add coplanar wavegudie example

docs/_toc.yml

@@ -42,6 +42,7 @@ parts:
     - file: photonics/examples/refinement.py
     - file: photonics/examples/propagation_loss.py
     - file: electronics/examples/capacitor.py
+    - file: electronics/examples/coplanar_waveguide.py
 
   - caption: Julia Examples
     chapters:

docs/electronics/examples/coplanar_waveguide.py

@@ -0,0 +1,140 @@
+# ---
+# jupyter:
+#   jupytext:
+#     formats: py:percent,md:myst
+#     text_representation:
+#       extension: .py
+#       format_name: percent
+#       format_version: '1.3'
+#       jupytext_version: 1.15.0
+#   kernelspec:
+#     display_name: Python 3
+#     name: python3
+# ---
+# %% [markdown]
+# # Coplanar waveguide
+
+# In this example we calculate effective epsilon of the coplanar waveguides from {cite}`Jansen1978`
+
+# %% tags=["hide-input"]
+
+from collections import OrderedDict
+
+import matplotlib.pyplot as plt
+import numpy as np
+import scipy.constants
+import shapely
+import shapely.ops
+from shapely.geometry import LineString, box
+from skfem import Basis, ElementTriP0
+from skfem.io.meshio import from_meshio
+from tqdm import tqdm
+
+from femwell.maxwell.waveguide import compute_modes
+from femwell.mesh import mesh_from_OrderedDict
+
+
+# %%
+def mesh_waveguide_1(filename, wsim, hclad, hsi, wcore_1, wcore_2, hcore, gap):
+    core_l = box(-wcore_1 - gap / 2, -hcore / 2, -gap / 2, hcore / 2)
+    core_r = box(gap / 2, -hcore / 2, wcore_2 + gap / 2, hcore / 2)
+    gap_b = box(-gap / 2, -hcore / 2, gap / 2, hcore / 2)
+    clad = box(-wsim / 2, -hcore / 2, wsim / 2, -hcore / 2 + hclad)
+    silicon = box(-wsim / 2, -hcore / 2, wsim / 2, -hcore / 2 - hsi)
+
+    combined = shapely.ops.unary_union([core_l, core_r, clad, silicon])
+
+    polygons = OrderedDict(
+        surface=LineString(combined.exterior),
+        interface=LineString(
+            [
+                (-wcore_1 - gap, -hcore / 2),
+                (wcore_2 + gap, -hcore / 2),
+            ]
+        ),
+        core_l_interface=core_l.exterior,
+        core_l=core_l,
+        core_r_interface=core_r.exterior,
+        core_r=core_r,
+        gap_b=gap_b,
+        clad=clad,
+        silicon=silicon,
+    )
+
+    resolutions = dict(
+        core_r={"resolution": 0.004, "distance": 2},
+        core_l={"resolution": 0.004, "distance": 2},
+        gap_b={"resolution": 0.004, "distance": 2},
+        silicon={"resolution": 0.1, "distance": 5},
+        interface={"resolution": 0.2, "distance": 1},
+    )
+
+    return mesh_from_OrderedDict(
+        polygons, resolutions, filename=filename, default_resolution_max=30
+    )
+
+
+# %% tags=["hide-output"]
+frequencies = np.linspace(1e9, 18e9, 18)
+gaps = [0.02, 0.06, 0.1, 0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2]
+epsilon_effs = np.zeros((len(gaps), len(frequencies), 2), dtype=complex)
+
+for i, gap in enumerate(tqdm(gaps)):
+    for j, frequency in enumerate(tqdm(frequencies, leave=False)):
+        mesh = from_meshio(
+            mesh_waveguide_1(
+                filename="mesh.msh",
+                wsim=30,
+                hclad=100,
+                hsi=0.64,
+                wcore_1=0.6,
+                wcore_2=0.6,
+                hcore=0.005,
+                gap=gap,
+            )
+        )
+        mesh = mesh.scaled((1e-3,) * 2)
+
+        basis0 = Basis(mesh, ElementTriP0(), intorder=4)
+        epsilon = basis0.zeros().astype(complex)
+        epsilon[basis0.get_dofs(elements="silicon")] = 9.9 + 0.0005
+        epsilon[basis0.get_dofs(elements="clad")] = 1.0
+        epsilon[basis0.get_dofs(elements="gap_b")] = 1.0
+        epsilon[basis0.get_dofs(elements="core_l")] = (
+            1 - 1j * 1 / (18e-6 * 1e-3) / scipy.constants.epsilon_0 / frequency
+        )
+        epsilon[basis0.get_dofs(elements="core_r")] = (
+            1 - 1j * 1 / (18e-6 * 1e-3) / scipy.constants.epsilon_0 / frequency
+        )
+        # basis0.plot(np.real(epsilon), colorbar=True).show()
+
+        modes = compute_modes(
+            basis0,
+            epsilon,
+            wavelength=scipy.constants.speed_of_light / frequency,
+            mu_r=1,
+            num_modes=2,
+            metallic_boundaries=True,
+        )
+        print("effective epsilons", modes.n_effs**2)
+        modes[0].show("E", part="real", plot_vectors=True, colorbar=True)
+        modes[1].show("E", part="real", plot_vectors=True, colorbar=True)
+
+        epsilon_effs[i, j] = modes.n_effs**2
+
+# %% tags=["hide-input"]
+plt.xlabel("Frequency / Ghz")
+plt.ylabel("Effective dielectric constant")
+
+for i, gap in enumerate(gaps):
+    plt.plot(frequencies / 1e9, epsilon_effs[i, :, 0].real)
+    plt.annotate(
+        xy=(frequencies[-1] / 1e9, epsilon_effs[i, :, 0].real[-1]), text=str(gap), va="center"
+    )
+
+    plt.plot(frequencies / 1e9, epsilon_effs[i, :, 1].real)
+    plt.annotate(
+        xy=(frequencies[-1] / 1e9, epsilon_effs[i, :, 1].real[-1]), text=str(gap), va="center"
+    )
+
+plt.show()

docs/references.bib

@@ -328,3 +328,17 @@ @article{Klenner2016
   month         = may,
   pages         = {11043}
 }
+@article{Jansen1978,
+  title         = {High-Speed Computation of Single and Coupled Microstrip Parameters Including Dispersion,  High-Order Modes,  Loss and Finite Strip Thickness},
+  volume        = {26},
+  issn          = {0018-9480},
+  url           = {http://dx.doi.org/10.1109/TMTT.1978.1129316},
+  doi           = {10.1109/tmtt.1978.1129316},
+  number        = {2},
+  journal       = {IEEE Transactions on Microwave Theory and Techniques},
+  publisher     = {Institute of Electrical and Electronics Engineers (IEEE)},
+  author        = {Jansen,  R.H.},
+  year          = {1978},
+  month         = feb,
+  pages         = {75–82}
+}