References

Companion papers

• J. C. Travers and C. Brahms, “Differentiable physical models for ultrashort-pulse retrieval,” in preparation. — the inverse problem: the retrieval protocol and what each forward model recovers from simulated TG-FROG measurements.

• J. C. Travers and C. Brahms, “A dispersive and spatial model of transient-grating frequency-resolved optical gating,” in preparation. — the coherent slab, the timing reduction, chromatic focal fields, finite collection and the fixed-field validation of the forward model.

The validation chapter summarises their results.

If you use croak in published work, please cite the first paper, together with the software version you used: the all-version software archive is doi:10.5281/zenodo.22182305, and the repository’s CITATION.cff gives both citations.

Foundational work

• N. 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), doi:10.1364/OPTICA.6.000495. — the COPRA algorithm and the least-squares / projection analysis that croak’s solvers build on.

• R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2000). — the standard reference on FROG, its geometries and the trace (FROG) error.

• D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993). — the original FROG.

Uncertainty & statistics

• Z. Wang, E. Zeek, R. Trebino, and P. Kvam, “Determining error bars in measurements of ultrashort laser pulses,” J. Opt. Soc. Am. B 20, 2400–2405 (2003), doi:10.1364/JOSAB.20.002400. — the bootstrap (data-resampling) method for FROG error bars.

• B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, 1993). — the parametric, nonparametric and residual bootstrap.

• T. J. DiCiccio and B. Efron, “Bootstrap confidence intervals,” Statist. Sci. 11, 189–228 (1996). — BCa (bias-corrected and accelerated) intervals for skewed estimators. croak implements bias correction without the acceleration term (BC), not BCa; see uncertainty theory.

• G. A. F. Seber and C. J. Wild, Nonlinear Regression (Wiley, 1989). — the \(\hat\sigma^2 (J^\top J)^{-1}\) local covariance approximation of a nonlinear least-squares fit, with its regularity and noise assumptions.

Related techniques

• M. Miranda et al., “Simultaneous compression and characterization of ultrashort laser pulses using chirped mirrors and glass wedges” (d-scan), Opt. Express 20, 688–697 (2012), doi:10.1364/OE.20.000688.

• D. Spangenberg, E. Rohwer, M. H. Brügmann, and T. Feurer, “Ptychographic ultrafast pulse reconstruction” (time-domain ptychography), Opt. Lett. 40, 1002–1005 (2015), doi:10.1364/OL.40.001002.

Software and data sources

• ModelPNPS.jl — the companion papers’ instrument simulator: an open-source Julia package (built on Luna.jl) that simulates PNPS measurements in three dimensions from the underlying propagation physics. It produced the validation datasets summarised in Validation, including the reduced scans shipped in examples/data/.

• optmat — curated, validated optical properties of gases, glasses, crystals and metals (MIT; Zenodo, doi:10.5281/zenodo.23422879). Every built-in material and gas index in croak is optmat’s recommended model; optmat’s manual cites the primary source of each.

• Luna.jl — an open-source (MIT) Julia package for nonlinear optical pulse propagation. croak’s bundled chirped-mirror tables are taken from Luna’s PhysData module, and read_simulated_scan() reads the HDF5 files written by Luna’s scansave.