Fiber sheath v1¶

Passive self-aligning Nanoscribe fiber sheath that drops onto an on-chip lens.

A Nanoscribe (IP-S) test structure for a passive, self-aligning fiber sheath that drops onto an on-chip lens. The fiber gets pushed into the sheath, lands on three index-matching bumps, and is held against the lens with a small air gap underneath. Optical glue is later applied; the bumps keep the fiber from sitting on a stray particle and the membrane keeps the glue off the lens.

                              ___________
                            /             \         <- funnel  (15..345 deg)
                           |               |           ID 124 -> 250, wall 20 um
                           |               |           height 50 um
                            \             /
                            +-------------+
                            |   fiber     |        <- sheath top (15..345 deg)
                            |   (125 OD)  |           ID 124, OD 250
                            |             |           height 750 um
                            |             |
                            +-------------+
                            |             |        <- sheath bottom
                            |             |           ID 130, OD 250
                            |             |           height 50 um
                            +-------------+
       . . . o . . . . . . . o . . . . . . . o   <- 3 bumps (r=50, hemi r=3)
       =============================================  <- membrane (2 um, OD 250)
       |xxx|     |xxx|     |xxx|     |xxx|     |xxx|  <- base ring segments
       |xxx|     |xxx|     |xxx|     |xxx|     |xxx|     0..60, 120..180, 240..300
       ___________ /\ ____________                       ID 75, OD 250, h ~ 8 um
                  /  \ <- lens (Cartesian-oval aspheric, apex 5 um)
       ============================================  <- PEC (substrate / mirror)
       z = 0

Files¶

generate_geometry.py — designs the lens and emits 3 STL files + geometry_params.json + lens_profile.npz.
simulate_optics.py — runs a Tidy3D FDTD simulation of the lens + membrane + fiber + PEC stack and writes a fresh timestamped report in reports/.
stl/region1_lens_core.stl — high-resolution writing region. r ≤ 75 um, z ∈ [-0.5, 13] um. Contains the lens, the inner part of the 3-segment base ring, the inner part of the membrane, and the three bumps.
stl/region2_inner_sheath.stl — no-stitching writing region. r ≤ 75 um, z ≥ 13 um. Contains the inner wall of the sheath bore (where the fiber lives).
stl/region3_outer_support.stl — bulk support infrastructure. Everything outside r = 75 um for all z.

The split is sized to the ~150 um Nanoscribe writing field. Write order on the tool: region 1 first (highest resolution, the lens), region 2 second (no stitching across the optical bore), region 3 last (support that may be stitched freely).

Geometry parameters (microns / degrees)¶

part	parameter	value
Lens	apex height	7.0
Lens	shape	aplanatic hyperboloid (K = −n², R = h_apex·(n−1))
Lens	outer radius (design)	≈ 10.6
Lens	gap above the apex	3.0
Lens	apparent fiber face (in air)	≈ 13.31
Base ring	inner / outer diameter	75 / 250
Base ring	height	10.0
Base ring	arc segments	0–60°, 120–180°, 240–300°
Membrane	thickness	2.0
Membrane	outer diameter	250
Bumps	hemisphere radius	3.0
Bumps	orbit radius / angles	50 / 30°, 150°, 270°
Sheath gap	angular	30° (sheath spans 15–345°)
Sheath bottom	ID / OD / height	130 / 250 / 50
Sheath top	ID / OD / height	124 / 250 / 750
Funnel	ID (bottom → top)	124 → 250
Funnel	wall thickness / height	20 / 50
Total height	top of funnel above PEC	860

Indices (780 nm): IP-S resin n = 1.51, air n = 1.0. Fiber is Thorlabs 630HP at 780 nm: 125 µm clad, 3.5 µm core, NA = 0.12 (n_core 1.4583, n_clad 1.4533), MFD ≈ 5.4 µm. (Change FIBER_CORE_RADIUS_UM, N_FIBER_CORE, N_FIBER_CLAD in generate_geometry.py to target a different fiber.)

The sheath slit spans 15°–45° in azimuth (a 30° gap), so the tube wall covers 45°–375° (i.e. wraps past 0°). The gap sits directly over the 0°–60° base-ring spoke for mechanical support.

Running it¶

# from this directory
pip install trimesh manifold3d scipy tidy3d

python generate_geometry.py     # -> stl/*.stl, geometry_params.json, lens_profile.npz
python simulate_optics.py       # -> reports/report_YYYYMMDD_HHMMSS.md + figures/

simulate_optics.py submits one FDTD job to the Tidy3D cloud per invocation. Each run writes a fresh report_<timestamp>.md — re-runs never overwrite a prior report. Override knobs via environment variables:

variable	default	meaning
`SHEATH_WL0`	1.550	center wavelength (um)
`SHEATH_BW`	0.1	spectral bandwidth (um)
`SHEATH_NWL`	41	number of wavelength samples
`SHEATH_MIN_STEPS`	14	minimum grid cells per wavelength
`SHEATH_RUN_TIME`	6e-13	FDTD run time, seconds
`SHEATH_SIMXY`	30.0	transverse FDTD window (um)
`SHEATH_FIBLEN`	15.0	fiber stub length above the face (um)
`SHEATH_NOTES`	""	free-form notes appended to the report

Lens design¶

generate_geometry.py ships two lens design families and selects one with the module-level LENS_DESIGN constant.

Hyperboloid (default). An aplanatic conic surface with conic constant K = −n² and vertex radius R = h_apex·(n−1), sized so that the back focal point lands exactly on the PEC at z = 0:

z(r) = h_apex − sag(r),
sag(r) = (r²/R) / (1 + √(1 − (1+K)(r/R)²))

This focuses collimated light from above (in air) stigmatically to a point inside the resin. The fiber beam at the lens position is very close to collimated (Rayleigh range ≫ propagation distance), so this is a good approximation. The lens extends out to where sag(r) = h_apex (lens skirt meets the PEC plane), capped at LENS_R_CAP = 14 um to stay inside the scaffold ID with margin. At h_apex = 7 um, r_max ≈ 10.6 um — large enough to cover the full SMF-28 mode.

Cartesian oval (alternate). The unique surface that is stigmatic between the virtual fiber face (its paraxial image after the resin slab, z_v = 8 + 5/1.51 = 11.31 um) and a focus on the PEC. The oval condition is

n_air · √(r² + (z_v − z_s)²) + n_resin · √(r² + z_s²) = K
K = n_air (z_v − h_apex) + n_resin · h_apex

For this very compact geometry the natural oval extent is small (r_max ≈ 2 um at h_apex = 5 um), so it under-fills the beam aperture and the lens edge behaves as a diffractive obstacle. Useful as a comparison case.

The chosen profile is numerically tabulated and saved to lens_profile.npz for use by the simulator.

Simulation scope¶

FDTD is expensive, so the simulation only covers the optical core, not the 800 um sheath. The simulated stack is

z ≤ 0                : PEC
z = 0 .. 5           : resin lens (Cartesian oval, revolved)
z = 5 .. 8           : air gap
z = 8 .. 10          : resin membrane
z = 10 .. 13         : resin / index-matching glue
z = 13 ..            : SMF-28-like fiber (core + cladding)

The bumps live at r = 50 um (well outside the FDTD window) so they are implicit — the 3 um zone between membrane and fiber face is modeled as a uniform resin layer (the glue + bump composite).

A fundamental HE11 mode source is launched downward from inside the fiber. A mode monitor at the same plane records the returned amplitude in the +z direction. Coupling efficiency is

CE(f) = |amps('+', mode_index=0, f)|²

(the source is normalized to unit launched modal power).

Results¶

First preflight (baseline)¶

Sheath v1 — Optical Simulation Report¶

Generated: 2026-05-27T11:57:36
Wavelength range: 1.520 – 1.580 um (31 points)
Center wavelength: 1.550 um
Peak coupling efficiency: 0.2030 at 1.558 um
Mean coupling over the band: 0.1625

1. Structure geometry¶

The full Nanoscribe build is the chip-to-fiber sheath described in README.md. Critical z-levels (in microns above the PEC substrate):

level	z (um)
PEC substrate (and lens base)	0.00
Lens apex	5.000
Top of 3-segment base ring	8.00
Top of membrane	10.00
Top of bumps / fiber face	13.00
Sheath top end	810.0
Funnel top	860.0

Material indices: resin (IP-S) n = 1.51, fiber core n = 1.4504, fiber cladding n = 1.4447.

2. Lens design¶

The lens is a Cartesian-oval refractive surface designed to image the fiber face stigmatically onto the PEC plane. The air–resin interface height z_s® satisfies

$$ n_{air} \sqrt{r^2 + (z_v - z_s)^2} + n_{resin} \sqrt{r^2 + z_s^2} = K, $$

where the virtual object position is

$$ z_v = z_{mem,bot} + (z_{fiber} - z_{mem,bot}) / n_{resin} = 11.311 \text{ um}, $$

and K is set by the on-axis ray: K = n_air (z_v − h_apex) + n_resin h_apex.

Apex height h_apex = 5.000 um (chosen below the 8 um base ring height to leave a 3.00 um air gap under the membrane)
Outer radius r_max = 2.078 um (where the surface meets z = 0)
Effective NA in air = sin(arctan(r_max / (z_v − h_apex))) ≈ 0.313

Lens profile

3. Simulation domain¶

Transverse window: 18.00 × 18.00 um
Vertical extent: z ∈ [-1.08, 22.09] um
Grid: auto with 11 cells per wavelength at λ₀
Boundary conditions: PML in x, y, z; PEC structure at z ≤ 0
Symmetry: (1, −1, 0) — Ex-polarized HE11 mode
Run time: 0.35 ps

Source plane (ModeSource, '−z' direction) at z = 17.80 um. ModeMonitor at the same plane collects the returned ('+z') amplitude.

Permittivity cross-sections

4. Fiber mode¶

Step-index SMF-28-like fiber (core radius 4.1 um, n_core 1.4504, n_clad 1.4447). The mode solver finds the fundamental HE11; the source injects mode 0 with unit modal power.

Fiber mode

5. FDTD field¶

The launched mode propagates down through the cladding, glue layer, membrane, air gap, and Cartesian-oval lens. The PEC at z = 0 reflects the converging wavefront, which retraces back up through the lens and recouples into the fiber mode.

|E|^2 in xz

|E|^2 at the PEC

6. Round-trip coupling efficiency¶

Coupling efficiency is computed from the mode monitor amplitudes as

CE(f) = |amps('+', mode_index=0, f)|^2

which, given the unit-power ModeSource normalization, is the fraction of launched power that returns into the fiber's fundamental mode.

Coupling efficiency vs wavelength

Numerical summary

Peak: CE = 0.2030 at λ = 1.558 um
Mean over band: 0.1625
Min over band: 0.1309

Raw data¶

Coupling efficiency CSV: figures/20260527_115627_coupling.csv
Geometry parameters: ../geometry_params.json
Lens profile (npz): ../lens_profile.npz
STL files: ../stl/

Final report¶

Sheath v1 — Optical Simulation Report¶

Generated: 2026-05-27T12:31:31
Wavelength range: 0.750 – 0.810 um (31 points)
Center wavelength: 0.780 um
Peak coupling efficiency: 0.5502 at 0.758 um
Mean coupling over the band: 0.4195

1. Structure geometry¶

The full Nanoscribe build is the chip-to-fiber sheath described in README.md. Critical z-levels (in microns above the PEC substrate):

level	z (um)
PEC substrate (and lens base)	0.00
Lens apex	7.000
Top of 3-segment base ring	10.00
Top of membrane	12.00
Top of bumps / fiber face	15.00
Sheath top end	812.0
Funnel top	862.0

Material indices: resin (IP-S) n = 1.51, fiber core n = 1.4583, fiber cladding n = 1.4533.

2. Lens design¶

Design family: hyperboloid. Aplanatic hyperboloid (K = -n^2, R = h_apex (n-1)) — collimated air -> point focus at PEC inside resin.

For the hyperboloid (default), the air-side surface follows the aplanatic conic

$$ z® = h_{apex} - \dfrac{r^2 / R}{1 + \sqrt{1 - (1 + K)(r/R)^2}}, \qquad K = -n_{resin}^2, \quad R = h_{apex} (n_{resin} - 1), $$

so collimated light from above is focused stigmatically onto the PEC at z = 0 inside the resin.

Paraxial reference: viewed through the 5.0 um resin layer above the lens, the fiber face appears at

$$ z_v = z_{mem,bot} + (z_{fiber} - z_{mem,bot}) / n_{resin} = 13.311 \text{ um}. $$

Apex height h_apex = 7.000 um (chosen below the 10.0 um base ring to leave a 3.00 um air gap under the membrane)
Outer radius r_max = 10.616 um (where the surface meets z = 0, capped at LENS_R_CAP from generate_geometry.py)
Effective NA in air ≈ 0.860

Lens profile

3. Simulation domain¶

Transverse window: 10.00 × 10.00 um
Vertical extent: z ∈ [-0.62, 18.62] um
Grid: auto with 9 cells per wavelength at λ₀
Boundary conditions: PML in x, y, z; PEC structure at z ≤ 0
Symmetry: (1, −1, 0) — Ey-polarized HE11 mode
Run time: 0.60 ps

Tidy3D cloud cost¶

Pre-run estimate: 0.0250 FlexCredits
Actual cost: nan FlexCredits

Source plane (ModeSource, '−z' direction) at z = 16.80 um. ModeMonitor at the same plane collects the returned ('+z') amplitude.

Permittivity cross-sections

4. Fiber mode¶

Step-index fiber model (core radius 1.75 um, n_core 1.4583, n_clad 1.4533, design wavelength 780 nm). The mode solver finds the fundamental HE11; the source injects mode 0 with unit modal power.

Fiber mode

Measured mode-field diameter (MFD)¶

The MFD is computed four ways from the FDTD-solved mode at the source plane so it can be compared directly to fiber datasheets:

definition	value (um)
Gaussian fit, x-cut (	E
Gaussian fit, y-cut (	E
2^nd-moment (D4σ of	E
Petermann II (coupling-relevant)	5.039

Reference fibers @ 780 nm: HI780 ≈ 5.0 µm, 630HP ≈ 4.4 µm, SM800 ≈ 5.6 µm. For 630HP coupling, the simulated MFD should land near 4.4 µm — if not, change FIBER_CORE_RADIUS_UM / N_FIBER_CORE / N_FIBER_CLAD in generate_geometry.py and re-run.

Mode cross-section + Gaussian fit

5. FDTD field¶

The launched mode propagates down through the cladding, glue layer, membrane, air gap, and Cartesian-oval lens. The PEC at z = 0 reflects the converging wavefront, which retraces back up through the lens and recouples into the fiber mode.

|E|^2 in xz