import gdsfactory as gf
from qpdk import PDK, cells
from qpdk.cells.airbridge import cpw_with_airbridges
from qpdk.tech import LAYER, route_bundle_sbend_cpw
PDK.activate()
@gf.cell
def resonator_compact(coupling_gap: float = 20.0) -> gf.Component:
"""Compact coupled resonator with S-bend CPW routes."""
c = gf.Component()
res = c << cells.resonator_coupled(
coupling_straight_length=300, coupling_gap=coupling_gap
)
res.movex(-res.size_info.width / 4)
left = c << cells.straight()
right = c << cells.straight()
w = res.size_info.width + 100
left.move((-w, 0))
right.move((w, 0))
route_bundle_sbend_cpw(
c,
[left["o2"], right["o1"]],
[res["coupling_o1"], res["coupling_o2"]],
cross_section=cpw_with_airbridges(
airbridge_spacing=250.0, airbridge_padding=20.0
),
)
c.kdb_cell.shapes(LAYER.SIM_AREA).insert(c.bbox().enlarged(0, 100))
c.add_port(name="o1", port=left["o1"])
c.add_port(name="o2", port=right["o2"])
return c
component = resonator_compact(coupling_gap=15.0)
_c = component.copy()
_c.draw_ports()
_c
/home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/gdsfactory/components/bends/bend_s.py:68: UserWarning: {'width': 10.0} ignored for cross_section 'coplanar_waveguide'
xs = gf.get_cross_section(cross_section, width=width)

QPDK Coupled Resonator — Driven Simulation¶
This notebook builds a compact coupled resonator from QPDK cells, converts etch layers to conductor geometry, and runs a Palace driven simulation to extract S-parameters and visualize the electric field at resonance (~7.78 GHz).
Palace is an open-source 3D electromagnetic simulator supporting eigenmode, driven (S-parameter), and electrostatic simulations.
Requirements:
- Quantum PDK:
uv pip install qpdk - GDSFactory+ account for cloud simulation
Convert QPDK etch layers to conductor geometry¶
import warnings
import klayout.db as kdb
from qpdk.tech import LAYER as QPDK_LAYER
from gsim.common.polygon_utils import decimate
sim_area_layer = (QPDK_LAYER.SIM_AREA[0], QPDK_LAYER.SIM_AREA[1])
etch_layer = (QPDK_LAYER.M1_ETCH[0], QPDK_LAYER.M1_ETCH[1])
CPW_LAYERS = {"SUBSTRATE": (1, 0), "SUPERCONDUCTOR": (2, 0), "VACUUM": (3, 0)}
layout = component.kdb_cell.layout()
sim_region = kdb.Region(
component.kdb_cell.begin_shapes_rec(layout.layer(*sim_area_layer))
)
etch_region = kdb.Region(component.kdb_cell.begin_shapes_rec(layout.layer(*etch_layer)))
etch_polys = decimate(list(etch_region.each()))
etch_region = kdb.Region()
for poly in etch_polys:
etch_region.insert(poly)
if sim_region.is_empty():
warnings.warn("No polygons found on SIM_AREA", stacklevel=2)
if etch_region.is_empty():
warnings.warn("No polygons found on M1_ETCH", stacklevel=2)
conductor_region = sim_region - etch_region
etched = gf.Component("etched_component")
el = etched.kdb_cell.layout()
for name, region in [
("SUPERCONDUCTOR", conductor_region),
("SUBSTRATE", sim_region),
("VACUUM", sim_region),
]:
idx = el.layer(*CPW_LAYERS[name])
etched.kdb_cell.shapes(idx).insert(region)
for port in component.ports:
etched.add_port(name=port.name, port=port)
etched

Configure simulation¶
from gsim.common.stack import Layer, LayerStack
from gsim.common.stack.materials import MATERIALS_DB
from gsim.palace import DrivenSim
# Build a CPW stack matching the etched component layers
substrate_thickness = 500
vacuum_thickness = 500
stack = LayerStack(pdk_name="qpdk")
stack.layers["SUBSTRATE"] = Layer(
name="SUBSTRATE",
gds_layer=(1, 0),
zmin=0.0,
zmax=substrate_thickness,
thickness=substrate_thickness,
material="sapphire",
layer_type="dielectric",
)
stack.layers["SUPERCONDUCTOR"] = Layer(
name="SUPERCONDUCTOR",
gds_layer=(2, 0),
zmin=substrate_thickness,
zmax=substrate_thickness,
thickness=0,
material="aluminum",
layer_type="conductor",
)
stack.layers["VACUUM"] = Layer(
name="VACUUM",
gds_layer=(3, 0),
zmin=substrate_thickness,
zmax=substrate_thickness + vacuum_thickness,
thickness=vacuum_thickness,
material="vacuum",
layer_type="dielectric",
)
stack.dielectrics = [
{
"name": "substrate",
"zmin": 0.0,
"zmax": substrate_thickness,
"material": "sapphire",
},
{
"name": "vacuum",
"zmin": substrate_thickness,
"zmax": substrate_thickness + vacuum_thickness,
"material": "vacuum",
},
]
stack.materials = {
"sapphire": MATERIALS_DB["sapphire"].to_dict(),
"aluminum": MATERIALS_DB["aluminum"].to_dict(),
"vacuum": MATERIALS_DB["vacuum"].to_dict(),
}
sim = DrivenSim()
sim.set_geometry(etched)
sim.set_stack(stack)
sim.add_cpw_port("o1", layer="SUPERCONDUCTOR", s_width=10.0, gap_width=6.0, offset=2.5)
sim.add_cpw_port("o2", layer="SUPERCONDUCTOR", s_width=10.0, gap_width=6.0, offset=2.5)
sim.set_driven(fmin=7.75e9, fmax=7.8e9, num_points=300, save_fields_at=[7.78e9])
save_fields_at: 7.78 GHz snapped to 7.78 GHz (nearest sample point)
sim.set_output_dir("./sim_qpdk_resonator")
sim.mesh(preset="default")
sim.plot_mesh(show_groups=["superconductor", "P", "sapphire", "vacuum"])
Exception in callback Task.__step()
handle: <Handle Task.__step()>
Traceback (most recent call last):
File "/home/bench/prg/mambaforge/lib/python3.12/asyncio/events.py", line 88, in _run
self._context.run(self._callback, *self._args)
RuntimeError: cannot enter context: <_contextvars.Context object at 0x7f9bdc50f4c0> is already entered
Exception in callback Task.__step()
handle: <Handle Task.__step()>
Traceback (most recent call last):
File "/home/bench/prg/mambaforge/lib/python3.12/asyncio/events.py", line 88, in _run
self._context.run(self._callback, *self._args)
RuntimeError: cannot enter context: <_contextvars.Context object at 0x7f9bdc50f4c0> is already entered
Exception in callback Task.__step()
handle: <Handle Task.__step()>
Traceback (most recent call last):
File "/home/bench/prg/mambaforge/lib/python3.12/asyncio/events.py", line 88, in _run
self._context.run(self._callback, *self._args)
RuntimeError: cannot enter context: <_contextvars.Context object at 0x7f9bdc50f4c0> is already entered
Exception in callback Task.__step()
handle: <Handle Task.__step()>
Traceback (most recent call last):
File "/home/bench/prg/mambaforge/lib/python3.12/asyncio/events.py", line 88, in _run
self._context.run(self._callback, *self._args)
RuntimeError: cannot enter context: <_contextvars.Context object at 0x7f9bdc50f4c0> is already entered
Exception in callback Task.__step()
handle: <Handle Task.__step()>
Traceback (most recent call last):
File "/home/bench/prg/mambaforge/lib/python3.12/asyncio/events.py", line 88, in _run
self._context.run(self._callback, *self._args)
RuntimeError: cannot enter context: <_contextvars.Context object at 0x7f9bdc50f4c0> is already entered
Task was destroyed but it is pending!
task: <Task pending name='Task-6' coro=<_async_in_context.<locals>.run_in_context() done, defined at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/utils.py:57> wait_for=<Task pending name='Task-8' coro=<Kernel.shell_main() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/kernelbase.py:597> cb=[Task.__wakeup()]> cb=[ZMQStream._run_callback.<locals>._log_error() at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/zmq/eventloop/zmqstream.py:563]>
/home/bench/prg/mambaforge/lib/python3.12/logging/__init__.py:170: RuntimeWarning: coroutine 'Kernel.shell_main' was never awaited
currentframe = lambda: sys._getframe(1)
RuntimeWarning: Enable tracemalloc to get the object allocation traceback
Task was destroyed but it is pending!
task: <Task pending name='Task-8' coro=<Kernel.shell_main() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/kernelbase.py:597> cb=[Task.__wakeup()]>
Task was destroyed but it is pending!
task: <Task pending name='Task-9' coro=<_async_in_context.<locals>.run_in_context() done, defined at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/utils.py:57> wait_for=<Task pending name='Task-10' coro=<Kernel.shell_main() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/kernelbase.py:597> cb=[Task.__wakeup()]> cb=[ZMQStream._run_callback.<locals>._log_error() at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/zmq/eventloop/zmqstream.py:563]>
Task was destroyed but it is pending!
task: <Task pending name='Task-10' coro=<Kernel.shell_main() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/kernelbase.py:597> cb=[Task.__wakeup()]>
Task was destroyed but it is pending!
task: <Task pending name='Task-11' coro=<_async_in_context.<locals>.run_in_context() done, defined at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/utils.py:57> wait_for=<Task pending name='Task-12' coro=<Kernel.shell_main() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/kernelbase.py:597> cb=[Task.__wakeup()]> cb=[ZMQStream._run_callback.<locals>._log_error() at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/zmq/eventloop/zmqstream.py:563]>
Task was destroyed but it is pending!
task: <Task pending name='Task-12' coro=<Kernel.shell_main() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/kernelbase.py:597> cb=[Task.__wakeup()]>
Exception in callback Task.__step()
handle: <Handle Task.__step()>
Traceback (most recent call last):
File "/home/bench/prg/mambaforge/lib/python3.12/asyncio/events.py", line 88, in _run
self._context.run(self._callback, *self._args)
RuntimeError: cannot enter context: <_contextvars.Context object at 0x7f9bdc50f4c0> is already entered
Task was destroyed but it is pending!
task: <Task pending name='Task-14' coro=<Kernel.shell_main() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/kernelbase.py:597> cb=[Task.__wakeup()]>
/home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/trame_vtk/modules/vtk/serializers/helpers.py:29: RuntimeWarning: coroutine 'Kernel.shell_main' was never awaited
data[idx * nb_components : (idx + 1) * nb_components]
RuntimeWarning: Enable tracemalloc to get the object allocation traceback
Task was destroyed but it is pending!
task: <Task pending name='Task-13' coro=<_async_in_context.<locals>.run_in_context() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/utils.py:60> wait_for=<Task pending name='Task-14' coro=<Kernel.shell_main() running at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/ipykernel/kernelbase.py:597> cb=[Task.__wakeup()]> cb=[ZMQStream._run_callback.<locals>._log_error() at /home/bench/dev/gds/dev/gsim/.venv/lib/python3.12/site-packages/zmq/eventloop/zmqstream.py:563]>
Widget(value='<iframe src="http://localhost:34817/index.html?ui=P_0x7f9b01f38c50_0&reconnect=auto" class="pyvi…
palace-9690f793 completed 4m 38s
Extracting results.tar.gz...
Downloaded 29 files to /home/bench/dev/gds/dev/gsim/nbs/sim-data-palace-9690f793
Port mapping: Port 1: o1, Port 2: o2

Port mapping: Port 1: o1, Port 2: o2

Field visualization — top view at conductor layer¶
from pathlib import Path
import numpy as np
import pyvista as pv
from scipy.interpolate import griddata
pv.OFF_SCREEN = True
results_dir = Path(results.files["port-S.csv"]).parent
# Find the resonance frequency from S21 minimum
res_idx = np.argmin(results.s21.db)
freq_ghz = results.freq[res_idx]
print(f"Resonance at {freq_ghz:.4f} GHz (S21 = {results.s21.db[res_idx]:.1f} dB)")
# Extract quality factor from the resonance dip
s21_db = results.s21.db
s21_mag = 10 ** (s21_db / 20.0)
# Method 1: -3 dB bandwidth (half-power points)
s21_min_mag = s21_mag[res_idx]
baseline = np.median(s21_mag) # transmission away from resonance
dip_depth = baseline - s21_min_mag
half_depth = s21_min_mag + dip_depth / 2
half_power_db = 20 * np.log10(half_depth)
# Find the left and right half-power indices
left_idx = np.argmin(np.abs(s21_db[:res_idx] - half_power_db))
right_idx = res_idx + np.argmin(np.abs(s21_db[res_idx:] - half_power_db))
f_left = results.freq[left_idx]
f_right = results.freq[right_idx]
bw_ghz = f_right - f_left
Q_bw = freq_ghz / bw_ghz if bw_ghz > 0 else np.inf
print(f"-3 dB bandwidth: {bw_ghz:.6f} GHz")
print(f"Loaded quality factor Q ~ {Q_bw:.0f}")
# Method 2: Lorentzian fit to |S21| for refined Q estimate
from scipy.optimize import curve_fit
def lorentzian_dip(f, f0, Q, dip_depth, baseline):
"""Lorentzian dip: baseline - dip_depth / (1 + (2*Q*(f-f0)/f0)**2)"""
return baseline - dip_depth / (1 + (2 * Q * (f - f0) / f0) ** 2)
freq = results.freq
mask = np.abs(freq - freq_ghz) < 0.01 # ±10 MHz fit window
if mask.sum() > 5:
popt, pcov = curve_fit(
lorentzian_dip,
freq[mask],
s21_mag[mask],
p0=[freq_ghz, Q_bw, dip_depth, baseline],
bounds=(
[freq_ghz - 0.01, 100, 0, 0],
[freq_ghz + 0.01, 1e6, 2 * baseline, 2 * baseline],
),
)
f0_fit, Q_fit, dip_fit, base_fit = popt
Q_err = np.sqrt(np.diag(pcov))[1]
print(f"Lorentzian fit: f0 = {f0_fit:.4f} GHz, Q = {Q_fit:.0f} ± {Q_err:.0f}")
else:
print("Insufficient points for Lorentzian fit.")
# Load volume field data
vol_dir = results_dir / "paraview/driven/excitation_1"
vol_path = sorted(vol_dir.rglob("*.pvtu"))[-1]
vol = pv.read(str(vol_path))
print(f"Volume: {vol.n_points:,} points, {vol.n_cells:,} cells")
Resonance at 7.7768 GHz (S21 = -1.2 dB)
-3 dB bandwidth: 0.006689 GHz
Loaded quality factor Q ~ 1163
Lorentzian fit: f0 = 7.7767 GHz, Q = 1059 ± 5
Volume: 1,366,840 points, 136,684 cells
import matplotlib.pyplot as plt
# Slice volume at conductor plane (z = substrate_thickness)
vol_slice = vol.slice(normal="z", origin=(0, 0, substrate_thickness))
# Build interpolation grid from data bounds
vpts = vol_slice.points
x_pad, y_pad = 5, 5
xi = np.linspace(vpts[:, 0].min() - x_pad, vpts[:, 0].max() + x_pad, 800)
yi = np.linspace(vpts[:, 1].min() - y_pad, vpts[:, 1].max() + y_pad, 400)
Xi, Yi = np.meshgrid(xi, yi)
def plot_topview(pts, data, title, cmap="turbo"):
gi = griddata(pts[:, :2], data, (Xi, Yi), method="linear")
fig, ax = plt.subplots(figsize=(14, 6))
vmax = np.nanpercentile(gi, 98)
im = ax.pcolormesh(Xi, Yi, gi, cmap=cmap, shading="auto", vmin=0, vmax=vmax)
fig.colorbar(im, ax=ax, fraction=0.046, pad=0.02)
ax.set_title(title)
ax.set_aspect("equal")
ax.set_xlabel("x (µm)")
ax.set_ylabel("y (µm)")
valid = ~np.isnan(gi)
if valid.any():
rows = np.any(valid, axis=1)
cols = np.any(valid, axis=0)
ax.set_xlim(xi[cols][0], xi[cols][-1])
ax.set_ylim(yi[rows][0], yi[rows][-1])
fig.tight_layout(pad=0.5)
plt.show()
plot_topview(
vpts,
np.linalg.norm(vol_slice.point_data["E_real"], axis=1),
f"Electric field |E| at {freq_ghz:.4f} GHz — (V/m)",
)
