Slot waveguide Purcell study

Dipole above a Si3N4 slot waveguide at 780nm; Purcell factor vs. geometry.

Dry-run and batch scripts for Tidy3D simulations of a dipole above a Si3N4 slot waveguide at 780 nm.

Workflow

1. Generate the dry-run report, geometry plots, mode profiles, and cost estimates:

python -m slot_waveguide_purcell.dry_run --estimate-costs

1. Review reports/dry_run_report.html.

2. Only after approving the projected FlexCredit costs, run the billed batch:

python -m slot_waveguide_purcell.run_batch --run

1. Analyze downloaded simulation data and render the final report:

python -m slot_waveguide_purcell.analyze_results

The batch runner refuses to start any billed run with unknown estimated cost, or with estimated cost above the configured approval threshold.

Results

Dry-run preflight (baseline)

Slot Waveguide Purcell FDTD Dry Run

This is a pre-flight report. No billed FDTD solve is launched by this dry run.

Geometry and numerical assumptions

• Coordinate system: waveguide propagation is x, slot transverse direction is y, vertical stack is z.
• The dipole is Ey polarized and centered over the slot because that orientation couples to the high-field slot mode.
• The point dipole is placed 5 nm inside the n=1.8 crystal rather than exactly on the material boundary.
• The no-waveguide reference is interpreted as SiO2 substrate, 200 nm n=1.8 crystal directly on the substrate, and 300 nm PVA above.
• Purcell factor is planned as total emitted power from each slot-waveguide simulation divided by the no-waveguide reference emitted power at the same wavelength.
• Collection efficiency is planned as fundamental guided-mode power at the left plus right mode monitors divided by total emitted power through the six-surface box.
• The active grid is intentionally small: two Si3N4 heights and three slot widths at a 450 nm total waveguide footprint.

Parameter	Value
center wavelength	780 nm
wavelength span	730-830 nm
wavelength points	21
SiO2 index	1.444
Si3N4 index	2.0
crystal index	1.8
PVA index	1.5
crystal thickness	200 nm
PVA thickness	300 nm
fine mesh near slot/crystal	30 x 10 x 10 nm
minimum steps per wavelength	20
run time	2.50e-12 s
shutoff	1e-05
FlexCredit approval threshold	0.500 FC

Planned simulation sweep

Name	WG	height nm	slot nm	WG width nm	rail nm	cells	Tidy3D task name
base_no_waveguide	no	0	-	-	-	5,669,280	slot_purcell_base_no_waveguide
h150_slot050_w450	yes	150	50	450	200.0	6,429,600	slot_purcell_h150_slot050_w450
h150_slot100_w450	yes	150	100	450	175.0	6,429,600	slot_purcell_h150_slot100_w450
h150_slot150_w450	yes	150	150	450	150.0	6,429,600	slot_purcell_h150_slot150_w450
h300_slot050_w450	yes	300	50	450	200.0	7,113,600	slot_purcell_h300_slot050_w450
h300_slot100_w450	yes	300	100	450	175.0	7,113,600	slot_purcell_h300_slot100_w450
h300_slot150_w450	yes	300	150	450	150.0	7,113,600	slot_purcell_h300_slot150_w450

Projected costs

Name	estimated FlexCredit	status
base_no_waveguide	0.1419	ok
h150_slot050_w450	0.1943	ok
h150_slot100_w450	0.1841	ok
h150_slot150_w450	0.1841	ok
h300_slot050_w450	0.2139	ok
h300_slot100_w450	0.2026	ok
h300_slot150_w450	0.2026	ok

Known-cost total: 1.3235 FC

Representative geometry cross-sections

base_no_waveguide

Item	Description
simulation name	base_no_waveguide
include slot waveguide	False
wavelength grid	730-830 nm, 21 points
dipole	Ey, x=0, y=0, z=5.0 nm
substrate	SiO2, n=1.444, z < 0
crystal	n=1.8, 200 nm thick, z=0.0-200.0 nm
PVA	n=1.5, 300 nm thick
mesh override	dx=30 nm, dy=10 nm, dz=10 nm near slot/crystal

base_no_waveguide xz

base_no_waveguide yz

base_no_waveguide xy_dipole

base_no_waveguide mesh_xz

h150_slot050_w450

Item	Description
simulation name	h150_slot050_w450
include slot waveguide	True
wavelength grid	730-830 nm, 21 points
dipole	Ey, x=0, y=0, z=155.0 nm
substrate	SiO2, n=1.444, z < 0
crystal	n=1.8, 200 nm thick, z=150.0-350.0 nm
PVA	n=1.5, 300 nm thick
mesh override	dx=30 nm, dy=10 nm, dz=10 nm near slot/crystal
Si3N4	n=2.0, height=150 nm
slot width	50 nm
total waveguide footprint	450 nm
rail width	200.0 nm each
mode collection	fundamental mode at x=±2.25 um; summed over both directions

h150_slot050_w450 xz

h150_slot050_w450 yz

h150_slot050_w450 xy_dipole

h150_slot050_w450 xy_waveguide

h150_slot050_w450 mesh_xz

h150_slot050_w450 local mode profile

h150_slot100_w450

Item	Description
simulation name	h150_slot100_w450
include slot waveguide	True
wavelength grid	730-830 nm, 21 points
dipole	Ey, x=0, y=0, z=155.0 nm
substrate	SiO2, n=1.444, z < 0
crystal	n=1.8, 200 nm thick, z=150.0-350.0 nm
PVA	n=1.5, 300 nm thick
mesh override	dx=30 nm, dy=10 nm, dz=10 nm near slot/crystal
Si3N4	n=2.0, height=150 nm
slot width	100 nm
total waveguide footprint	450 nm
rail width	175.0 nm each
mode collection	fundamental mode at x=±2.25 um; summed over both directions

h150_slot100_w450 xz

h150_slot100_w450 yz

h150_slot100_w450 xy_dipole

h150_slot100_w450 xy_waveguide

h150_slot100_w450 mesh_xz

h150_slot100_w450 local mode profile

h150_slot150_w450

Item	Description
simulation name	h150_slot150_w450
include slot waveguide	True
wavelength grid	730-830 nm, 21 points
dipole	Ey, x=0, y=0, z=155.0 nm
substrate	SiO2, n=1.444, z < 0
crystal	n=1.8, 200 nm thick, z=150.0-350.0 nm
PVA	n=1.5, 300 nm thick
mesh override	dx=30 nm, dy=10 nm, dz=10 nm near slot/crystal
Si3N4	n=2.0, height=150 nm
slot width	150 nm
total waveguide footprint	450 nm
rail width	150.0 nm each
mode collection	fundamental mode at x=±2.25 um; summed over both directions

h150_slot150_w450 xz

h150_slot150_w450 yz

h150_slot150_w450 xy_dipole

h150_slot150_w450 xy_waveguide

h150_slot150_w450 mesh_xz

h300_slot050_w450

Item	Description
simulation name	h300_slot050_w450
include slot waveguide	True
wavelength grid	730-830 nm, 21 points
dipole	Ey, x=0, y=0, z=305.0 nm
substrate	SiO2, n=1.444, z < 0
crystal	n=1.8, 200 nm thick, z=300.0-500.0 nm
PVA	n=1.5, 300 nm thick
mesh override	dx=30 nm, dy=10 nm, dz=10 nm near slot/crystal
Si3N4	n=2.0, height=300 nm
slot width	50 nm
total waveguide footprint	450 nm
rail width	200.0 nm each
mode collection	fundamental mode at x=±2.25 um; summed over both directions

h300_slot050_w450 xz

h300_slot050_w450 yz

h300_slot050_w450 xy_dipole

h300_slot050_w450 xy_waveguide

h300_slot050_w450 mesh_xz

h300_slot100_w450

Item	Description
simulation name	h300_slot100_w450
include slot waveguide	True
wavelength grid	730-830 nm, 21 points
dipole	Ey, x=0, y=0, z=305.0 nm
substrate	SiO2, n=1.444, z < 0
crystal	n=1.8, 200 nm thick, z=300.0-500.0 nm
PVA	n=1.5, 300 nm thick
mesh override	dx=30 nm, dy=10 nm, dz=10 nm near slot/crystal
Si3N4	n=2.0, height=300 nm
slot width	100 nm
total waveguide footprint	450 nm
rail width	175.0 nm each
mode collection	fundamental mode at x=±2.25 um; summed over both directions

h300_slot100_w450 xz

h300_slot100_w450 yz

h300_slot100_w450 xy_dipole

h300_slot100_w450 xy_waveguide

h300_slot100_w450 mesh_xz

h300_slot100_w450 local mode profile

h300_slot150_w450

Item	Description
simulation name	h300_slot150_w450
include slot waveguide	True
wavelength grid	730-830 nm, 21 points
dipole	Ey, x=0, y=0, z=305.0 nm
substrate	SiO2, n=1.444, z < 0
crystal	n=1.8, 200 nm thick, z=300.0-500.0 nm
PVA	n=1.5, 300 nm thick
mesh override	dx=30 nm, dy=10 nm, dz=10 nm near slot/crystal
Si3N4	n=2.0, height=300 nm
slot width	150 nm
total waveguide footprint	450 nm
rail width	150.0 nm each
mode collection	fundamental mode at x=±2.25 um; summed over both directions

h300_slot150_w450 xz

h300_slot150_w450 yz

h300_slot150_w450 xy_dipole

h300_slot150_w450 xy_waveguide

h300_slot150_w450 mesh_xz

Expected post-run outputs

• Spectral total emitted flux for the no-waveguide reference.
• Spectral total emitted flux for every slot-waveguide geometry.
• Spectral guided power into mode 0 at left and right mode monitors.
• Coupling efficiency versus wavelength for each geometry.
• Purcell factor versus wavelength for each geometry.
• 2D heatmaps at 780 nm for Purcell factor and coupling efficiency across height and slot width.
• Field-intensity cross-sections for the best coupling-efficiency geometry.

Final report

Slot Waveguide Purcell FDTD Report

Center-wavelength summary is reported at 780.0 nm.

Summary

Name	total flux	guided power	coupling efficiency	Purcell	billed cost
base_no_waveguide	4419.2	-	-	1.0000	0.0250 FC
h150_slot010_w450	10890	3315.8	0.3045	2.4642	0.0250 FC
h150_slot025_w450	10306	2676.5	0.2597	2.3321	0.0282 FC
h150_slot050_w450	8447.5	1757.4	0.2080	1.9115	0.0250 FC
h150_slot100_w450	6364.3	994.06	0.1562	1.4401	0.0250 FC
h150_slot150_w450	5371.7	687.78	0.1280	1.2155	0.0250 FC
h300_slot010_w450	11348	3250.7	0.2865	2.5679	0.0253 FC
h300_slot025_w450	10703	2831	0.2645	2.4219	0.0311 FC
h300_slot050_w450	8717.4	1873.1	0.2149	1.9726	0.0250 FC
h300_slot100_w450	6575.5	1007.3	0.1532	1.4879	0.0250 FC
h300_slot150_w450	5593.7	677.39	0.1211	1.2658	0.0250 FC

Spectral Metrics

Coupling efficiency versus wavelength

Purcell factor versus wavelength

Sweep Heatmaps

Coupling efficiency heatmap at 780 nm

Purcell factor heatmap at 780 nm

Field Intensity Cross-Sections

No-waveguide reference

Base reference |E|^2 at dipole plane

Base reference |E|^2 x-z center plane

Base reference |E|^2 y-z center plane

Best coupling geometry

Best coupling geometry at 780 nm: h150_slot010_w450.

Best-coupling |E|^2 at dipole plane

Best-coupling |E|^2 at waveguide plane

Best-coupling |E|^2 x-z center plane

Best-coupling |E|^2 y-z center plane

Notes

• Coupling efficiency sums mode 0 power collected by the left and right mode monitors and divides by the six-surface emitted flux.
• Purcell factor divides each emitted flux spectrum by the no-waveguide reference emitted flux spectrum.
• The raw arrays are saved in data/metrics.npz.

Downloads

FDTD simulation study only -- no GDS/STL deliverable files exist in this tree.

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Source: nanophotonic_devices/cavity_purcell/slot_waveguide_purcell_v1/