2.5% 3 µm × 3 µm SSC @ 1550 nm

Target & SMF parameters

The last field is the mode-field diameter the SSC facet presents to the SMF (the optimized device delivers ≈ 11.5 × 10.0 µm, geometric mean ≈ 10.7 µm). Set it equal to the bare WG MFD to see the loss without a converter.

Gaussian–Gaussian overlap model for a quick estimate; the reported design numbers below come from the true-segment 3D BPM.

Mode field cross-section — blue: SMF Gaussian, red dashed: bare WG mode, green: expanded SSC-tip mode. Larger overlap with the SMF means lower loss.

• The SMF-28 mode-field diameter is ~10.4 µm at 1550 nm, while a 2.5% Δ, 3×3 µm silica core guides only a 3.9 µm (D4σ) mode — the bare butt-coupling loss is 3.32 dB.
• The 3 µm core thickness is fixed by deposition, so the converter must be drawn in the mask plane only: segment width and duty lower the local effective index and let the mode swell in both x and y.
• At 2.5% Δ every gap is a strong scatterer. A coarse fixed pitch (e.g. 2.8 µm) adds ~0.5 dB of segment radiation, so the pitch is kept as short as the 0.5 µm rule allows wherever the duty is mid-range — and the segments widen gradually so the facet mode is large without pushing the duty to the rule limit too early.
• Target: SMF coupling loss ≤ 0.3 dB, minimum linewidth / gap ≥ 0.5 µm.

Chip waveguide 3 µm solid (20 µm lead) → segmented section whose segments widen from 3 µm toward the SMF facet while their duty falls. Each period starts with a gap, then a tooth; the facet is cut at the end of the last tooth. The segment list is generated from a small gene vector:

So the gap is pinned at 0.5 µm near the chip (high duty), the pitch drops to P_min = 1.21 µm through the mid-duty region where scattering would be strongest, and the tooth is pinned at 0.5 µm near the facet (low duty). Every tooth and gap is ≥ 0.5 µm by construction (1 nm grid, rounded up). The BPM is one-way, so contra-directional Bragg reflection is screened analytically by the band rule.

• ① gene → structure: the 7-gene vector builds the tooth list (z₀, z₁, w₀, w₁) with the local minimum-pitch rule — the same list that is written to the GDS.
• ② 3D BPM run: launch the 3×3 µm chip eigenmode and propagate through every real tooth and gap (scalar, paraxial Crank–Nicolson ADI, dx = 0.12 µm, dz ≤ 0.25 µm, absorbing boundaries).
• ③ fitness: Loss = −10·log10 |⟨E_SMF | E_out⟩|² [dB] at the facet — taper radiation and facet mismatch both included.
• ④ select · cross · mutate: tournament selection + BLX-α crossover + Gaussian mutation, elitism 2, population 16.
• ⑤ iterate: 14 generations (224 BPM runs), then the best candidate is re-verified on a finer grid (dx = 0.10 µm, dz ≤ 0.2 µm).

# ga_widen.py (excerpt)
def fitness(genes):
    des   = from_genes(genes)                      # WideningSSC: tooth list, DRC by construction
    psi,_ = bpm.run(chip_mode, segmented_slices(des, grid, plat, dz=0.25))
    return -10*log10(grid.overlap_raw(psi, smf))   # dB, smaller is better

# The mode solver and the BPM share the same 5-point Laplacian, so an eigenmode
# propagates unchanged (500 um self-overlap 0.99999999) -- no mode-beating artefact.

A pure-Python pipeline (tooth-list generator → self-written ADI 3D BPM with numba → genetic algorithm → gdstk) was run for the target spec: chip waveguide 3 µm × 3 µm solid on the left, 7.1 µm-wide low-duty SMF facet on the right, thickness fixed at 3 µm, every tooth and gap ≥ 0.5 µm.

The chip mode (3.9 µm) expands through the widening, thinning segments to ≈ 11.5 × 10.0 µm at the facet. Compared with the earlier uniform-width (3 µm) design with a fixed 2.02 µm pitch (0.294 dB, kept below as the reference), widening the segments lowers the facet-mode limit to 0.159 dB and the dense mid-section pitch keeps the segment radiation small, so the device reaches 0.239 dB.

Method check: a 2D full-wave FDTD of 60 µm segmented sections (pitch 2.0–2.8 µm, duty 0.3–0.75) gives segment losses within −0.06 / +0.02 dB of the paraxial BPM (fdtd2d_calibration.json), so the paraxial BPM is slightly optimistic for segment scattering — a realistic expectation is ≈ 0.24–0.27 dB. The calculation is scalar (polarization-averaged); facet Fresnel reflection is excluded (index-matched butt coupling).

Everything needed to reproduce the result above:

• ssc_optimized.gds — GA-optimized mask layout: SSC_2p5_3um_1550 (533 widening segments, chip 3 µm → SMF facet 7.1 µm), SSC_B2B_TEST (SSC – 3 mm WG – SSC), REF_STRAIGHT; layers (1,0) core, (2,0) facet marker, (10,0) text.
• ssc_reference.gds — the reference uniform-width segmented SSC (0.294 dB) for comparison.
• seg_vp.py — widening, minimum-pitch segment generator with DRC and Bragg-band rules.
• ssc_core.py — platform (1550 nm silica Sellmeier, Δ → n_core), FD mode solver, ADI-CN 3D BPM, tooth/gap slicing.
• ga_widen.py — GA driver (7 genes, true-segment BPM fitness).
• verify_widen.py — dx = 0.10 µm verification and tolerance study.
• make_gds_widen.py · make_figures_widen.py — GDS and figure generation.
• fdtd2d_check.py — 2D FDTD vs paraxial BPM calibration of segment loss.
• final_design.json · verify_results.json · ga_widen_A.json — design, verification and GA records.
• ssc_result_summary.png — full result figure.
• ssc_compare.png — reference vs. optimized comparison figure.

Run with python3 ga_widen.py → python3 verify_widen.py → python3 make_gds_widen.py (needs numpy, scipy, numba, gdstk, matplotlib). The GA takes ≈ 40 min on 2 cores; always re-validate the final candidate on the fine grid (dx ≤ 0.10 µm). The earlier uniform-width study (scripts, solid inverse-taper alternative) is kept in archive_uniform/.