GASFIR: General Approximator for Strong-Field Ionization Rates

GASFIR is a Python package implementing the ionization-rate retrieval framework introduced in:

Agarwal, Scrinzi & Yakovlev — General approximator for strong-field ionization rates
Physical Review A 113, L021101 (2026) — 10.1103/vxgm-kdtt

It addresses the long-standing problem of determining accurate, time-resolved ionization rates for atoms in strong laser fields — a quantity fundamental to attosecond science. By fitting a five-parameter kernel to ionization probabilities computed for a set of few-cycle laser pulses, GASFIR retrieves sub-optical-cycle ionization dynamics within and beyond the strong-field approximation.

Three calculation methods are provided:

1. GASFIR — semi-analytic kernel, Eqs. (2), (3), (7) of the paper; fast
2. Exact SFA — full numerical saddle-point integration of the SFA kernel, Eq. (6). Selected via kernel_type="exact_SFA" and currently implemented for the hydrogen ground state only (use it with the H_SFA parameters)
3. QS — quasistatic (tunneling) limit, Eq. (9); connects to ADK/PPT theory

All internal quantities are in atomic units unless stated otherwise.

📖 Documentation

Full documentation — installation, user guide, worked examples, and the complete API reference — is hosted on Read the Docs:

→ https://gasfir.readthedocs.io

The docs are versioned: latest tracks the main branch and each release tag (e.g. v1.0.0) has its own frozen version, selectable from the flyout menu.

---

Installation

Core only — ionization calculations

pip install gasfir

Installs: numba, numpy, scipy, pandas. No fitting library required.

With fitting & retrieval pipeline

pip install gasfir[retrieval]

Adds: lmfit, emcee, cma (CMA-ES), tqdm, corner.

Full development install

pip install gasfir[retrieval,dev,docs]

Conda environment (recommended)

conda env create -f environment.yml
conda activate gasfir
pip install -e ".[retrieval,dev,docs]"

To recreate environment.yml after changing dependencies:

conda env export -n gasfir --no-builds | grep -v "^prefix:" > environment.yml

---

Quick Start

Ionization probability

from gasfir import create_pulse, get_parameters, get_diabatic_ionization_probability

# create_pulse(wavelength_nm, intensity_Wcm2, CEP_rad, duration_optical_cycles)
laser = create_pulse(800, 1e14, 0, 6)

params = get_parameters("Hydrogen_SFA")
prob = get_diabatic_ionization_probability(pulse=laser, param_dict=params)
print(f"P = {prob:.4e}")

Time-resolved ionization rate

from gasfir import get_diabatic_ionization_rate
import matplotlib.pyplot as plt

t = laser.get_tgrid(dt=0.25)   # time grid in atomic units
rates = get_diabatic_ionization_rate(t_grid=t, pulse=laser, param_dict=params)

plt.semilogy(t, rates)
plt.xlabel("Time (a.u.)")
plt.ylabel("Ionization rate (a.u.)")
plt.tight_layout()
plt.show()

Pulse types

Any pulse object can be passed to every calculation function (pulse=...).

from gasfir import create_pulse
from gasfir.pulse import create_pulse_ellip, SumOfPulses, TIPTOE, DataPulse
import numpy as np

# 1. Linearly polarized cos^N pulse (N=8 default) — the usual workhorse
laser = create_pulse(800, 1e14, 0, 6)          # 800 nm, 1e14 W/cm², CEP 0, 6 cycles

# 2. Elliptical / circular polarization (ellip_frac=1 → circular)
ell = create_pulse_ellip(800, 1e14, 0, 6, ellip_frac=2)

# 3. Two-colour (or arbitrary) superposition
two_colour = SumOfPulses([create_pulse(800, 1e14, 0, 6),
                          create_pulse(400, 2e13, 0, 6)])

# 4. TIPTOE pump–probe: strong pump fixed, weak probe scanned in delay
pump  = create_pulse(800, 3e14, 0, 3)
probe = create_pulse(800, 1e13, 0, 1)
scanner = TIPTOE(pump, probe)
delays  = scanner.return_delay_array()         # Nyquist-sampled delay grid
field_at_tau = scanner.at_delay(delays[0])     # a SumOfPulses at that delay

# 5. From your own data — supply E(t) OR A(t) on a time grid (atomic units;
#    A(t) must vanish at both ends). Use it like any other pulse.
t = np.linspace(-400, 400, 8001)
A = np.exp(-(t/150)**2) * np.sin(0.057 * t) / 0.057
my_pulse = DataPulse(t=t, A=A)                 # E(t) derived as -dA/dt

See the Laser Fields guide for full details (pump–probe scanning, boundary conditions, combining pulses).

Available parameter sets

from gasfir import get_parameters

print(get_parameters())           # list all names
params = get_parameters("He_Hacc5_QS")

---

Unit Conversions — AtomicUnits

AtomicUnits provides named two-way conversions so you never have to reason about which direction to multiply or divide.

from gasfir import AtomicUnits

# Length
AtomicUnits.nm_to_au(800)          # 800 nm → a.u.
AtomicUnits.au_to_nm(1.0)          # Bohr radius in nm (≈ 0.0529)
AtomicUnits.angstrom_to_au(0.529)
AtomicUnits.m_to_au(5.29e-11)

# Time
AtomicUnits.fs_to_au(2.42)         # 2.42 fs → a.u.
AtomicUnits.au_to_fs(100)          # 100 a.u. → fs

# Energy
AtomicUnits.eV_to_au(13.6)         # hydrogen IP in a.u. (≈ 0.5)
AtomicUnits.au_to_eV(0.5)          # ≈ 13.6 eV

# Electric field
AtomicUnits.Vm_to_au(5.14e11)      # ≈ 1 a.u. of field
AtomicUnits.VA_to_au(51.4)         # same in V/Å

# Laser wavelength ↔ angular frequency
AtomicUnits.wavelength_nm_to_omega_au(800)     # ≈ 0.0570 a.u.
AtomicUnits.omega_au_to_wavelength_nm(0.0570)  # ≈ 800 nm

# Photon energy ↔ angular frequency (ħ = 1 in a.u.)
AtomicUnits.photon_energy_eV_to_omega_au(1.55)
AtomicUnits.omega_au_to_photon_energy_eV(0.057)

# Laser intensity ↔ field amplitude
AtomicUnits.intensity_Wcm2_to_field_au(1e14)   # E₀ in a.u. (≈ 0.0534)
AtomicUnits.field_au_to_intensity_Wcm2(0.0534) # back to W/cm²
AtomicUnits.intensity_Wcm2_to_au(1e14)         # intensity in a.u. (≠ field amplitude)

Note intensity_Wcm2_to_au returns intensity in atomic units (I × factor, dimensionally I in a.u.). intensity_Wcm2_to_field_au returns the electric field amplitude (√(I × factor)), which is ~18× larger and what you usually need.

---

Keldysh Parameter

The Keldysh parameter γ = ω√(2Iₚ) / E₀ separates the tunnel (γ ≪ 1) and multiphoton (γ ≫ 1) ionization regimes.

Compute γ for a given pulse

laser = create_pulse(800, 1e14, 0, 6)
gamma = laser.get_keldysh_parameter(Ip_au=0.5)   # hydrogen
print(f"γ = {gamma:.3f}")  # ≈ 1.07 → near the tunnel/multiphoton border

Design a pulse for a target γ

from gasfir import AtomicUnits

Ip = 0.5   # hydrogen (a.u.)

# 10-photon resonance wavelength (ω = Ip/10)
wl = AtomicUnits.omega_au_to_wavelength_nm(Ip / 10)   # ≈ 911 nm

# Intensities for the three main regimes
I_multi  = AtomicUnits.intensity_for_keldysh(4.0,  wl, Ip)  # γ=4, multiphoton
I_border = AtomicUnits.intensity_for_keldysh(1.0,  wl, Ip)  # γ=1, border
I_tunnel = AtomicUnits.intensity_for_keldysh(0.25, wl, Ip)  # γ=0.25, deep tunnel

print(f"γ=4   →  I = {I_multi:.2e} W/cm²")
print(f"γ=1   →  I = {I_border:.2e} W/cm²")
print(f"γ=0.25→  I = {I_tunnel:.2e} W/cm²")

Find the wavelength for a target γ at fixed intensity

wl = AtomicUnits.wavelength_for_keldysh(gamma=1.0, intensity_Wcm2=1e14, Ip_au=0.5)
print(f"λ for γ=1 at 1e14 W/cm²: {wl:.0f} nm")   # ≈ 749 nm

---

Ionization Potentials

GASFIR ships NIST first ionization potentials for all 118 elements:

from gasfir import get_ionization_potential

get_ionization_potential("Ar")      # 0.5792 a.u. (15.76 eV)
get_ionization_potential("helium")  # 0.9036 a.u. — full names work too
get_ionization_potential("Diamond") # None — not an element

---

Parameter Fitting & Retrieval

Requires pip install gasfir[retrieval]

Fitting functions live in gasfir.fitting and gasfir.retrieval — not in the top-level gasfir namespace.

Results are saved to <medium_name>/ by default (JSON, HDF5 chain, corner plot, trace plot, LaTeX summary).

Known medium — full pipeline

import pandas as pd
from gasfir import create_pulse
from gasfir.retrieval import RetrievalConfig, retrieve

data = pd.DataFrame({
    "pulses": [create_pulse(800, I, 0, 6) for I in intensities],
    "Y":      measured_probabilities,
})

# output saved to ./Hydrogen_SFA/
cfg = RetrievalConfig(medium_name="Hydrogen_SFA")
result = retrieve(data_NA=data, config=cfg)

for name in result.var_names:
    v = result.params[name]
    print(f"  {name} = {v.value:.4g} ± {v.stderr:.2g}")

After the LS phase the pipeline automatically compares fitted values against the stored reference and prints a Nσ table. After emcee it saves:

• Hydrogen_SFA_publication_corner.pdf — posterior corner plot
• Hydrogen_SFA_trace.pdf — walker trace
• Hydrogen_SFA_fit_summary.tex — LaTeX parameter table + correlation matrix
• Hydrogen_SFA_retrieval_result.json — full result for reload

Cold start — atom (E_g from NIST)

For elements not yet in the GASFIR parameter store, E_g is looked up automatically from the NIST database; no initial guess is required:

cfg = RetrievalConfig(
    medium_name="Kr",        # krypton — E_g auto-resolved: 0.5145 a.u.
    cma_maxiter=5000,        # broader search for an unknown system
)
result = retrieve(data_NA=data, config=cfg)

Cold start — crystal (E_g must be supplied)

For crystals, the gamma-point band gap from DFT is unreliable for ultrafast dynamics — E_g must always be provided explicitly:

cfg = RetrievalConfig(
    medium_name="MyMaterial",
    initial_params={"E_g": 0.30},   # a.u. — only required field
    is_crystal=True,
    ret_electron_density=True,
    cma_maxiter=5000,
)
result = retrieve(data_NA=data, config=cfg)

Physical defaults are used for all other parameters; the cold-start notice prints the energy scale and source so you always know what was assumed.

Post-processing an existing MCMC chain

from gasfir.retrieval import post_process_mcmc

# Drop a parameter, add a derived one, re-snap and re-plot
post_process_mcmc(
    medium_name="Diamond_TBmBJ",
    output_dir="Diamond_TBmBJ",
    original_stored_params={"E_g": 0.235, "a1": 14, ...},
    drop_vars=["a0"],
    derived_exprs={"a0_per_au3": f"a0 / {6.74**3}"},
    latex_mapping={"E_g": r"$E_g$ [a.u.]"},
    is_crystal=True,
)

Low-level: residual function + manual lmfit

import lmfit
from gasfir.fitting import ret_residual_function

residual = ret_residual_function(data, uncertainty_Nadiabatic=0.05)

p = lmfit.Parameters()
p.add("E_g", value=0.5, vary=False)
p.add("a0",  value=5.0, min=0.01)
p.add("a1",  value=3.5, min=0.1)
p.add("a2",  value=2.0, min=0.0)
p.add("a3",  value=1.0)
p.add("a4",  value=0.0, vary=False)

result = lmfit.minimize(residual, p, method="least_squares")
lmfit.report_fit(result)

---

Development

First-time contributor setup

Run once after cloning — this gets you a working environment and the git hooks (auto-format on commit, test reminder on push):

git clone https://gitlab.mpcdf.mpg.de/gaf/gasfir.git
cd gasfir
conda env create -f environment.yml
conda activate gasfir
pip install -e ".[retrieval,dev,docs]"
pre-commit install --hook-type pre-commit --hook-type pre-push

(Minimal variant if you only need the dev tools: pip install -e ".[dev]" then the same pre-commit install line.)

Running tests

pytest tests/                                            # all tests
pytest tests/ --cov=src/gasfir --cov-report=html        # with coverage
pytest tests/test_gasfir.py -v                          # one file, verbose
pytest tests/test_integration.py::TestPerformanceIntegration  # performance only

Test pulses use physically motivated parameters defined in tests/physics.py (hydrogen Ip = 0.5 a.u., 10-photon wavelength ≈ 911 nm, intensities at γ = 0.25 / 1.0 / 4.0, 1 optical cycle).

Code quality

black src/ tests/         # format
isort src/ tests/         # sort imports
flake8 src/ tests/        # lint
mypy src/                 # type-check

Linter versions are pinned in the [dev] extras so local and CI formatting always agree.

Pre-commit hooks (recommended)

Install the git hooks once per clone so formatting is fixed automatically and you're reminded to run tests before pushing:

pre-commit install --hook-type pre-commit --hook-type pre-push

• on git commit — black + isort auto-format changed files and flake8 lints them (a clean commit is guaranteed to pass the CI lint stage);
• on git push — a reminder to run the local checks before CI does.

Building documentation

cd docs && make html
cd docs && make livehtml   # live reload

---

Versioning and Releases

The version is defined only in pyproject.toml; __init__.__version__ reads it at runtime via importlib.metadata.

Tagging a release

# 1. Bump version in pyproject.toml
# 2. Update CHANGELOG.md
# 3. Commit: git commit -m "chore: release vX.Y.Z"
# 4. Tag and push:
git tag vX.Y.Z
git push origin vX.Y.Z

CI/CD pipeline (GitLab)

Trigger	Stage	Action
Every branch / MR	test	lint, type-check, pytest (Python 3.10–3.12)
main push	build	wheel + sdist, Sphinx docs
main push	publish	TestPyPI (automatic)
vX.Y.Z-alpha/beta/rc tag	publish	TestPyPI (automatic)
vX.Y.Z stable tag	publish	PyPI (manual approval)

Install from TestPyPI to verify before the production release:

pip install --index-url https://test.pypi.org/simple/ \
            --extra-index-url https://pypi.org/simple/ \
            gasfir==X.Y.Z

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Contributing

1. Fork and create a branch: git checkout -b feature/my-feature
2. Follow the code style (Black + isort + flake8 + mypy, Google-style docstrings)
3. Add tests; all new public functions need type annotations and a docstring
4. Open a merge request against main

Commit messages follow Conventional Commits: feat:, fix:, docs:, refactor:, test:, chore:

---

License

MIT — see LICENSE.

Citation

If you use GASFIR in your research, please cite the paper:

@article{Agarwal2026gasfir,
  title     = {General approximator for strong-field ionization rates},
  author    = {Agarwal, Manoram and Scrinzi, Armin and Yakovlev, Vladislav S.},
  journal   = {Physical Review A},
  volume    = {113},
  pages     = {L021101},
  year      = {2026},
  publisher = {American Physical Society},
  doi       = {10.1103/vxgm-kdtt},
  url       = {https://doi.org/10.1103/vxgm-kdtt}
}

Support

• Documentation: https://gasfir.readthedocs.io
• Issues: https://gitlab.mpcdf.mpg.de/gaf/gasfir/issues
• Email: manoram.agarwal@mpq.mpg.de

Acknowledgments

Developed at the Max Planck Institute for Quantum Optics (MPQ).

See the CHANGELOG for a full history of changes.