Roadmap

optmat began with the gases used in gas-filled fibres and cells, and with the properties a simulation of nonlinear propagation in them needs first: the refractive index across the spectrum and the Kerr response. The aim is the same for every property and every material that follows. Take the data from the primary literature with their provenance, check them on record, fit physical models with honest uncertainties, and keep the published alternatives available for comparison.

A major item starts as an enhancement proposal (OEP). That means a new medium, a new family of properties or models, a changed default or convention, or a redesigned interface. Accepted proposals are listed first, then drafts, then the informal items.

Accepted enhancement proposals

OEPs that have been accepted and are not yet final, each waiting to be picked up or being implemented.

None at present: OEPs 1-6 are Final (see the OEP index).

Draft enhancement proposals

OEPs under discussion. Their scope may change, and implementation has not been accepted. The OEP index lists every proposal and its current status.

• OEP 7 — Strong-field dissociation of small molecules: the products a pulse leaves (Draft). It covers the products one molecule is left with at the end of an 800 nm pulse, from a few cycles to 30 fs:

  • ionisation into each state of the ion, then each state’s fragmentation (the sudden limit first);

  • post-ionisation coupling;

  • dications;

  • neutral channels.

  The molecules are O2, N2, N2O, NO2, O3 and N2O5. It also gives a labelled recombination-limited bound on the atoms. The plasma kinetics after the pulse stays outside optmat. The data are curated (TC-954 to TC-981); what is missing is listed in its section 5.

• OEP 8 — The bound two-photon resonances of the noble gases for propagation (Draft; Reviewed). Q8–Q10 are resolved by the maintainer (TC-1055). Phase 1 supplies He, Xe and Ar coefficients and weak-field applications, plus the local He 1s2s nonlinear reference model with its light shifts. It includes the approved decay quantities, Drake’s on-shell perturbative kernel and Bondy’s helium decay rate, after extraction. Xe and Ar strong-field multilevel dynamics and general frequency-dependent or two-colour dynamics remain deferred. The empirical bandwidth estimate is not a universal error bound. The xenon dispersive validation failure and missing shifts, photoionisation and pressure data remain explicit; Ne and Kr remain refused until their strengths are resolved.

  The initial application is the disappearance of an Ar VUV RDW near the two-photon ionisation threshold under a self-compressing 6 fs, 800 nm pump, with He as a second target (TC-1056). Start the solprop investigation with OEP 6’s continuum coefficients: compare pump-ionisation baselines and evaluate perturbative VUV pair-spectral loss on the generated fields. OEP 8’s lowest bound lines are at different wavelengths. This diagnostic need not wait for OEP 8, and it does not provide the continuum’s missing time-dependent loss current or decide which mechanism dominates. optmat supplies material properties and basic data; solprop owns the resulting polarisation, electron accounting, plasma coupling and propagation energy balance (TC-1057). The internal atomic fixtures test material coefficients and conventions.

The informal items below record work not fully covered by these proposals. When a proposal is added or revised, an informal item is removed only if the proposal covers it in full. Otherwise the item links the proposal, states what it covers and keeps the remaining work explicit. Moving work into a proposal does not mean it is implemented.

Gases: what comes next

• VUV RDW suppression in argon and helium (TC-1056). A solprop investigation, using OEP 6’s existing continuum coefficients and the bound coefficients as OEP 8 provides them. Use the evolving complex VUV field, spatial overlap and neutral density, not the input pump duration. Resolve the impact of near-threshold gaps and unresolved structure; do not replace them by zero. Compare pump ionisation, VUV two-photon ionisation, and both, including absorption and plasma feedback. A causal continuum loss/ionisation rule belongs in a solprop SEP (OEP 8 Q6; TC-1057), with a coupled optmat OEP only for additional material quantities, models or interfaces it requires. An effective continuum matched to OEP 6’s cross sections is a candidate for the SEP, not an approved response; integrated yield agreement alone does not validate its transient polarisation or electron accounting. Distinguish pump-driven detuning from the ultimate observable cut-off, and the spectral centroid from the blue edge and detection limit. The pressure scan alone does not distinguish the hypotheses. Fix the dataset’s actual input duration before specifying simulation fixtures.

• Beyond OEP 8’s approved first scope (Q8–Q9; TC-1055). Derive and qualify a general frequency-dependent/two-colour response in solprop, with a coupled optmat proposal for any additional material inputs (TC-1057), and establish when excited-state Raman couplings, shared-continuum loss and correlated dephasing matter for strong multilevel excitation. Include pump-induced dressing where the RDW overlaps the intense pump. These are deferred scientific tasks, not consequences of approving Q8–Q10. Higher bound series near threshold still need strengths; the existing low levels do not bound their loss.

• Raman and ionisation parameters for propagation (TC-439). The aim is that solprop holds no material parameters of its own. optmat takes over the conversion from the literature, and solprop keeps only the response kernels and the molecules’ rate formulas.

  • Done: the Raman lines of seven gases and N2O’s bands (Raman lines), the response functions of the gases, dry air and fused silica (The Raman response, TC-685 to TC-696), the ionisation parameters (Ionisation), and the rates of the noble gases and the molecules (Ionisation rates, TC-652; Ionisation rates of molecules, TC-673 to TC-684).

  • Next:

    • the ionisation rates: the disagreement of the two measured yields (TC-660), for which a one-electron calculation of the 42 fs pulse is wanted; hydrogen, 400 nm and 1030 nm; all-electron static rates of Kr and Xe, and of Ne and Ar below 1.7e14 W/cm², where the tabulated ones are in doubt (TC-669); for the molecules, a calculation at a finite frequency, all-electron static rates of O2, CO2, N2O and CH4, and SF6’s coefficients (TC-680, TC-681);

    • N2O’s rotational lines, once its rotational constants are curated;

    • modern H2 and D2 level energies (Komasa et al.) in place of Stoicheff’s;

    • the 11-39 % excess of the model’s H2 and D2 gains over the measured ones (TC-542);

    • the Q-branch widths of CO2 and N2O, and N2O’s depolarisation ratios (stopgaps now);

    • Q-branch line mixing (TC-527, TC-688). Above about 2 amagat for N2 (and dry air), 4 for O2 and 13 for CO2, the Q(J) lines overlap. Collisions then transfer coherence between them, and the branch narrows towards a single line. Today the response warns there and treats the lines as independent, which overstates the branch’s dephasing. The plan:

      • a relaxation matrix W for each band, whose diagonal is today’s per-J widths (so nothing changes at low density), with off-diagonal rates from a fitting law such as the modified exponential gap (Koszykowski et al. 1987, curated as ExponentialGapLaw) or the energy-corrected sudden law, with detailed balance imposed;

      • the response from the eigen-decomposition of Omega + iW. This is still a sum of damped oscillators, now with complex amplitudes, so the response’s form and the propagation code’s use of it are unchanged. Its eigenvalues depend on the density, which the low-rank tabulation already absorbs;

      • validation against the collapsed branch: Mikhailov’s widths of N2’s Q branch at 15-114 atm (curated), Rosasco et al.’s first-order mixing coefficients at 0.2-2 atm (curated, but they fail the detailed-balance sum rule, TC-527), and Millot et al.’s O2 spectra;

      • the same for the rotational S lines of CO2, which overlap near 13 amagat;

    • the structure coefficients of CH4, SF6 and N2O;

    • the polarizabilities of the remaining cations;

    • reference rates for the gases without them: the papers requested below, and TDSE calculations where the literature leaves a gap (TC-444).

• The molecules in the extreme ultraviolet. Brion & Thomson’s compilation of absolute photoabsorption (H2, N2, O2, CO, CO2, N2O, CH4 and SF6, 5-80 eV, 5 %) and Olney et al.’s dipole sums are curated. A complex index of the molecules above their ionisation thresholds, built as the noble gases’ is, comes next.

• The infrared beyond OEP 3. What OEP 3 leaves out:

  • SF6’s infrared treatment. Its input is a measured, broadened cross-section, so it needs a Kramers-Kronig reference with its resolution, baseline and truncation errors. Its cross-sections also show weak absorption at 1.5-5 µm, inside its declared range (OEP 3, §13 Q14).

  • A complex index for the weak bands (OEP 3, Option F). Damped oscillators or smoothed band shapes would qualify pure CO2 at its laser lines, and the weak-band regions of N2O and CH4.

  • Air across its trace gases’ bands (OEP 3, Q13; TC-809). The full CIPM-2007 air widens only to 1499-1516 and 1548-1562 nm beyond its constituents’ intersection: the trace CH4, N2O and CO2’s band-rule poles fill their gaps. A representation of the traces with their bands folded, and N2O’s ultraviolet absorption below 320 nm, would widen it further.

• Completing the curated records. Values that were recorded in a record’s notes before the format could hold them become datasets (TC-316): magnetic susceptibilities, higher refractivity virials, molar Kerr constants and Kerr virials, vibrational corrections to the polarizability, band-integrated cross sections.

• High pressure. The density dependence of the third-order response (the pair coefficients of χ⁽³⁾), and the higher refractivity virials, for fibres filled to tens of bar. The second refractivity virial of the gases that have none (O2, D2, N2O, CO, O3); OEP 4 records their omission in mixtures.

solprop

optmat supplies the material properties used by solprop. The integration interface and remaining responsibilities on the propagation side are:

• the recommended model of each gas;

• Lorentz–Lorenz density scaling;

• the process-aware Kerr and third-harmonic coefficients, through the model’s exact time-domain form (see Third-order nonlinearity). For solprop’s SEP 6, which evaluates every four-wave quartet leg by leg, the manual now gives where the fits are supported: the legs of the data, each gas’s resonance limits and the evidence on bounds for the legs beyond (TC-864 to TC-868); how to use them is solprop’s decision. A public, tested record of it on the model, HyperpolarizabilityModel.support, so that solprop does not copy the numbers, is implemented by OEP 5 (TC-870); the polyatomic gases’ missing resonances stay with the papers we are looking for (below).

• the Raman responses of the gases, dry air and fused silica (The Raman response), and the ionisation rates and parameters, through solprop’s SEP 3. The snapshots tests/data/solprop_raman.json, tests/data/solprop_raman_response.json and tests/data/solprop_ionisation.json record historical solprop snapshots for the parity targets (TC-439, TC-690). The page’s section Using it in a propagation code gives the cost of per-line widths along a density gradient and the low-rank tabulation that removes it.

• solprop’s solids, so that it keeps no solid data either:

  • its window crystals and glass (CaF2, MgF2, BaF2, sapphire, N-BK7);

  • its silver and aluminium;

  • fused silica, with its Raman response and its n2 paired (TC-692, TC-696).

  The primary papers are now curated (TC-543 to TC-625): the crystals have their primary formulas made absolute (The window crystals), and silver, gold, copper and aluminium are table models (The metals). Further sources for the metals (TC-626 to TC-648) took the tables to the soft x-ray range and aluminium to 0.8 nm-200 µm, and SCHOTT’s data sheet and Weber’s handbook brought N-BK7 and sapphire’s extraordinary ray (TC-649 to TC-651). Each solid covered by those snapshots has a recommended model.

• the preparation on optmat’s side is OEP 1. That covers:

  • the declared surface, identities and flags;

  • overrides;

  • the polarizability derivative;

  • the EOS inverse and transport;

  • compositions and the air model;

  • the Raman groups;

  • the rate energy;

  • the silica bundle;

  • the fixtures, the first release and the integration page.

  The adapters themselves are solprop’s.

• the finite-density mixture law of the gas index, for solprop’s SEP 11, is OEP 4, with the mixture’s density.

optmat will never depend on solprop.

Solids: glasses and crystals

Glasses and crystals share one subpackage, optmat.solid (TC-318). Fused silica is the first (see Fused silica):

• its complex index from 25 nm to 125 µm (Franta et al.’s model refitted to the absolute refractometry);

• its n2 with the Raman part, the Raman fraction set by the measured Raman gain (TC-696);

• its Raman response: Hollenbeck & Cantrell’s (the default), Lin & Agrawal’s with its isotropic and anisotropic parts, and Blow & Wood’s (The Raman response).

The curated records already hold the data for what comes next (TC-325 to TC-392, TC-543 to TC-651), for silica and the other 162 solids they cover:

• Two-photon absorption: beta at 193-800 nm of silica grades, the fluorides, sapphire, quartz and BBO, and a model of its dispersion with the band gap.

• Ionisation and damage:

  • multiphoton and field (Keldysh) ionisation rates and their inputs;

  • avalanche coefficients;

  • the laser-damage thresholds against pulse length.

• Temperature: a temperature-dependent recommended model of silica. Leviton & Frey’s absolute indices and dn/dT (Corning 7980, 30-300 K) are curated, with their formula as a model (leviton_2008/sellmeier), and so are Matsuoka et al.’s (108-356 K) and Waxler & Cleek’s (73-293 K) indices; Daimon & Masumura’s dn/dT of CaF2.

• More materials: CaF2, MgF2, BaF2, sapphire and N-BK7 now have their formulas (The window crystals), silver, gold, copper and aluminium their tables (The metals), and crystalline silicon its refitted universal dispersion model at 20 degrees C (Crystalline silicon). LiF, YAG and KGW next:

  • their indices from primary measurements;

  • Franta’s models where they exist (MgF2, Al2O3 films);

  • the n2 already curated (Adair, DeSalvo, Ensley, Patwardhan, Kabacinski and others).

• Silicon, further:

  • a temperature-dependent complex index: Franta et al.’s 2017 model needs its unprinted parameters from the authors (TC-1088); Frey et al.’s formula covers the window from 20 to 300 K;

  • the band-to-band absorption beyond 1.15 µm, which the model’s tail cannot follow, and doped silicon’s free carriers;

  • Herzinger et al.’s Si table (an AIP PAPS deposit) and Dash & Newman (1955), not yet in the library (TC-1083, TC-1085).

• Catalogues: vendor catalogues as comparison sources, and the spread between melts and vendors as part of the stated uncertainty.

• Open questions (TC-393, TC-399):

  • the grade dependence near the 2.73 µm OH band, where the recommended model departs from Malitson’s glasses by up to 5e-5;

  • the electrostrictive part of nanosecond n2 data;

  • silica’s Raman gain below 25 cm⁻¹, where Hollenbeck & Cantrell’s shape is 1.6-2.4 times Stolen et al.’s low-frequency law (TC-695).

Crystals

For second-order nonlinear optics:

• the principal refractive indices of uniaxial and biaxial crystals, and their temperature dependence;

• the second-order susceptibility tensor (\(d_{ij}\)), and its dispersion through Miller’s rule;

• the third-order response;

• the conventions for axes and tensor components that such data need, made explicit in the vocabulary.

Infrastructure

• Releases: on PyPI, and documentation hosted online. The first tagged version, and the test that a clean install ships its data, were part of OEP 1. Publishing and hosting remain open.

• Read-only registries (OEP 1, Q31): the registry functions return plain dicts of read-only models. Returning read-only mappings would change their return types.

• Numerical regression across platforms (OEP 1, Q32): gas Raman golden checks now compare canonical identity records with an arithmetic tolerance; public digests remain exact. Nonlinear refit checks compare predictions, the full objective and uncertainty-scaled parameter displacements. See Development checks. Verification on other numerical platforms, including the exact digest checks for other model families (libm, CoolProp), remains part of setting up CI.

• Continuous integration: CI running the full gate on every pull request.

Papers and data we are looking for

The papers below would improve the weakest parts of the models. Each is cited by a paper already curated. If you have access to one, or know of better data, please open an issue. Many of the papers requested earlier are now curated (TC-543 to TC-625); what they left open is below.

Gases:

• Vacuum-ultraviolet refractometry of the noble gases between their first resonance and 140 nm:

  • G. I. Chashchina, V. I. Gladushchak and E. Ya. Shreider, Opt. Spectrosc. 24, 542 (1968), argon;

  • G. I. Chashchina and E. Ya. Shreider, Opt. Spectrosc. 27, 79 (1969), krypton and xenon;

  • R. Abjean, A. Mehu and A. Johannin-Gilles, C. R. Acad. Sci. B 271 (1970).

• The electronic absorption onsets and two-photon states of the polyatomic gases (TC-865): CO2’s weak absorption below its first band near 147.5 nm, SF6’s onset (only absorption evidence is curated: none detected at Ityaksov et al.’s sampled wavelengths down to 197.7 nm, TC-869), and the lowest two-photon states of CO2, CH4, SF6, N2O and O3. Without them these gases’ support records give no E2 and no derived band edge (TC-870).

• An accuracy margin below each resonance (OEP 5, Q8): how far below \(E_1\) or \(E_2\) the fitted polynomial stays within its stated accuracy. It would be published as information on the support record, never as a rule, if optmat had evidence for one; it has none today.

• Two-photon ionisation and absorption of the noble gases (the curation of TC-872 to TC-942; Two-photon ionisation and absorption). The papers requested in the first round are curated; what they left open is:

  • krypton’s two-photon ionisation cross section in a vector-drawn or tabulated form (OEP 6, Q2): every curve so far is a scan (L’Huillier, Tang and Lambropoulos 1989; Fink and Johnson 1990; McGuire 1981). Leads they cite include:

    • A. L’Huillier, L. Jönsson and G. Wendin, Phys. Rev. A 33, 3938 (1986);

    • B. Ritchie, Phys. Rev. A 16, 2080 (1977);

    • K. C. Kulander, Phys. Rev. A 36, 2726 (1987);

  • xenon between its two thresholds (Q3): only a scanned MQDT curve (Gangopadhyay et al. 1986);

  • any measured two-photon ionisation cross section of argon or neon;

  • measured bound two-photon strengths of He, Ne and Ar, and the higher members of every series (OEP 8);

  • material inputs for the continuum’s time-resolved two-photon loss (TC-903; OEP 8, Q6; TC-1057): identify them with a solprop SEP for the propagation response; use a coupled optmat OEP for new material quantities, models or interfaces. Tier-3 TDSE runs support the pair-frequency rule for the helium and argon continua (TC-1049), but no published small-split amplitude is curated. Explicit approximate responses are possible candidates; their transient behaviour is not thereby qualified;

  • Dakka et al.’s photoionisation rate factor (OEP 6, Q7; TC-892).

• Converged ab initio dispersion, and the magnetic susceptibilities, of krypton and xenon. These would give Kr and Xe the theory backbone that He, Ne and Ar have.

• Ultraviolet refractometry of SF6 below 458 nm, where its fit has no refractive data but Shelton’s harmonics: Wilmouth & Sayres’s scattering at 264-363 nm lies about 2 % above the model, and Ityaksov et al.’s at 198-270 nm about 5 % (TC-712, TC-150).

• Neon’s refractivity virial (TC-744): Achtermann et al.’s 1993 optical B_R of neon and Huot and Bose’s B_ε, both as cited by Garberoglio and Harvey (2020). The package uses Orcutt and Cole’s static value, about three times theirs and the ab initio one. Both papers are curated (TC-771) and confirm the comparison. The choice of B_R is the author’s (OEP 4, Q18).

• The mixtures’ cross second virials and densities near ambient, for OEP 4’s Phase 2. The citations are as printed by Tkaczuk et al. (2020) and Gernert (2013):

  • J. Brewer and G. W. Vaughn, J. Chem. Phys. 50, 2960 (1969);

  • M. L. Martin et al., Aust. J. Chem. 35, 1525 (1982);

  • W. F. Vogl and K. R. Hall, Physica 59, 529 (1972);

  • N. K. Kalfoglou and J. G. Miller, J. Phys. Chem. 71, 1256 (1967);

  • Vatter et al., Ber. Bunsenges. Phys. Chem. 100, 73 (1996);

  • Blancett et al.’s (1970) He–Ar and Kestin et al.’s (1981) He–Ne and Ne–Ar mixture densities.

  All are curated (TC-780 to TC-784). Still wanted: a complete copy of Blancett et al. (the library’s scan clips pp. 82-88), and density data of the Ne–Ar mixtures and of air’s pairs (N2–O2, Ar–N2, Ar–O2) near ambient, whose absence leaves those defaults provisional (TC-779).

• Infrared refractivity of the molecular gases, OEP 3’s validators (TC-756). The five candidates of OEP 3’s literature search are curated (TC-802 to TC-806): Rollefson and Havens’s CH4 (1.7-15 um), Matsumoto’s CO2 at 10.6 um and Tsankova et al.’s static CO are validators of the fits; Legay (1955) measured HCl alone; Mitrofanov et al.’s group delay of air at 3.7-4.15 um is recorded without a dataset, for want of a quantity for a group delay whose zero is not stated and of air as a registered material. Still wanted: Statescu, Phil. Mag. 30, 737 (1915), CO2’s infrared index by the prism method. No measurement of CO or N2O between 2 and 12 um was found.

• Hohm’s measured polarizabilities against temperature: U. Hohm, Dissertation, TU Braunschweig (1989), the α(ω, T) of Ar, H2, O2 and CH4 that Hohm & Kerl fit but do not tabulate; and which of Hohm’s two 1994 xenon measurements, 0.31 % apart, is right (TC-606).

• The molecules’ polarizability away from their reference temperature: an opt-in correction, linear in T - T_ref where a coefficient is measured (N2, O2, CO2; TC-730), with its wavelength dependence checked, and a model for H2’s rotational average far from room temperature. OEP 1 exposes the reference temperature and the coefficients only (its §7.13).

• Molecular photoabsorption: the JILA Data Center Report No. 32 tabulations. Olney et al.’s S(−2) of N2O is 4.7 % above the one recomputed from Chan et al.’s published spectrum (TC-606).

• Third-order response:

  • the calibration of the Maryland group’s absolute n2: the supplemental material of J. K. Wahlstrand, Y.-H. Cheng and H. M. Milchberg, Phys. Rev. Lett. 109, 113904 (2012);

  • any measured hyperpolarizability of N2O.

• Ionisation:

  • static polarizabilities of Kr+, Xe+ and the molecular cations;

  • tunnelling structure coefficients (MO-ADK or weak-field asymptotic) for CH4, SF6 and N2O: L. B. Madsen et al., Phys. Rev. A 85, 053404 (2012) and 87, 013406 (2013);

  • D. W. Turner, A. D. Baker, C. Baker and C. R. Brundle, Molecular Photoelectron Spectroscopy (Wiley, 1970): the original of the N2O and CO2 vertical energies;

  • a modern threshold of SF6 (Frost et al.’s 1967 value is of unstated kind);

  • the source of solprop’s PPT Stark shift and dipole correction, which are not in Ilkov et al. 1992 (perhaps L. Bergé et al., Rep. Prog. Phys. 70, 1633 (2007));

  • the PPT originals: A. M. Perelomov, V. S. Popov and M. V. Terent’ev, Sov. Phys. JETP 23, 924 (1966); A. M. Perelomov and V. S. Popov, Sov. Phys. JETP 25, 336 (1967), which would settle the factor of 2 in Ilkov et al.’s Eq. (8);

  • R. H. Garvey, C. H. Jackman and A. E. S. Green, Phys. Rev. A 12, 1144 (1975): the model potentials behind Batishchev et al.’s and Trinh et al.’s rates.

• Raman:

  • for Q-branch line mixing: relaxation-matrix (exponential-gap or energy-corrected sudden) parameters of N2, O2 and CO2 fitted to Q-branch spectra up to tens of atmospheres, and tabulated Q-branch widths or time-domain dephasing measured above 10 atm, where the branch has collapsed;

  • the vibrational O and S branches (their anisotropic elements beyond H2’s and D2’s), and the line shapes below the Dicke cutoff (TC-686, TC-688);

  • the rotational constants of N2O (a primary source; the Weber volume has none);

  • the Q-branch widths of CO2 and N2O, and N2O’s depolarisation ratios;

  • Komasa et al.’s 2011 Supporting Information (the per-level uncertainties), and a vocabulary quantity for rovibrational level energies to hold their tables;

  • whether Murray & Javan’s (1972) D2 widths are half or full widths (TC-586).

• Ozone: an independent zero-point vibrational correction to its polarizability, and the supplementary material of Christodouleas et al. (2010). The higher dispersion orders of its measured-absorption term (the GVD and beyond), which are repeated gradients of the grid rather than derivatives of the evaluated spline (TC-732).

Solids (the fused-silica models and the data curated for the next ones; TC-399, TC-393, TC-325 onwards):

• solprop’s solids (TC-546, TC-619, TC-648):

  • silver and gold beyond 12.4 µm: measured far-infrared data, such as M. A. Ordal et al., Appl. Opt. 26, 744 (1987) (gold); only Drude curves are curated;

  • the vacuum ultraviolet of silver and gold (40-200 nm), where the curated sources spread by 20-50 % in k (TC-646): a modern measurement of both n and k;

  • MgF2’s temperature dependence: A. Feldman et al., NBS Tech. Note 993 (1979);

• Silica’s linear index:

  • Popova et al. (1972), the IR data behind Kitamura’s model;

  • the numbers behind Tan, Lemon & French’s 2003 VUV constants (figures only);

  • J. H. Wray and J. T. Neu, J. Opt. Soc. Am. 59, 774 (1969): silica to 1100 K.

• Franta’s model: the supplement of the 2025 Ta2O5 paper.

• Raman gain: a second absolute measurement of fused silica’s Raman gain, bulk or in a pure-silica-core fibre (TC-696 rests on Stolen & Ippen’s one), and its polarised and depolarised spectra, to test Lin & Agrawal’s isotropic and anisotropic parts.

• n2: D. Milam, M. J. Weber and A. J. Glass, Appl. Phys. Lett. 31, 822 (1977), the fluoride crystals’ n2; the other originals behind Weber, Milam & Smith’s 1978 tables.

• Damage and ionisation: B. C. Stuart et al., J. Opt. Soc. Am. B 13, 459 (1996); L. Sudrie et al., Phys. Rev. Lett. 89, 186601 (2002); Keldysh, Sov. Phys. JETP 20, 1307 (1965).