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ModelPNPS

ModelPNPS is a Julia package for forward modelling of PNPS (Parametrized Nonlinear Process Spectrum) pulse-characterisation measurements. Given an input pulse and an experimental geometry, it generates the trace a real apparatus would record, by full spatially-resolved nonlinear propagation through the measurement medium using Luna.jl.

The point is a faithful numerical experiment rather than a fast 1-D approximation: the simulated trace contains the effects that the analytic forward models inside retrieval algorithms neglect. Because the input pulse is known exactly, such traces are ground truth for testing and developing retrieval algorithms. ModelPNPS does the forward modelling only; the retrieval half is its companion package, Croak, which reads the scan files ModelPNPS writes and retrieves the pulse from them.

Simulated TG-FROG traces of a 1 fs, 260 nm pulse after 9.5, 24 and 40 µm of fused silica

Simulated TG-FROG traces of a 1 fs, 260 nm pulse after 9.5, 24 and 40 µm of fused silica — the substrate-thickness series of the reference paper below. The transient grating, the phase-matched four-wave-mixing signal, the geometrical delay smearing and the chromatic aperture response all emerge from the propagation; none is imposed.

The paper

ModelPNPS was built for, and is described in:

J. C. Travers and C. Brahms, Extreme ultrashort pulse retrieval with differentiable physical forward models (in preparation, 2026). (Placeholder — this reference will be updated on publication.)

The paper uses ModelPNPS as a first-principles virtual TG-FROG instrument: a transform-limited 1 fs pulse at 260 nm illuminates a four-hole boxcar mask, the three transmitted beamlets are focused into a fused silica substrate, and the tilted, spatially separated fields are propagated coherently with full angular-spectrum dispersion, diffraction and the Kerr nonlinearity. The signal is collected through an apertured window in the far field, delay by delay, exactly as a spectrometer would record it. The paper specifies this instrument in detail, bounds every approximation the simulation itself makes (at or below the $10^{-4}$ level, with the delayed Raman response treated separately), and uses the resulting traces to validate retrieval models against the dispersion, beam-geometry and collection physics of few-femtosecond deep-ultraviolet measurements. The retrievals themselves are done with Croak, which implements the paper's differentiable forward models and solvers. If you use ModelPNPS in published work, please cite the paper.

Scope

The aim is a complete PNPS trace-modelling package — 3D numerical models of the major pulse-characterisation experiments, built so that the simulated trace reflects the real physics of the measurement:

  • Spatial effects — finite beam size, mode shape, beam overlap and crossing geometry, diffraction, apertures and mask edges.
  • Phase-matching — the wavelength- and angle-dependent efficiency of the nonlinear process across the interaction volume.
  • Dispersion — material dispersion of the nonlinear medium and the associated pulse reshaping during propagation.
  • Walkoff — spatial and temporal walkoff between the interacting beams.
  • Chromatic vignetting — the wavelength-dependent spatial filtering of the signal beam by the collection optics.
  • Real nonlinear efficiency — the true χ⁽ⁿ⁾ conversion, not an idealised instantaneous-thin-medium response.

These effects matter most where the analytic forward models break down: broadband DUV/VUV pulses, thick media, strongly phase-mismatched geometries.

Current status

The currently implemented process is TG-FROG (Transient-Grating FROG): a degenerate four-wave-mixing measurement in a thin solid substrate, modelled with two beam schemes (hollow-fibre HE₁₁ mode through a four-hole boxcar mask, or a simplified Gaussian-beam baseline) and a choice of signal-extraction windows. A self-diffraction beam layout is also available, as the input geometry for the planned SD-FROG process. See Trace Simulation for the full description and worked examples, and the PNPS Framework page for the broader taxonomy and roadmap.

Beyond the core forward model, the package can inject a measured or separately simulated pulse in place of the analytic Gaussian (Input Pulses), add the delayed nuclear response (Nonlinear Response), and propagate a real carrier-resolved field instead of an envelope (Field-Resolved Mode) — the last of these being how the envelope approximation itself gets tested at single-cycle durations.

Runs on a GPU, and that is the fast way

A full delay scan at realistic grid sizes is hours of work per delay point on CPUs. On an NVIDIA GPU the whole propagation runs on the device: 42 s per delay point on an H200 against 1.9 h on two CPU cores, a factor of about

  1. See Running on a GPU. The CPU path remains fully supported

and is intended for a SLURM cluster, one task per delay.

The unit tests stay laptop-fast either way, by exercising every primitive without the propagation step, plus one tiny end-to-end smoke run.

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