Quick Start

meow Introduction and Quick Start

import meow as mw
import numpy as np

Installation

pip install meow-sim

Quick Start

1. Structure

First create the structures to be simulated. A {class}~.meow.structures.Structure is a collection of a {class}~.meow.geometries.Geometry with a {class}~.meow.materials.Material.

NOTE: meow expects the propagation direction to be the z-axis! This makes the zx-plane parallel with the chip and the y-axis perpendicular to the chip. Keep this in mind when creating your structures.

length = 10.0

oxide = mw.Structure(
    material=mw.silicon_oxide,
    geometry=mw.Box(
        x_min=-1.0,
        x_max=1.0,
        y_min=-1.0,
        y_max=0.0,
        z_min=0.0,
        z_max=length,
    ),
)

core = mw.Structure(
    material=mw.silicon,
    geometry=mw.Box(
        x_min=-0.45 / 2,
        x_max=0.45 / 2,
        y_min=0.0,
        y_max=0.22,
        z_min=0,
        z_max=length,
    ),
)

structures = [oxide, core]
mw.visualize(structures)

NOTE: you can also extrude structures from a gds file. See {class}~.meow.gds_structures.GdsExtrusionRule.

2. Cells

Once you have a list of {class}~.meow.structures.Structure objects, they need to be divided into cells. A {class}~.meow.cell.Cell is a combination of those structures with 2D meshing info ({class}~.meow.mesh.Mesh2d) and a cell length.

num_cells = 5

cells = mw.create_cells(
    structures=structures,
    mesh=mw.Mesh2D(
        x=np.linspace(-1, 1, 101),
        y=np.linspace(-1, 1, 101),
        # specify possible conformal mesh specifications here:
        # bend_radius=2.0,
        # bend_axis=1,
        ez_interfaces=True,
    ),
    Ls=np.array([length / num_cells for _ in range(num_cells)]),
)

A cell should be a region of (approximate) constant cross section. We can use the {func}~.meow.visualize.visualize function to show the cross section of a cell:

mw.visualize(cells[0])

3. Cross Sections

A {class}~.meow.cell.Cell contains all the {class}~.meow.structures.Structure info, but does not take any {class}~.meow.environment.Environment information (such as temparature or wavelength) into account. This information is important as it influences the refractive index of the {class}~.meow.cross_section.CrossSection.

Therefore, combining a {class}~.meow.cell.Cell with an {class}~.meow.environment.Environment yields a {class}~.meow.cross_section.CrossSection:

env = mw.Environment(wl=1.55, T=25.0)
css = [mw.CrossSection.from_cell(cell=cell, env=env) for cell in cells]
mw.visualize(css[0])

4. Find Modes (FDE)

We can now compute multiple {class}~.meow.modes.Modes per {class}~.meow.cross_section.CrossSection using {func}~.meow.fde.tidy3d.compute_modes:

num_modes = 4

modes: list[list[mw.Mode]] = []
for cs in css:
    modes_in_cs = mw.compute_modes(cs, num_modes=num_modes)
    modes.append(modes_in_cs)

# show Ex component of the first mode (idx 0)
# of the first cell (idx 0):
mw.visualize(modes[0][0], fields=["Ex"])
# show Hx component of the second mode (idx 1)
# of the first cell (idx 0):
mw.visualize(modes[0][1], fields=["Hx"])

NOTE: above, the {class}~.meow.modes.Modes of the {class}~.meow.cross_section.CrossSection are calculated sequentially. However, you're invited to try calculating the modes concurrently as well 😉

5. Calculate S-matrix (EME)

The S-matrix of a collection of modes can now easily be calculated with {func}~.meow.eme.tidy3d.compute_s_matrix. This step uses the sax circuit solver under the hood. The resulting S-matrix has is formated such that S[0][0] is the complex reflection coefficient from the fundamental mode into the backwards propagating fundamental mode. S[num_modes][0] is the transmission from the fundamental mode into the fundamental mode, following the pattern S[<to_port>][<from_port>]. The mapping from ports to indices is provided in port_map.

S, port_map = mw.compute_s_matrix(modes, cells)
print(port_map)
mw.visualize((abs(S), port_map))

{'left@0': 0, 'left@1': 1, 'left@2': 2, 'left@3': 3, 'right@0': 4, 'right@1': 5, 'right@2': 6, 'right@3': 7}

That's it! this was a quick introduction to the meow library!