Benchmarks Luminescent against Tidy3D and Lumerical FDTD using the directional coupler from Liu & Poon, arXiv:2506.16665, Sec. 3.1. The device is GDSFactory’s generic coupler: two 500 nm × 220 nm Si arms, a 236 nm gap, and a 20 µm coupling length, with SiO2 cladding above and below. Si uses a lossless Lorentzian fit to the paper’s Palik model (n = 3.4729 at 1550 nm); SiO2 is constant n = 1.4425. The domain is the device plus 1 µm margins: 42 × 6.5 × 2.22 µm³ (the paper uses 42 × 7 × 4 µm³). TE0 enters o1 (lower left) at 1550 nm with a λ/12 source bandwidth (the paper uses 20 nm). The energy shutoff is 1e-4 (1e-3 for nres ≤ 10; the paper uses 1e-5). We report the cross-port (o3) transmission, the excess loss, the solve time, and the peak memory against resolution.
Paper values (Tidy3D 2.7.7 on cloud A100 GPUs, Lumerical 2025 R1 on a 24-core CPU):
| nres | Tidy3D cross T | Lumerical cross T | Tidy3D time | Lumerical time | Lumerical memory |
|---|---|---|---|---|---|
| 6 | 69.7 % | 49.3 % | 17 s | 148 s | 0.35 GB |
| 10 | – | – | 35 s | 336 s | 0.92 GB |
| 15 | 44.8 % | 41.1 % | 66 s | 1293 s | 2.42 GB |
Setup¶
import os, time, json, threading, subprocess
import numpy as np
import psutil
import matplotlib.pyplot as plt
import gdsfactory as gf
from gdsfactory.technology import LogicalLayer, LayerLevel, LayerStack
import luminescent as lumi
gf.gpdk.PDK.activate()
nres_list = [6, 10, 15]
h_wg = 0.22
wavelength = 1.55
# bandwidth = wavelength / 4
bandwidth = wavelength / 12
wavelengths = np.linspace(1.54, 1.56, 21).tolist()
# domain margins [um]
margin = 1
zmargin = 1
zmin, zmax = -zmargin, h_wg + zmarginlumi backend: ~/Luminescent/bin/lumi
def setup(path, nres):
# Si: lossless single-Lorentzian fit to the paper's Palik model (frequency in units of c / wavelength); SiO2: constant
materials = {
"Si": lumi.material(n=3.4729, epsilon=8.36218, dispersion=[lumi.lorentzian(3.0, 0, 3.2882)]),
"SiO2": lumi.material(1.4425),
}
WG = 1, 0
layer_stack = LayerStack(
layers={
"core": LayerLevel(
layer=LogicalLayer(layer=WG),
thickness=h_wg,
zmin=0,
material="Si",
mesh_order=0,
),
}
)
# GDSFactory generic coupler: gap 0.236, length 20, dx 10, dy 4
dc = gf.components.coupler(gap=0.236, length=20)
xmin, ymin = dc.bbox_np()[0]
xmax, ymax = dc.bbox_np()[1]
bbox = [[xmin - margin, ymin - margin, zmin], [xmax + margin, ymax + margin, zmax]]
# 10 um port extensions, cropped to the domain
ext = gf.components.extend_ports(dc, length=10)
dbu = ext.kcl.dbu
arms = gf.kdb.Region(ext.begin_shapes_rec(ext.kcl.layer(*WG)))
window = gf.kdb.Region(gf.kdb.Box(*(round(v / dbu) for v in (bbox[0][0], bbox[0][1], bbox[1][0], bbox[1][1]))))
c = gf.Component()
c.add_polygon(arms & window, layer=WG)
for p in dc.ports:
c.add_port(p.name, center=p.center, width=p.width, orientation=p.orientation, layer=WG)
c.plot()
frames = [
lumi.plane_frame(
"wg",
start=[-1.2, zmin],
stop=[1.2, zmax],
wls_mode_solver=[wavelengths[0], wavelength, wavelengths[-1]],
)
]
sources = [
lumi.gf_source("o1", c, layer_stack, margin, frame="wg", wl=wavelength, bandwidth=bandwidth)
]
monitors = [lumi.gf_monitor(p, c, layer_stack, frame="wg") for p in ["o1", "o2", "o3", "o4"]]
lumi.mesh(path, c, layer_stack, materials, zmin, zmax)
lumi.setup(
path=path,
wl=wavelength,
wls=wavelengths,
materials=materials,
background="SiO2",
boundaries=["PML", "PML", "PML"],
PML_decay=[0.001, 0.001, 0.1],
bbox=bbox,
frames=frames,
sources=sources,
monitors=monitors,
nres=nres,
tmax=1000, # periods
shutoff=1e-4,
views=[lumi.view("Hz", z=h_wg / 2)],
shot_every=10,
)
return cSimulate¶
def gpu_used():
out = subprocess.run(["nvidia-smi", "--query-gpu=memory.used", "--format=csv,noheader,nounits"], capture_output=True, text=True).stdout
return sum(float(v) for v in out.split()) / 1024 # GB
def solve_with_stats(path):
"""solve, tracking wall time, peak GPU memory (above baseline) and peak solver host RSS"""
peak = {"gpu": 0.0, "host": 0.0}
base = gpu_used()
me = psutil.Process()
done = threading.Event()
def poll():
while not done.is_set():
peak["gpu"] = max(peak["gpu"], gpu_used() - base)
rss = 0
for p in me.children(recursive=True):
try:
rss += p.memory_info().rss
except psutil.Error:
pass
peak["host"] = max(peak["host"], rss / 1024**3)
time.sleep(0.5)
t = threading.Thread(target=poll)
t.start()
t0 = time.time()
try:
lumi.solve(path)
finally:
done.set()
t.join()
stats = {"runtime": time.time() - t0, "gpu_GB": peak["gpu"], "host_GB": peak["host"]}
json.dump(stats, open(os.path.join(path, "stats.json"), "w"))
return statsfor nres in nres_list:
path = os.path.join("runs", f"dc_nres{nres}")
setup(path, nres)
print(solve_with_stats(path))
using simulation folder runs/dc_nres6
========================================
backend using simulation folder runs/dc_nres6
========================================
setting up simulation...
processing geometry bodies...
generating voxels...
voxelation: 10.947417 seconds (509.27 M allocations: 20.249 GiB, 27.56% gc time, 128.57% compilation time)
Yee mode λ=0.9935: neff 2.4904
Yee mode λ=1.0: neff 2.4779
Yee mode λ=1.0065: neff 2.4654
making sources o1 ...
making monitors o1 o2 o3 o4 ...
========================================
run: runs/dc_nres6
processor: GPU
cpu threads: 48
nres: 6.0
courant: 0.9
subpixel_smoothing: 1
boundaries: [:PML :PML; :PML :PML; :PML :PML]
sources
o1: -11, -1.63, 0
monitors
o1: -10, -1.63, 0
o2: -10, 2.37, 0
o3: 30, 2.37, 0
o4: 30, -1.63, 0
original size: (566, 94, 26)
padded size: (617, 118, 44)
cell count: 3,203,464
step size: 43.0 steps/period
source duration: 3.93 periods
max time: 1,000 periods
max steps: 43,000
max load: 137,748,952,000 cell-steps
energy decay threshold: 0.001
========================================
running simulation...
accumulating dft field...
period 10, decay: 0.96, 1.49 seconds/period, 92.22 Mcells/s
period 20, decay: 0.95, 0.014 seconds/period, 9784.0 Mcells/s
period 30, decay: 0.94, 0.014 seconds/period, 9827.27 Mcells/s
period 40, decay: 0.94, 0.013 seconds/period, 10651.21 Mcells/s
period 50, decay: 0.94, 0.013 seconds/period, 10855.54 Mcells/s
period 60, decay: 0.94, 0.014 seconds/period, 9930.49 Mcells/s
period 70, decay: 0.94, 0.013 seconds/period, 10796.22 Mcells/s
period 80, decay: 0.94, 0.013 seconds/period, 10771.31 Mcells/s
period 90, decay: 0.93, 0.013 seconds/period, 10729.2 Mcells/s
period 100, decay: 0.92, 0.015 seconds/period, 9247.08 Mcells/s
period 110, decay: 0.9, 0.013 seconds/period, 10775.44 Mcells/s
period 120, decay: 0.72, 0.013 seconds/period, 10750.96 Mcells/s
period 130, decay: 0.183, 0.015 seconds/period, 9428.14 Mcells/s
period 140, decay: 0.025, 0.013 seconds/period, 10914.89 Mcells/s
period 150, decay: 0.01, 0.012 seconds/period, 11171.22 Mcells/s
period 160, decay: 0.007, 0.015 seconds/period, 9448.71 Mcells/s
period 170, decay: 0.006, 0.012 seconds/period, 11117.84 Mcells/s
period 180, decay: 0.006, 0.015 seconds/period, 9397.01 Mcells/s
period 190, decay: 0.005, 0.013 seconds/period, 10790.21 Mcells/s
period 200, decay: 0.005, 0.013 seconds/period, 10776.03 Mcells/s
period 210, decay: 0.004, 0.014 seconds/period, 9903.24 Mcells/s
period 220, decay: 0.004, 0.013 seconds/period, 10792.92 Mcells/s
period 230, decay: 0.003, 0.012 seconds/period, 11076.01 Mcells/s
period 240, decay: 0.002, 0.013 seconds/period, 10668.04 Mcells/s
period 244.09 stop on energy decay
10389.65 Mcells/s
simulation completed.
{'runtime': 137.52924180030823, 'gpu_GB': 1.3603515625, 'host_GB': 2.5383262634277344}
using simulation folder runs/dc_nres10
========================================
backend using simulation folder runs/dc_nres10
========================================
setting up simulation...
processing geometry bodies...
generating voxels...
voxelation: 27.278463 seconds (1.40 G allocations: 53.044 GiB, 35.67% gc time, 54.05% compilation time)
Yee mode λ=0.9935: neff 2.4662
Yee mode λ=1.0: neff 2.4544
Yee mode λ=1.0065: neff 2.4427
making sources o1 ...
making monitors o1 o2 o3 o4 ...
========================================
run: runs/dc_nres10
processor: GPU
cpu threads: 48
nres: 10.0
courant: 0.9
subpixel_smoothing: 1
boundaries: [:PML :PML; :PML :PML; :PML :PML]
sources
o1: -11, -1.63, 0
monitors
o1: -10, -1.63, 0
o2: -10, 2.37, 0
o3: 30, 2.37, 0
o4: 30, -1.63, 0
original size: (944, 151, 41)
padded size: (1027, 189, 68)
cell count: 13,199,004
step size: 68.0 steps/period
source duration: 3.94 periods
max time: 1,000 periods
max steps: 68,000
max load: 897,532,272,000 cell-steps
energy decay threshold: 0.001
========================================
running simulation...
accumulating dft field...
period 10, decay: 0.97, 1.57 seconds/period, 571.02 Mcells/s
period 20, decay: 0.97, 0.107 seconds/period, 8423.7 Mcells/s
period 30, decay: 0.96, 0.104 seconds/period, 8612.45 Mcells/s
period 40, decay: 0.96, 0.101 seconds/period, 8888.18 Mcells/s
period 50, decay: 0.96, 0.099 seconds/period, 9084.59 Mcells/s
period 60, decay: 0.96, 0.099 seconds/period, 9096.54 Mcells/s
period 70, decay: 0.96, 0.098 seconds/period, 9132.22 Mcells/s
period 80, decay: 0.96, 0.098 seconds/period, 9164.78 Mcells/s
period 90, decay: 0.96, 0.098 seconds/period, 9170.14 Mcells/s
period 100, decay: 0.95, 0.098 seconds/period, 9173.61 Mcells/s
period 110, decay: 0.92, 0.101 seconds/period, 8927.29 Mcells/s
period 120, decay: 0.52, 0.098 seconds/period, 9175.69 Mcells/s
period 130, decay: 0.002, 0.098 seconds/period, 9179.19 Mcells/s
period 135.53 stop on energy decay
8930.73 Mcells/s
simulation completed.
{'runtime': 157.68253374099731, 'gpu_GB': 3.6103515625, 'host_GB': 3.8725433349609375}
using simulation folder runs/dc_nres15
========================================
backend using simulation folder runs/dc_nres15
========================================
setting up simulation...
processing geometry bodies...
generating voxels...
voxelation: 39.680508 seconds (3.35 G allocations: 124.395 GiB, 33.61% gc time, 62.37% compilation time)
Yee mode λ=0.9935: neff 2.4597
Yee mode λ=1.0: neff 2.4483
Yee mode λ=1.0065: neff 2.4368
making sources o1 ...
making monitors o1 o2 o3 o4 ...
========================================
run: runs/dc_nres15
processor: GPU
cpu threads: 48
nres: 15.0
courant: 0.9
subpixel_smoothing: 1
boundaries: [:PML :PML; :PML :PML; :PML :PML]
sources
o1: -11, -1.63, 0
monitors
o1: -10, -1.63, 0
o2: -10, 2.37, 0
o3: 30, 2.37, 0
o4: 30, -1.63, 0
original size: (1414, 217, 59)
padded size: (1539, 271, 96)
cell count: 40,038,624
step size: 101.0 steps/period
source duration: 3.94 periods
max time: 1,000 periods
max steps: 101,000
max load: 4,043,901,024,000 cell-steps
energy decay threshold: 0.0001
========================================
running simulation...
accumulating dft field...
period 10, decay: 0.97, 1.96 seconds/period, 2065.48 Mcells/s
period 20, decay: 0.96, 0.56 seconds/period, 7196.84 Mcells/s
period 30, decay: 0.96, 0.56 seconds/period, 7267.09 Mcells/s
period 40, decay: 0.96, 0.55 seconds/period, 7388.42 Mcells/s
period 50, decay: 0.96, 0.53 seconds/period, 7686.33 Mcells/s
period 60, decay: 0.96, 0.53 seconds/period, 7686.16 Mcells/s
period 70, decay: 0.96, 0.53 seconds/period, 7686.1 Mcells/s
period 80, decay: 0.96, 0.53 seconds/period, 7657.71 Mcells/s
period 90, decay: 0.95, 0.53 seconds/period, 7658.56 Mcells/s
period 100, decay: 0.95, 0.53 seconds/period, 7660.89 Mcells/s
period 110, decay: 0.92, 0.53 seconds/period, 7686.09 Mcells/s
period 120, decay: 0.127, 0.53 seconds/period, 7685.75 Mcells/s
period 130, decay: 0.002, 0.53 seconds/period, 7686.39 Mcells/s
period 140, decay: 0.001, 0.53 seconds/period, 7686.17 Mcells/s
period 150, decay: 0.001, 0.53 seconds/period, 7654.03 Mcells/s
period 160, decay: 0.001, 0.54 seconds/period, 7553.68 Mcells/s
period 170, decay: 0.001, 0.53 seconds/period, 7686.14 Mcells/s
period 180, decay: 0.001, 0.53 seconds/period, 7653.88 Mcells/s
period 190, decay: 0.001, 0.53 seconds/period, 7687.95 Mcells/s
period 200, decay: 0.001, 0.53 seconds/period, 7686.03 Mcells/s
period 210, decay: 0.001, 0.53 seconds/period, 7686.28 Mcells/s
period 220, decay: 0.001, 0.53 seconds/period, 7658.04 Mcells/s
period 230, decay: 0.0, 0.53 seconds/period, 7659.09 Mcells/s
period 231.92 stop on energy decay
7614.26 Mcells/s
simulation completed.
{'runtime': 287.3348059654236, 'gpu_GB': 11.5478515625, 'host_GB': 5.112232208251953}
Results¶
wls = np.array(wavelengths)
i = np.argmin(abs(wls - wavelength))
rows = []
fig, ax = plt.subplots(1, 2, figsize=(10, 4))
for nres in [6, 10, 15]:
path = os.path.join("runs", f"dc_nres{nres}")
if not os.path.exists(os.path.join(path, "solution.json")):
continue
m = lumi.load(path)["monitors"]
a1 = m["o1"]["modes"][0]["-"]
T3 = np.abs(m["o3"]["modes"][0]["+"] / a1) ** 2 # cross
T4 = np.abs(m["o4"]["modes"][0]["+"] / a1) ** 2 # through
loss = -10 * np.log10(T3 + T4)
f = os.path.join(path, "stats.json")
st = json.load(open(f)) if os.path.exists(f) else {}
rows.append((nres, T3[i], T4[i], loss[i], st.get("runtime"), st.get("gpu_GB"), st.get("host_GB")))
ax[0].plot(wls, T3, label=f"nres {nres}")
ax[1].plot(wls, loss, label=f"nres {nres}")
fmt = lambda v, f: "–" if v is None else format(v, f)
print("nres cross T through T excess loss runtime GPU mem host mem")
for nres, t3, t4, l, rt, g, h in rows:
print(f"{nres:4d} {100*t3:6.1f} % {100*t4:7.1f} % {l:8.3f} dB {fmt(rt, '5.0f'):>5} s {fmt(g, '5.2f'):>5} GB {fmt(h, '5.2f'):>5} GB")
ax[0].set(xlabel="wavelength [um]", ylabel="cross transmittance")
ax[1].set(xlabel="wavelength [um]", ylabel="excess loss [dB]")
ax[0].legend()
plt.tight_layout()
plt.show()loading solution from runs/dc_nres6
may take a minute if simulation folder is remotely mounted
loading solution from runs/dc_nres10
may take a minute if simulation folder is remotely mounted
loading solution from runs/dc_nres15
may take a minute if simulation folder is remotely mounted
nres cross T through T excess loss runtime GPU mem host mem
6 43.6 % 51.4 % 0.223 dB 138 s 1.36 GB 2.54 GB
10 41.3 % 57.8 % 0.040 dB 158 s 3.61 GB 3.87 GB
15 43.3 % 55.8 % 0.038 dB 287 s 11.55 GB 5.11 GB
Fig. 4a comparison¶
# paper Fig. 4a, digitized
nres_paper = [6, 10, 15, 20, 25]
T_tidy3d = [0.697, 0.579, 0.448, 0.492, 0.456]
T_lumerical = [0.493, 0.451, 0.411, 0.446, 0.431]
plt.figure(figsize=(5, 3.5))
plt.plot(nres_paper, T_lumerical, "o-", color="red", label="Lumerical")
plt.plot(nres_paper, T_tidy3d, "o-", color="blue", label="Tidy3D")
plt.plot([r[0] for r in rows], [r[1] for r in rows], "o-", color="black", label="Luminescent")
plt.xlabel("nres (cells per wavelength)")
plt.ylabel("transmission")
plt.title("Cross port TE0 at 1550 nm")
plt.grid(alpha=0.3)
plt.legend()
plt.show()
Movie¶
nres_list = [6]