Functionality overview#

Curated, validated optical properties of materials, with the provenance of every number.

optmat provides the optical response of materials used in ultrafast and nonlinear optics, in gases, glasses, crystals and metals:

  • the refractive index and its dispersion, from the extreme ultraviolet to the infrared;

  • the complex index across absorption thresholds and bands;

  • the Kerr and third-harmonic coefficients;

  • the Raman response of the molecular gases, dry air and fused silica;

  • the strong-field ionisation rates of the noble gases and of molecules, and the parameters those rates are built from;

  • two-photon continuum cross sections and bound-excitation records for noble gases.

Each value can be traced to the paper, table and page it came from, together with:

  • the technique and the conditions of the measurement;

  • the state the value refers to;

  • any correction applied to what was printed.

The package provides published formulas, curated tables, and fitted models. Their descriptions state which sources they rest on and what is known about their accuracy.

The source code, issue tracker and contribution history are at LupoLab/optmat on GitHub.

Why optmat#

Reliable simulations need material data whose conditions, conventions and limitations are understood. Our motivation is to fix transcription errors, incorrect readings of measurement conditions and inappropriate applications of models, and to evaluate data that have not been systematically assessed. optmat provides reference implementations of published fits and develops new fits from the best available data and analysis. Their provenance and the calculations behind them remain available for inspection and reproduction.

refractiveindex.info is an invaluable resource for the optics community, and we do not seek to replace it. Our goals are different and complementary: systematic evaluation of source data, explicit physical conventions, reproducible fits and validated implementations for simulations.

From sources to predictions#

Every number keeps its provenance. Values are taken exactly as printed, by script from the paper’s tables or by hand from its text with the page. The source record says how each was measured or calculated, at what state, with what uncertainty, and whether it is someone else’s value reproduced. A misprint is corrected by an erratum that records the printed value, the correction, the reason and the evidence; the printed value itself is never edited (The curated data).

Every check is on record. The review register (The review register) records what was transcribed and how it was checked, every correction, every decision taken in fitting, and every question left open. The code, the data and this manual cite it by entry.

The models are physical. A gas’s dispersion is modelled as the dipole oscillator-strength distribution of its atoms or molecules:

  • the resonance lines at their spectroscopic energies;

  • effective oscillators for the rest of the distribution;

  • the vibrational bands of the infrared-active molecules from HITRAN;

  • ab initio values and sum rules where they exist.

The spectroscopic lines constrain the model alongside the fitted data. Read Fitting dispersion models for the construction and Gas dispersion: accuracy and limitations for the supported accuracy; the physical form alone does not establish accuracy outside the qualified range.

For fused silica, Franta et al.’s universal dispersion model represents the complex dielectric function through its excitations:

  • interband and excitonic transitions;

  • the Urbach tail;

  • phonon bands.

Its construction preserves causality, passivity, and the sum rule. Other solid models implement published formulas or interpolate curated tables; Solids: conventions and models explains these representations and their derivatives.

Density is handled carefully. A measurement is reduced with the density its source meant, real-gas or ideal. The conversion to a refractive index goes through Lorentz–Lorenz with the refractivity virial coefficient and the magnetic term (Conventions). At the level of parts per million these corrections bring precision metrology and ab initio theory into agreement.

Uncertainties are stated and tested:

  • every fit stores its covariance;

  • leave-one-dataset-out refits show the sensitivity of fitted models to their data;

  • measurements not used in a fit are kept as validators;

  • the accuracy pages of this manual are checked against the stored fits by the test suite.

The nonlinear response is process-aware. The second hyperpolarizability is modelled as a function of all four frequencies of a process, so one model gives the Kerr effect, third-harmonic generation and four-wave-mixing channels. The fitted data and resonance limits determine its support (Third-order nonlinearity).

Responses are checked against experiment and exact theory. The noble gases’ ionisation rates are validated against numerical solutions of the Schrödinger equation and against measured yields (Ionisation rates). The Raman lines are checked against measured gains (Raman lines).

Available data and models#

  • The curated records: 762 source records: 8481 datasets and 197,804 values, 259 errata and 780 published formulas.

  • 15 gases: He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CO, CO2, CH4, SF6, N2O and O3.

    • A fitted refractive-index model for every gas:

      • helium and argon at the accuracy of ab initio theory;

      • ozone as a complex index built from its measured absorption;

      • how well each model is known, and how it compares with the formulas in use, on Gas dispersion: accuracy and limitations.

    • The complex index of the noble gases in the extreme ultraviolet (The extreme ultraviolet).

    • A model of the second hyperpolarizability of every gas, with its accuracy on Third-order accuracy.

    • The Raman response:

      • the Raman lines of N2, O2, H2, D2, CO2, CH4 and SF6, and N2O’s vibrational bands (Raman lines);

      • the response functions of the gases and of dry air (The Raman response).

    • Ionisation:

  • Solids: 95 of the records hold data of glasses, crystals and metals: 2027 datasets for 163 materials:

    • the linear index and the band gap;

    • n2 and the Raman response;

    • two-photon and multiphoton absorption;

    • ionisation and laser damage.

  • Fused silica (Fused silica):

    • its complex index from 25 nm to 125 µm, Franta et al.’s universal dispersion model refitted to the absolute refractometry, which it follows to about 2e-5 in the transparent window;

    • its n2 from 350 nm to 3.5 µm, with the Raman fraction set by the measured Raman gain and the dependence on pulse duration;

    • its Raman response function and consistent nonlinear bundles (Fused silica).

  • Crystalline silicon (Crystalline silicon): its complex index from 31 nm to 143 µm at 20 °C, Franta et al.’s universal dispersion model refitted to the absolute refractometry and the measured absorption edge.

  • The window crystals and N-BK7 (The window crystals): CaF2, MgF2, BaF2, sapphire and SCHOTT’s N-BK7, each its source’s Sellmeier formula made absolute.

  • The metals (The metals): silver, gold and copper from 3-4 nm to 12.4 µm (copper to 56 µm), aluminium from 0.8 nm to 200 µm, as curated tables joined by range.

Where the package goes next is on the Roadmap:

  • the models of the other solids, and their two-photon absorption, ionisation and damage;

  • the molecules in the extreme ultraviolet;

  • line mixing in the dense molecular gases, and the remaining reference rates.

Finding a starting point#

Follow Installation and the Quick start to evaluate the properties above. The User guide develops their conventions, physical models, and validation in reading order. From a paper to a model introduces the source records, datasets, and review register; The data gives the full reference.

The API reference is organised into core, gas, and solid interfaces. Package architecture and contribution workflows belong to the Developers guide.

AI-assisted development and verification#

AI agents assist with literature curation, code, tests, and documentation under the direction of John C. Travers. Source-specific extraction scripts and checks against published values support the curated records. The review register records corrections, decisions, and unresolved questions.

The tests check physical identities, numerical references, and executable examples. Separate verification runs reproduce extractions and stored fits. About optmat explains the roles of AI assistance, source verification, and repeatable calculations.