Electrode Absorption

1.

```python

import matplotlib.pyplot as plt import numpy as np import doModels.RefractiveIndex as ri from collections import OrderedDict from femwell.maxwell.waveguide import compute_modes from femwell.mesh import mesh_from_OrderedDict from shapely.geometry import LineString, Polygon from tqdm import tqdm import matplotlib.pyplot as plt import matplotlib.colors as mcolors from matplotlib.patches import Patch from shapely.geometry import Polygon, box from shapely.ops import clip_by_rect from skfem import Basis, ElementTriP0, Mesh from skfem.io import from_meshio

from femwell.maxwell.waveguide import compute_modes from femwell.mesh import mesh_from_OrderedDict

```

```python

def plot_domains_with_legend(mesh, ax=None): if ax is None: fig, ax = plt.subplots() ax.set_aspect(1)

basis0 = Basis(mesh, ElementTriP0())
subdomains = list(mesh.subdomains.keys() - {"gmsh:bounding_entities"})
subdomain_colors = basis0.zeros() * np.nan

for i, subdomain in enumerate(subdomains):
    subdomain_colors[basis0.get_dofs(elements=subdomain)] = i

n_sub = len(subdomains)
cmap = plt.get_cmap("rainbow", n_sub)
norm = mcolors.BoundaryNorm(np.arange(n_sub + 1) - 0.5, ncolors=n_sub)
ax = basis0.plot(subdomain_colors, plot_kwargs={"norm": norm}, ax=ax, cmap=cmap)

legend_handles = [
    Patch(color=cmap(i), label=subdomain) for i, subdomain in enumerate(subdomains)
]
ax.legend(handles=legend_handles, bbox_to_anchor=(1.05, 1), loc="upper left")

return ax

def mesh_waveguide( total_film_thickness=0.21, etch_depth=0.21, top_width=0.45, side_wall_angle=0, buffer_size=1.0, core_resolution=40.05, core_distance=1, default_resolution_max=20.6, show_plot=False, metal_thickness=0.2, metal_offset=0.5, ): slab_thickness = max(total_film_thickness - etch_depth, 0.0) bottom_width = 2 * np.tan(np.deg2rad(side_wall_angle)) + top_width total_slab_width = 4 + bottom_width

if slab_thickness > 0:
    core = Polygon([
        (-total_slab_width/2, 0),
        (+total_slab_width/2, 0),
        (+total_slab_width/2, slab_thickness),
        (+bottom_width/2, slab_thickness),
        (+top_width/2, total_film_thickness),
        (-top_width/2, total_film_thickness),
        (-bottom_width/2, slab_thickness),
        (-total_slab_width/2, slab_thickness),
        (-total_slab_width/2, 0)
    ])
else:
    core = Polygon([
        (-top_width/2, 0),
        (+top_width/2, 0),
        (+top_width/2, total_film_thickness),
        (-top_width/2, total_film_thickness),
        (-top_width/2, 0)
    ])

polygons = OrderedDict(
    metal=box(minx=-1, maxx=1, miny=total_film_thickness+metal_offset, maxy=total_film_thickness+metal_offset+metal_thickness),
    core=core,
    box=box(minx=-2, maxx=2, miny=-1, maxy=0),
    clad=box(minx=-2, maxx=2, miny=0, maxy=total_film_thickness+metal_offset+metal_thickness+1),
)

resolutions = {"core": {"resolution": core_resolution, "distance": core_distance},
               "metal": {"resolution": core_resolution, "distance": core_distance},
               }

mesh = from_meshio(mesh_from_OrderedDict(polygons, resolutions, default_resolution_max=default_resolution_max))

if show_plot:
    mesh.draw().show()
    plot_domains_with_legend(mesh)

return mesh

def fem_waveguide(mesh, n_core, n_clad, n_box, n_metal, wavelength=1.55, num_modes=2, order=2, plot=False): basis0 = Basis(mesh, ElementTriP0()) epsilon = basis0.zeros(dtype=complex)

for subdomain, n in {"core": n_core(wavelength), 
                     "box": n_box(wavelength), 
                     "clad": n_clad(wavelength),
                     "metal": n_metal(wavelength)}.items():
    epsilon[basis0.get_dofs(elements=subdomain)] = n**2

modes = compute_modes(basis0, epsilon, wavelength=wavelength, num_modes=num_modes, order=order)
if plot:
    for mode in modes:
        print(f"Effective refractive index: {mode.n_eff:.4f}")
        mode.show("E", part="real", colorbar=True)
        mode.show("E", part="imag", colorbar=True)

return modes
# return np.array([np.real(m.n_eff) for m in modes])

mesh = mesh_waveguide(show_plot=True, metal_offset=1) fem_waveguide(mesh, ri.silicon_nitride, ri.silica, ri.silica, ri.titanium_nitride, plot=False)

```

Modes(modes=(
    Mode(k: (6.177549735894596+0.4720954606369017j), n_eff:(1.5239407438286694+0.11646130556599275j))
    Mode(k: (6.167248056912366+0.4477687798488462j), n_eff:(1.5213994209738095+0.11046015274651436j))
))

```python

offsets = np.arange(0.5, 5, 0.1) n_effs = []

for offset in offsets: mesh = mesh_waveguide(metal_offset=offset) modes = fem_waveguide(mesh, ri.silicon, ri.silica, ri.silica, ri.titanium_nitride, plot=False) n_effs.append(modes[0].n_eff)

```

1. Visualize

```python alpha = 4np.pinp.abs(np.imag(n_effs))/(1.55e-6) # [1/m]

plt.figure() plt.semilogy(offsets, alpha, ".-") plt.xlabel("Metal offset (µm)") plt.ylabel("absorption coefficient (1/m)") plt.grid()

```

```python

```