Rueda et al. 2021: 0.29 mJ, 42 fs -> 8 fs, Ar 1500 mbar, 11 passes

0.29 mJ, 42 fs -> 8 fs, Ar 1500 mbar, 11 passes (Rueda et al., Opt. Express 29, 27004, 2021)

Paper: P. Rueda et al., Opt. Express 29, 27004 (2021), 10.1364/OE.435086
Script: benchmark/bench_rueda2021_8fs.py
Checks: 4 within tolerance, 0 outside

Note

Calibrated parameter. energy = 145 µJ instead of 290 µJ in the paper: x 0.5, as in the authors’ own simulation (pedestals, wavefront aberrations).

Paper and model

From the docstring of the script: what the paper describes, what the simulation uses, and what it leaves out.

Benchmark: 0.29 mJ, 42 fs -> 8 fs in a compact argon-filled MPC (lens-frame solver).

P. Rueda, F. Videla, T. Witting, G. A. Torchia, F. J. Furch, "8 fs laser pulses from a compact
gas-filled multi-pass cell", Opt. Express 29, 27004 (2021), doi:10.1364/OE.435086 (open access).

Few-cycle compression of a Ti:Sa CPA in a short, very concentric cell with only 11 passes, hence a
high B-integral per pass (the paper estimates 1.5 pi per round trip) and P/Pc ~ 1 at the nominal
energy. It complements the two Yb cases: 800 nm, a nearly octave-wide spectrum, self-steepening,
and visible space-time couplings, in a small cell.

                 paper                                          used here
laser            Ti:Sa CPA, 790 nm, 42 fs, nearly Fourier-      Gaussian 42 fs at 790 nm, flat phase
                 limited; 290 uJ at the first cavity mirror     (measured input not published)
energy           the authors' own 3D simulation multiplies the  energy = 0.5 x 290 uJ = 145 uJ
                 energy by 0.5 to reproduce the spectrum        (--set energy=290e-6: nominal)
                 (pedestals, wavefront aberrations)
mirrors          protected silver, RoC 300 mm, 2", R = 97 %     R = 0.97, flat, GDD = 0
                 flat in the authors' simulation
geometry         d = 584 mm, 11 passes through the focus         MPC(R=0.3, d=0.584, n_passes=11)
gas              Ar 1500 mbar, n2 from Wahlstrand 2012           Ar 1.5 bar, n2(1 bar) = 1.0e-23 m^2/W
compressor       12 bounces PC-70 + fused-silica wedges,         -480 fs^2 (assumption: -40 fs^2 per
                 after a 0.5 mm FS exit window                  bounce) + best fused-silica thickness

Measured: Fourier limit 5.0 fs in the text, but 6.2 fs for the spectrum of Fig. 3a (digitised in
data/; the simulation is compared with the latter), compressed 8.06 fs (SPIDER; limited by residual
third order), more than 6-fold broadening at 1/e, 85 % of the energy in the core of the focused
beam. The authors' simulation gives a space-time Strehl-like ratio of 0.91.
Transmission: the code counts one mirror bounce per pass (11), the experiment has 10 bounces on the
cavity mirrors; the 61.4 % chamber transmission of the paper also includes windows and steering
mirrors, so it is only shown for information.
Not modelled: ionisation (the paper suspects it explains the stronger blue shift of the measured
spectrum; the peak intensity is reported), the measured input spectrum and phase, chirped-mirror
GDD oscillations, the spectral response of the silver mirrors.

Usage: python bench_rueda2021_8fs.py [--quick] [--device cpu] [--set energy=290e-6] ...

Reference run


run	`run_38b076de`, 2026-11-05
code	thunder4d 1.0.0, git `ae152b3`, LensFrameSimulation
grid	Grid 120x120x360 (41 MB per field, cpu/scipy) \| box 1.13 x 1.13 mm, dx = 9.4 um \| T = 822 fs, dt = 2.28 fs \| lambda window 450-1307 nm
steps	phi_max = 0.02 rad, gouy_step = 0.05 rad, 1292 steps
run time	11 passes in 6.0 min (cpu, scipy)

../_images/rueda2021_8fs.png — Fig. 7 Standard figure of the reference run. Top: transmission, HG₀₀ fraction, homogeneity and B-integral vs pass; beam radius and peak intensity at the cell centre; output spectrum (with the measured or published spectrum when available). Bottom: compressed pulses vs the Fourier limit; output spatio-spectral trace S(θ, λ); fluence on the last mirror.

Comparison with the paper

output	simulation	paper	deviation	status	description
`transmission`	0.7151	0.737	-3 %		cell transmission (0.97^10; chamber incl. windows: 0.614)
`I_peak_max_Wcm2`	1.699e+13 W/cm2	< 1e+14	-83 %	ok	max peak intensity at the cell centre (Ar ionisation, order of magnitude)
`edge_fraction`	4.328e-08	< 0.001	-100 %	ok	max fluence fraction outside 70 % of the box (should be ~0) (numerical check)
`similarity_measured`	0.9513				spectral similarity with the measurement
`ftl_measured_fs`	6.178 fs				Fourier limit of the measured (digitised) spectrum
`ftl_fs`	6.284 fs	6.2 ±10%	+1 %	ok	Fourier limit (integrated spectrum) (FTL of the measured spectrum (Fig. 3a); text: 5.0 fs)
`fwhm_measured_pulse_fs`	8.419 fs				FWHM of the measured (digitised) pulse
`comp_fs`	6.852 fs	8.06	-15 %		compressed, -480 fs2 + 6.92 mm FS (SPIDER, limited by residual TOD)
`broadening_1e`	7.444	> 6	+24 %	ok	spectral width at 1/e, output / input (frequency) (> 6-fold at 1/e)
`core_energy_fraction`	0.9893	0.85	+16 %		far-field energy within diameter pi x w (1/e2 half width) (measured, focused beam)

Other outputs

output	simulation	description
`w0_um`	110.2 um	linear eigenmode waist (1/e2 radius)
`w_mirror_um`	675 um	linear mode on mirror (1/e2 radius)
`w0_injected_um`	110.2 um	injected waist (linear)
`P_over_Pc`	0.4900	input peak power / critical power
`B_estimate_rad`	42.45 rad	B-integral, matched-mode estimate
`B_rad`	25.14 rad	B-integral, on-axis peak
`F_mirror_max_Jcm2`	0.0340 J/cm2	max fluence on the mirrors
`eta00_final`	0.9911	HG00 fraction, output
`M2x`	1.003	M2 x (spectrally weighted)
`M2y`	1.003	M2 y (spectrally weighted)
`w_breathing`	0.3514	beam-size oscillation (max-min)/w_in
`span20_nm`	343.1 nm	-20 dB spectral width
`rms_width_nm`	63.43 nm	RMS spectral width
`lambda_centroid_nm`	779.9 nm	spectral centre of mass
`best_gdd_fs2`	-208.7 fs2	GDD maximising the peak power
`best_comp_fs`	8.174 fs	compressed with the best GDD
`best_peak_ratio`	0.7085	peak power / Fourier limit (best GDD)
`best_peak_power_GW`	10.66 GW	compressed peak power (best GDD)
`V_weighted_x`	0.9994	homogeneity, intensity weighted in 1/e2 (x)
`V_min_fwhm`	0.9994	min homogeneity within FWHM
`V_min_e2`	0.9947	min homogeneity within 1/e2
`comp_peak_ratio`	0.8752	peak power / Fourier limit (paper compressor)
`fs_thickness_mm`	6.915 mm	fused silica needed on top of the chirped mirrors

Measured data

Curves digitised from the paper, in benchmark/ (see the header of each file for the figure and the units):

spectrum: data/rueda2021_spectrum.csv
pulse: data/rueda2021_pulse.csv

Reproducing

cd benchmark
python bench_rueda2021_8fs.py --device cpu
python analyze.py rueda2021_8fs