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Finite-element mode solver

Finite-element mode solver#

You can mesh any component cross-section and solve the PDEs thanks to femwell mode - solver.

Unlike other mode solvers, this actually uses the component geometry instead of a hardcoded geometry.

You can directly compute the modes of a Gdsfactory cross-section (internally, it defines a “uz” mesh perpendicular to a straight component with the provided cross-section).

You can also downsample layers from the LayerStack, and modify both the cross-section and LayerStack prior to simulation to change the geometry. You can also define refractive indices on the active PDK.

try:
  import google.colab
  is_running_on_colab = True
  !pip install gdsfactory gplugins[femwell] > /dev/null
  !apt install python3-gmsh gmsh > /dev/null
  
except ImportError:
  is_running_on_colab = False

import matplotlib.pyplot as plt
import gdsfactory as gf
from tqdm.auto import tqdm
import numpy as np

from gplugins.femwell.mode_solver import compute_cross_section_modes
from gdsfactory.technology import LayerStack
from gdsfactory.cross_section import rib
from gdsfactory.generic_tech import LAYER_STACK

from skfem.io.meshio import from_meshio

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

import sys
import logging
from rich.logging import RichHandler
import gdsfactory as gf
from gdsfactory.generic_tech import get_generic_pdk

gf.config.rich_output()
PDK = get_generic_pdk()
PDK.activate()

logger = logging.getLogger()
logger.removeHandler(sys.stderr)
logging.basicConfig(level="WARNING", datefmt="[%X]", handlers=[RichHandler()])

filtered_layer_stack = LayerStack(
    layers={
        k: LAYER_STACK.layers[k]
        for k in (
            "core",
            "clad",
            "slab90",
            "box",
        )
    }
)

filtered_layer_stack.layers[
    "core"
].thickness = 0.22  # Perturb the layer_stack before simulating

filtered_layer_stack.layers[
    "slab90"
].thickness = 0.09  # Perturb the layer_stack before simulating

resolutions = {
    "core": {"resolution": 0.02, "distance": 2},
    "clad": {"resolution": 0.2, "distance": 1},
    "box": {"resolution": 0.2, "distance": 1},
    "slab90": {"resolution": 0.05, "distance": 1},
}

modes = compute_cross_section_modes(
    cross_section=rib(width=0.6),
    layer_stack=filtered_layer_stack,
    wavelength=1.55,
    num_modes=4,
    resolutions=resolutions,
)

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Info    : Done meshing 1D (Wall 0.0161029s, CPU 0.046674s)
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Info    : Done meshing 2D (Wall 0.0904249s, CPU 0.216828s)
Info    : 6657 nodes 13668 elements
Info    : Writing 'mesh.msh'...
Info    : Done writing 'mesh.msh'
Info    : Writing '/tmp/tmp2bm3dt2j/mesh.msh'...
Info    : Done writing '/tmp/tmp2bm3dt2j/mesh.msh'

2024-03-09 00:44:02.711 | WARNING  | gdsfactory.pdk:get_material_index:602 - UserWarning: get_material_index is deprecated

/opt/hostedtoolcache/Python/3.11.8/x64/lib/python3.11/site-packages/gdsfactory/pdk.py:602: UserWarning: get_material_index is deprecated
  warnings.warn("get_material_index is deprecated")

The solver returns the list of modes

mode = modes[0]
mode.show(mode.E.real, colorbar=True, direction="x")



../_images/f2e921ba093c46c7fc3d5dd8f01cf7fa4697a094606cebf331cae9a930a5ceff.png





You can use them as inputs to other femwell mode solver functions to inspect or analyze the modes:






print(modes[0].te_fraction)









0.9901230355084943











Sweep waveguide width#






widths = np.linspace(0.2, 2, 10)
num_modes = 4
all_neffs = np.zeros((widths.shape[0], num_modes))
all_te_fracs = np.zeros((widths.shape[0], num_modes))


for i, width in enumerate(tqdm(widths)):
    modes = compute_cross_section_modes(
        cross_section=gf.cross_section.strip(width=width),
        layer_stack=filtered_layer_stack,
        wavelength=1.55,
        num_modes=num_modes,
        resolutions=resolutions,
        wafer_padding=2,
        solver="scipy",
    )
    all_neffs[i] = np.real([mode.n_eff for mode in modes])
    all_te_fracs[i, :] = [mode.te_fraction for mode in modes]









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all_neffs = np.real(all_neffs)
plt.xlabel("Width of waveguide  µm")
plt.ylabel("Effective refractive index")
plt.ylim(1.444, np.max(all_neffs) + 0.1 * (np.max(all_neffs) - 1.444))
for lams, te_fracs in zip(all_neffs.T, all_te_fracs.T):
    plt.plot(widths, lams, c='k')
    plt.scatter(widths, lams, c=te_fracs, cmap="cool")
plt.colorbar().set_label("TE fraction")











../_images/e595e2dad33b3a3efa9149c54f1c1bfffe29d43bcd6bb2759bdeb96570fdb9e4.png









    
    

                

              

              
              
              
              
                
              
            

            
            
              
                



  

  

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