an animation, we need to define a function that plots each frame. Then we use matplotlib's FuncAnimation to create the animation. For this particular animation, we use 50 frames. For detail on FuncAnimation, please reference the documentation.

After the animation is created, we can display it directly in the notebook environment by using HTML. Here we see the incident pulse from the wider waveguide is squeezed into the narrower waveguide through the taper. Some field is reflected back or leaked out of the waveguide, leading to some insertion loss, which can be minimized by using a longer taper.

Creating a Frequency-Domain Animation¶

Using the phase parameter, the plot_field function allows us to apply a phase shift to frequency-domain monitors. Below, we will apply a $\pi$ phase shift to the Hz taper field component.

The apply_phase() is another convenient function for modifying the Fourier-transformed field phase. We will use it to change the field phase between $0$ and $-2 \pi$.