The PNPS Framework
ModelPNPS is organised around the PNPS (Parametrized Nonlinear Process Spectrum) formalism of Geib et al. (2019)[geib], which provides a single mathematical description for the whole family of self-referenced ultrashort-pulse measurement techniques — FROG, d-scan, MIIPS, time-domain ptychography and their many process variants. How the framework extends when the idealisations behind the standard forward models fail — dispersion in the nonlinear medium, the beam-crossing geometry, the chromatic collection aperture — is the subject of the paper ModelPNPS was built for[travers].
The PNPS trace
A PNPS measurement records a two-dimensional trace that depends on the pulse, the (angular) frequency $\omega$, and a method-specific parametrization variable $\delta$:
\[\tilde{T}(\delta, \omega; \tilde{E}) = \left| \mathcal{F}\!\left[ S_\delta[\tilde{E}](t) \right](\omega) \right|^2 .\]
Here $\tilde{E}$ is the complex pulse, $\mathcal{F}$ the Fourier transform, and $S_\delta$ the parametrized nonlinear-process signal operator. The signal operator combines
- a nonlinear process $N[\tilde{E}]$ that converts the pulse via a collinear nonlinearity, and
- a parametrization filter $\mathcal{H}_\delta(\omega)$ that applies the scanned modification (a delay, a glass insertion, a phase-pattern shift, …).
A measurement technique is therefore specified by a (process × parametrization) pair, and its standard name follows the pattern [Process]-[Parametrization] (e.g. SHG-FROG, SD-FROG, SHG-d-scan).
Nonlinear processes
| Process | Signal $N[\tilde{E}]$ | Notes |
|---|---|---|
| SHG | $\tilde{E}^2$ | second-harmonic generation |
| THG | $\tilde{E}^3$ | third-harmonic generation |
| SD | $\lvert\tilde{E}\rvert^2\tilde{E}$ | self-diffraction |
| PG | $\lvert\tilde{E}\rvert^2\tilde{E}$ | polarization gating |
| TG | degenerate four-wave mixing | transient grating; two gate beams + test |
| X- | $\tilde{E}\,\tilde{E}_\text{ref}$ | cross-correlation with a reference |
Parametrizations
| Parametrization | Variable | Filter | Family |
|---|---|---|---|
| Delay | delay $\tau$ | $e^{i(\omega+\Omega_0)\tau}$ | FROG |
| Glass insertion | thickness $z$ | $e^{i(\omega+\Omega_0)k(\omega)z}$ | d-scan |
| Pattern shift | phase-pattern shift | $e^{\pm i(\omega+\Omega_0)\delta}$ | MIIPS |
| Position | spatial/scan position | spatial filtering | ptychography |
Roadmap
ModelPNPS currently implements TG-FROG. The table below places the planned methods in the PNPS taxonomy and tracks their status. Several SHG/SFG-based methods depend on second-order nonlinearity support arriving in Luna.
| Technique | Process | Parametrization | Status |
|---|---|---|---|
| TG-FROG | TG (four-wave mixing) | delay | ✅ implemented |
| X-TG-FROG | TG + reference | delay | 🔜 planned |
| SD-FROG | SD | delay | 🟡 input geometry implemented |
| SHG-FROG | SHG | delay | ⏳ pending Luna SHG/SFG support |
| THG-FROG | THG | delay | ⏳ planned |
| X-FROG (SHG/SD/THG) | cross-correlation | delay | ⏳ planned |
| SHG-d-scan | SHG | glass insertion | ⏳ pending Luna SHG/SFG support |
| SD-d-scan | SD | glass insertion | 🔜 planned |
| Time-domain ptychography | SHG/THG/SD | position | ⏳ planned |
Legend: ✅ available · 🟡 partial · 🔜 planned next · ⏳ planned (may depend on upstream features).
The modelling goal is the same across every entry: capture the spatial, dispersive, phase-matching, walkoff and nonlinear-efficiency physics of the real experiment, so that the simulated trace is a usable ground truth for retrieval-algorithm development and validation.
- geibN. C. Geib, M. Zilk, T. Pertsch, and F. Eilenberger, "Common pulse retrieval algorithm: a fast and universal method to retrieve ultrashort pulses," Optica 6, 495–505 (2019).
- traversJ. 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.