[jtravs]

tools._zdw_near refined each sign change of the dispersion with a scalar Brent search, which evaluates the cladding's glass model on every iterate, about 190 evaluations per call. An index model evaluates an array at about the cost of one point, so this refines with four rounds of 33 samples and a final linear interpolation instead. It speeds up capillary_params, soliton_params and the zero-dispersion design target.

brentq is still used elsewhere in tools.py, so its import stays.

Timing

capillary_params at 14 um and 15 bar, on an Apple M5 Max. These are medians of 15 calls, repeated twice with the two searches alternating in one process. The machine was busy (load average 7 to 9), so read the ratios rather than the absolute times.

Gas	Brent	Array samples	Ratio
He	288 ms	100 ms	2.9
Ar	607 ms	253 ms	2.4
Kr	907 ms	351 ms	2.6

What changes in the results

• Physical zeros are unchanged. Across He, Ne, Ar, Kr, Xe and N2 at five radius and pressure pairs, they agree with Brent within 3.2e-9 relative, which is the noise of the differenced beta2. The new test holds this at 1e-8 on seven of those cases, against a Brent search over 200 nm to 3 um.
• A crash goes away. On main, xenon at 14 um and 15 bar raises ValueError from brentq, because Brent converges onto a pole of the differenced beta2 until the model returns NaN. It now reports 960.57 nm, which the same test confirms.
• A vacuum-ultraviolet pump can get a different answer. For pumps of 150 nm and shorter, the reported wavelength moved by up to 1.7e-3 relative in the same matrix (Ar and Xe; no such change at 200 nm and longer). The brackets involved hold 3 to 5 sign changes inside one sample interval. Brent lands on any of them, and this search takes the first upwards in frequency. Neither answer is a physical zero: these are artefacts of the differencing stencil crossing a line, and the pole test keeps them with either search. That predates this change and is now _zdw_near reports sign changes of the differenced beta2 beside a gas resonance as zeros #527.
• A sign change separated by non-finite samples is dropped, as one at the first sampling already was. Brent would have raised here.

Verification

• tests/test_tools.py, tests/test_design_solvers.py, tests/test_soliton_content.py and tests/modes/test_capillary.py: 323 passed, on numpy_ref.
• ruff, ruff format --check, basedpyright, codespell, numpydoc and poe changelog-check are clean.
• The new lines are fully covered, by the new tests and the existing pole test, in a coverage run over those tests.
• The full gate, slow lane and coverage lane were not run locally; CI gates them.

Related: #157 (the same question in modes.base.zdw) and #527.

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Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-11-05T00:00:21.928259Z	9ae77f3	PR opened
🔒 Security Review	✅ Completed 2026-11-05T00:01:10.974370Z	9ae77f3	PR opened

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