Geometry plotting

This notebook provides a tutorial for plotting tidy3d components before running them, to get a sense for the geometry.

import matplotlib.pylab as plt
import numpy as np

import tidy3d as td

td.config.logging_level = "error"

[00:00:57] WARNING  This version of Tidy3D was pip installed from the 'tidy3d-beta' repository on   __init__.py:103
                    PyPI. Future releases will be uploaded to the 'tidy3d' repository. From now on,                
                    please use 'pip install tidy3d' instead.                                                       

           INFO     Using client version: 1.9.0rc1                                                  __init__.py:121

Simple, 2D plotting

Geometries

All Geometry objects, such as Box, Sphere, Cylinder, and PolySlab, have a .plot() method that plots their geometries on a plane specified by coordinate=position syntax (eg. z=5.0).

cylinder = td.Cylinder(center=(0, 0, 0), radius=1, length=2, axis=0)
ax = cylinder.plot(x=0)
plt.show()

Structures

Structure objects, which combine a Geometry with a Medium, work the same way.

box = td.Structure(
    geometry=td.Box(center=(0.0, 0.0, 0), size=(4, 2.0, 0.5)),
    medium=td.Medium(permittivity=2.0),
)

ax = box.plot(x=0)

We can supply ax argument to the plot function to plot on a specific Matplotlib Axes, for example

# make 3 columns of axes
f, (ax1, ax2, ax3) = plt.subplots(1, 3, tight_layout=True, figsize=(10, 3))

# plot each axis of the plot on each subplot
ax1 = box.plot(x=0, ax=ax1)
ax2 = box.plot(y=0, ax=ax2)
ax3 = box.plot(z=0, ax=ax3)

The .plot() method returns either a new axis (if ax not supplied) or the orginal axis, so you can add more objects to the plot, or edit it through the ax handle.

sphere = td.Structure(
    geometry=td.Sphere(center=(0, 0, 0), radius=2), medium=td.Medium(permittivity=3)
)

ax = sphere.plot(x=0)

ax.set_xlim(-3, 3)
ax.set_ylim(-3, 3)
ax.set_title('my custom title: "just a sphere"')
plt.show()

Finally, since the geometry plotting us done using matplotlib Patches, you can supply optional keyword arguments to .plot() to change the display of the plot.

See matplotlib’s documentation on Patches for more information on arguments are accepted.

box1 = td.Box(center=(1.0, 0.0, 1), size=(0.5, 0.5, 0.5))
box2 = td.Box(center=(-1.0, 0.0, 1), size=(0.5, 0.5, 0.5))
box3 = td.Box(center=(0, 0.0, 0.0), size=(0.2, 0.2, 0.2))
box4 = td.Box(center=(0.0, 0.0, -0.8), size=(3, 0.5, 0.5))

ax = box1.plot(y=0, facecolor="crimson", edgecolor="black", alpha=1)
ax = box2.plot(y=0, ax=ax, facecolor="blueviolet", edgecolor="black", alpha=1)
ax = box3.plot(y=0, ax=ax, facecolor="black", edgecolor="black", alpha=1)
ax = box4.plot(y=0, ax=ax, facecolor="green", edgecolor="black", alpha=1)
ax = sphere.plot(
    y=0, ax=ax, facecolor="sandybrown", edgecolor="black", alpha=0.5, hatch="/"
)

Simulations

We can plot all components contained in Simulation with the Simulation.plot() method.

Let’s create a simulation with a source, monitor, and a bunch of randomly placed spheres made of 3 distinct Medium objects.

from numpy.random import random

L = 5  # length of simulation on all sides


def rand():
    return L * (random() - 0.5)


# make random list of structures
structures = [
    td.Structure(
        geometry=td.Sphere(center=(rand(), rand(), rand()), radius=1),
        medium=td.Medium(permittivity=np.random.choice([2.0, 2.5, 3.0, 3.5, 4.0])),
    )
    for i in range(20)
]

source = td.UniformCurrentSource(
    center=(0, 0, -L / 3),
    size=(L, L / 2, 0),
    polarization="Ex",
    source_time=td.GaussianPulse(
        freq0=100e14,
        fwidth=10e14,
    ),
)

monitor = td.FieldMonitor(
    center=(-L / 4, 0, 0), size=(L / 2, L, 0), freqs=[1], name="fields"
)

# make simulation from structures
sim = td.Simulation(
    size=(L, L, L),
    grid_spec=td.GridSpec.auto(wavelength=4),
    boundary_spec=td.BoundarySpec(
        x=td.Boundary.pml(num_layers=10),
        y=td.Boundary.periodic(),
        z=td.Boundary.pml(num_layers=10),
    ),
    structures=structures,
    sources=[source],
    monitors=[monitor],
    run_time=1e-12,
)

f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 10))
ax1 = sim.plot(x=0, ax=ax1)

# put the grid lines on the 2nd one
ax2 = sim.plot(x=0, ax=ax2)
ax2 = sim.plot_grid(x=0, ax=ax2)

Plotting Materials

with sim.plot we can plot each distinct material, source, monitor, and PML.

Note, all structures with same Medium show up as the same color.

f, axes = plt.subplots(1, 3, tight_layout=True, figsize=(10, 3))
for ax, axis in zip(axes, "xyz"):

    ax = sim.plot(**{axis: 0}, ax=ax)
    ax.set_title(f"axis={axis}, position=0.0")
plt.show()

We can even get fancy and plot the cross sections at different positions along the 3 axes.

npos = 5
positions = np.linspace(-L / 3, L / 3, npos)
f, axes = plt.subplots(3, npos, tight_layout=True, figsize=(npos * 3, 7))
for axes_range, axis in zip(axes, "xyz"):
    for ax, pos in zip(axes_range, positions):
        ax = sim.plot(**{axis: pos}, ax=ax)
        ax.set_title(f"{axis}={pos:.2f}")
plt.show()

Plotting Permittivity

With Simulation.plot_eps we can plot the continuously varying permittivity distribution on the plane.

f, axes = plt.subplots(1, 3, tight_layout=True, figsize=(10, 3))
for ax, axis in zip(axes, "xyz"):
    ax = sim.plot_eps(**{axis: pos}, ax=ax, alpha=0.98)
    ax.set_title(f"{axis}={pos:.2f}")
plt.show()

npos = 5
positions = np.linspace(-L / 3, L / 3, npos)
f, axes = plt.subplots(3, npos, tight_layout=True, figsize=(npos * 3, 7))
for axes_range, axis in zip(axes, "xyz"):
    for ax, pos in zip(axes_range, positions):
        ax = sim.plot_eps(**{axis: pos}, ax=ax, alpha=0.98)
        ax.set_title(f"{axis}={pos:.2f}")
plt.show()

Plotting Other Quantities

Structure + Medium

The Structure.medium refractive index values over frequency can be plotted with it’s .plot() method as well.

# import silver from material library
from tidy3d import material_library

Ag = material_library["Ag"]["Rakic1998BB"]

# make a star-shaped PolySlab
import numpy as np

r_in = 0.4
r_out = 1.0
inner_vertices = [
    (
        r_in * np.cos(2 * np.pi * i / 5 + np.pi / 2 - np.pi / 5),
        r_in * np.sin(2 * np.pi * i / 5 + np.pi / 2 - np.pi / 5),
    )
    for i in range(5)
]
outer_vertices = [
    (
        r_out * np.cos(2 * np.pi * i / 5 + np.pi / 2),
        r_out * np.sin(2 * np.pi * i / 5 + np.pi / 2),
    )
    for i in range(5)
]
star_vertices = []
for i in range(5):
    star_vertices.append(inner_vertices[i])
    star_vertices.append(outer_vertices[i])
poly_star = td.PolySlab(vertices=star_vertices, slab_bounds=(-1, 1), axis=2)

# make a star structure with silver as medium
silver_star = td.Structure(geometry=poly_star, medium=Ag)

# plot the structrue alongside the medium properties
freqs = np.linspace(1e14, 2e14, 101)
position = 0.0
axis = 2

f, (ax1, ax2) = plt.subplots(1, 2, tight_layout=True, figsize=(10, 4))
ax1 = silver_star.geometry.plot(z=0, edgecolor="black", ax=ax1)
ax2 = silver_star.medium.plot(freqs=freqs, ax=ax2)

Source + Source Time

Similarly, the Source.source_time amplitude over time can be plotted with its .plot() method.

cube_source = td.UniformCurrentSource(
    center=(0, 0, 0),
    size=(1, 1, 1),
    polarization="Ex",
    source_time=td.GaussianPulse(
        freq0=1e14,
        fwidth=1e13,
    ),
)

times = np.linspace(0, 0.2e-12, 1001)
position = 0.0
axis = 2

f, (ax1, ax2) = plt.subplots(1, 2, tight_layout=True, figsize=(10, 4))
ax1 = cube_source.geometry.plot(z=0, facecolor="sandybrown", edgecolor="black", ax=ax1)
ax2 = cube_source.source_time.plot(times=times, ax=ax2)

Monitor

freq_mon = td.FieldMonitor(
    center=(0, 0, 0),
    size=(1, 1, 1),
    freqs=list(np.linspace(1e14, 2e14, 11)),
    name="test",
)

position = 0.0
axis = 2

ax = freq_mon.geometry.plot(z=0, facecolor="blueviolet", edgecolor="black")

time_mon = td.FieldTimeMonitor(
    center=(0, 0, 0),
    size=(1, 1, 1),
    interval=10,
    name="test",
)

position = 0.0
axis = 2

ax = time_mon.geometry.plot(z=0, facecolor="blueviolet", edgecolor="black")