Ma et al. (2018): a single-shot cross-correlator for pulse contrast¶

Reading status. Open access (CC BY 4.0). The Read tool's PDF mode failed (poppler missing); the 11-page text was read through the macOS PDFKit text layer, which is clean. Equations (1) and (2) and Fig. 4c were checked on page images (Fig. 4c at 7x). The PDF and its figures are not in the repository. Anything not in the text is marked UNVERIFIED.

What the paper is¶

A review of one instrument. Petawatt lasers need a pulse contrast near 1e10, and the standard tool (a delay-scanning third-order cross-correlator) needs thousands of shots. The single-shot version crosses the pulse under test (PT) and a clean sampling pulse (usually its second harmonic) at a large angle in a nonlinear crystal. Where the beams meet at different times across the crystal, the sum-frequency signal at position x measures the PT at delay tau(x): time is encoded in space. The paper's key points:

• Window and resolution from geometry (eqs. 1, 2): T = W/c (n_T sin a + n_S sin b) and dtau = L/c (n_T cos a - n_S cos b), with W the width of the beam overlap, L the crystal length, a and b the angles of the two inputs to the signal beam. A larger angle gives a larger window and a worse resolution. Quasi-phase matching in PPLN allows larger angles (45 ps/cm; about 70 ps/cm for m = 3, 5).
• Dynamic range from reading the 100 spatial channels through delay-staggered fibres into one PMT: 1e10, up to 3e10 (a detector specification; a CCD reaches only about 1e6).
• Artefacts of time-to-space encoding: air scattering of the bright signal peak (1e-8 to 1e-6) and spikes from reflections between crystal faces at +-2 n L/c. Demonstration of the range: a 1.1 mm BK7 plate in the sampling arm makes three replicas (Fig. 4c).

What the engine can and cannot do here¶

paper element	engine
noncollinear SFG, phase matching, internal angles, indices (BBO, PPLN)	yes: crystal.phase_match
window and resolution from the crossing geometry, eqs. (1)-(2); position-to-delay mapping on a camera	yes: singleShotCorrelator instrument (BBO, any library crystal or given indices); area conserved
plate replicas in the sampling arm (Fig. 4c)	yes: crossCorrelator with gateArm (plate with ghosts, compiled at the second-harmonic wavelength)
dynamic-range floor, resolutionS	yes: crossCorrelator (dynamicRangeDb, resolutionS)
PPLN windows (QPM, 800 nm + 3.3 um assumed)	only through eq. (1) with the phase-matching calculator: the instrument's sampling pulse is the second harmonic or the pulse itself, so a 3.3 um sampling pulse cannot be set
not simulated by singleShotCorrelator	beam propagation in the crystal (conversion efficiency, depletion, the envelope of the signal across the overlap, walk-off); air scattering of the bright signal (1e-8 to 1e-6, paper p. 6); the stripe filter; reflections between the crystal faces (spikes at +-2 n L / c); the fibre array, delay-staggered fibres and the PMT. The engine's spatial sfg crystal on a Cartesian grid does reproduce the mapping at 20 degrees (slow test SpatialSfgOfTwoCrossedBeams_PutsAReplicaAtTheInstrumentsPosition), but a 40 degree, centimetre-wide, 50 ps case was not attempted

Eqs. (1) and (2) are therefore tested with the instrument, not only analytically; the physics of the instrument's artefacts (the paper's second half) is not.

Setup (run.py)¶

1. Geometry, analytic. phase_match("BBO", "sfg", "I", a=lambda, b=lambda/2, noncollinear=...) for 800 + 400 nm and 1053 + 526.5 nm, L = 1.5 mm; alpha, beta, n_T, n_S from its output, then eqs. (1) and (2). PPLN (LiNbO3, first-order QPM, 6 um, 800 nm + 3.3 um; the PT wavelength is UNVERIFIED: it is in the paper's ref. [26]): the angle where the engine's phase mismatch changes sign is found by bisection. m = 3 is a first-order grating of 2 um.
2. Fig. 4c. One crossCorrelator on a probe system (800 nm, 1 uJ) with gateArm: a 1.1 mm N-BK7 plate with three ghost orders acts on the second-harmonic gate only. 200 fs (quantitative check, dispersion negligible) and 50 fs (assumed, as Fig. 3); 200 dB range so nothing is hidden. This replaces the earlier Branched system (beam splitter, SHG, plate, SFG, delay study), which took two minutes; now 0.5 s.
3. Instrument dynamic range. crossCorrelator on a 50 fs pulse with pre-pulses 1e-6, 1e-9, 1e-11 at -10, -23, -34 ps and a 105 dB floor (the 3e10 range), without and with resolutionS = 1 ps.
4. singleShotCorrelator. BBO, delayIndex: "phase" (that choice makes the resolution exactly eq. (2)). (a) window and resolution at the largest angle of 800 nm (34 deg) and 1053 nm (40 deg) against section 1; resolution against L = 1, 1.5, 2 mm with phase and group indices. (b) 1053 nm, 40 deg, W = 20 mm, L = 1 mm, 50 fs pulse with pre-pulses 1e-3 at -20 ps and 1e-4 at -35 ps: where they land and how high.

Results¶

Left: eq. (2) resolution (solid) and eq. (1) window per cm (dashed) against the crossing angle inside BBO. Right: window per cm for the four cases against the paper's numbers.

Third-order signal of the crossCorrelator with the plate in the gate arm (blue line, 50 fs pulse), the replica peaks for 200 fs (orange) and 50 fs (open squares). Grey bars: R^(2k) from Fresnel. Black diamonds: the paper's Fig. 4c read off. Time axis as in the paper.

The crossCorrelator at 105 dB with three injected pre-pulses, without (blue) and with (orange) resolutionS = 1 ps. Both read -60 dB for 1e-6 and about -90 dB for 1e-9; the 1e-11 pre-pulse is below the floor. The 1 ps smoothing no longer moves the floor or the reported contrast.

Left: the singleShotCorrelator trace against position across the overlap for a 50 fs pulse with two pre-pulses; the black diamonds are the injected levels at x = T / slope (the time-to-space mapping of the paper). The peak at +5.3 mm (-60 dB) is the pre-pulse seen by the other beam: the second-harmonic gate carries the pre-pulse at e^2 = 1e-6 and the main pulse samples it at +20 ps (our reading of the engine's output, not a statement of the paper). Right: resolution against crystal length: eq. (2) (phase indices, crosses, matching the instrument to 1e-6) and the instrument with group indices (orange), which is 18 % larger.

Comparison table¶

quantity	paper (location)	ours	verdict
resolution, about 40 deg, 1-2 mm BBO	about 1 ps (p. 2)	instrument: 0.53 / 0.79 / 1.05 ps at L = 1 / 1.5 / 2 mm (1053 nm, 40 deg, phase indices = eq. 2; equal to the analytic value to 1e-6); with group indices 0.62 / 0.93 / 1.24 ps	agrees (brackets 1 ps)
largest crossing angle in BBO	about 40 deg (p. 2)	34 deg (800 nm), 40 deg (1053 nm) inside the crystal	agrees for 1053 nm
window per cm, BBO	not given; windows 50 / 70 ps (p. 9)	instrument = eq. (1): 32.4 (800) / 37.6 (1053) ps/cm (ratio 1.00000), implying W = 1.5 / 1.9 cm (W not given)	consistent, W UNVERIFIED
PPLN 6 um, m = 1, window	about 45 ps/cm (p. 4)	44.2 ps/cm at 37.4 deg (alpha 6.8, beta 30.5 deg)	agrees (PT wavelength assumed 800 nm, UNVERIFIED)
PPLN m = 3 (5)	about 70 ps/cm (p. 4)	81 ps/cm (period of that case not given)	larger as stated; value differs 16 %
crystal-face spike at 15 ps	2 n_S L / c (p. 7, Fig. 6a)	implies L = 1.33 mm in BBO (within the 1-2 mm of p. 2)	consistent; L of that figure UNVERIFIED
BK7 1.1 mm replica spacing	equal, about 11.3-11.8 ps read off Fig. 4c	11.628 ps = 2 n_g d / c	agrees
replica I	about 6e-4 (read off)	1.93e-3 (R^2 = 1.94e-3; gateArm, 200 fs); 1.74e-3 at 50 fs	0.5 decade above the paper
replica II	about 2.7e-6	3.73e-6 (R^4 = 3.77e-6); 2.9e-6 at 50 fs	agrees (0.14 decade)
replica III	about 8e-10 read off; "about 1e-9" (p. 6)	7.2e-9 (R^6 = 7.3e-9); 4.7e-9 at 50 fs	about 0.9 decade above the paper
pre-pulse at -20 ps (1e-3), -35 ps (1e-4)	time-to-space mapping, x = T / slope (Fig. 1)	instrument: position error 3e-5 pixel, level / injected 1.0000	engine self-consistency (analytic by construction)
dynamic range	1e10, 3e10 (pp. 1, 6)	detector specification; engine floor set to 105 dB and read back (-60.0, -89.9, -103.8 dB for 1e-6, 1e-9, 1e-11: the last is floor plus 1e-11, not resolved)	not a test of the paper (circular)
channels, fibre delay 1-1.5 m, 1 ns PMT	p. 5	not modelled; dt = dl n / c is 4.8-7.3 ns for n = 1.45 (UNVERIFIED core index)	arithmetic only

What agrees¶

The engine reproduces its own Fresnel ladder to 1.3 % (200 fs; the ratios are 0.993, 0.991, 0.987), the spacing exactly, and the geometric resolution and PPLN window within the paper's rounding. With a 50 fs pulse the replicas that went through the plate three, five and seven times are lower because the plate stretches them (the BK7 group-delay dispersion at 400 nm is 122 fs^2/mm): a real effect of a plate in the sampling arm, not an engine error (0.90, 0.76, 0.64 of R^(2k) with the gateArm version).

What does not reproduce¶

• Replicas I and III are 0.5 and 0.9 decade above Fig. 4c. The paper gives no plate angle, polarisation, coating, wavelength or attenuator calibration; an uncoated plate at normal incidence has R^2 = 1.9e-3 per order by Fresnel, which the engine reproduces to 1 %, so this is a setup difference (a tilted or coated plate, a sampling wavelength of 800 nm, a calibration of the fibre attenuators), not evidence against the engine. Not tuned. Replica III in the paper also sits among background fluctuations of 1e-9, so the read-off is uncertain.
• Resolved engine finding: crossCorrelator with resolutionS. An earlier version of this folder reported (minimal case repro_1.py, now deleted) that with resolutionS = 1 ps the floor rose to -92.9 dB and contrastAt_m10ps_db read -72.1 dB while the trace read -60 dB. The engine now normalises all three to the resolution-limited peak: trace -60.0 dB, floor -105.0 dB, report -60.0 dB. The two checks are hard.
• The dynamic range itself is a detector specification (fibre array and PMT), not simulated: the 105 dB floor is an input, so reading it back is circular.

What is left¶

• Not simulated by singleShotCorrelator: beam propagation in the crystal (efficiency, depletion, the envelope across the overlap, walk-off), air scatter of the signal, the stripe filter, crystal-face reflections of the signal (the 15 ps spikes), the fibre array and PMT. These are the paper's artefact discussion (Sec. 5) and its dynamic-range claims; none is compared here.
• The PT wavelength of the PPLN case, the beam width W, the crystal length of Fig. 6a and the plate geometry of Fig. 4c (UNVERIFIED / not stated).
• Fig. 6b angle pairs (20, 44) and (4, 78) deg: wavelengths not stated, so not evaluated.
• A sampling pulse of a different wavelength than the second harmonic (the PPLN case) in singleShotCorrelator.

Run: python3 build/paper_check.py ma-2018 (fast, about 7 s now); python3 run.py --tier full --figures for the committed figures.

How well the science matched¶

Reasons: A = the paper does not specify inputs (assumption); E = erratum or internal inconsistency; L = engine limitation (named); B = engine bug (named); U = UNVERIFIED reading.

quantity	paper	ours	verdict	most likely reason
window T = W (n_T sin a + n_S sin b) / c, eq. (1)	formula	instrument = analytic to 1e-7 (BBO 800 / 1053 nm)	agrees	none (formula check; W not given: A)
resolution dtau, eq. (2)	about 1 ps for 1-2 mm at about 40 deg	0.53-1.05 ps (phase indices); 0.62-1.24 ps (group indices)	agrees	eq. (2) uses phase indices; the group-index version is larger by 18 % (our reading of the physics, not in the paper)
PPLN window, 6 um, m = 1	about 45 ps/cm	44.2 ps/cm	agrees	A: PT wavelength assumed 800 nm (U); analytic only (L: instrument has no free sampling wavelength)
PPLN window, m = 3 (5)	about 70 ps/cm	81 ps/cm	partly	A: the grating period of that case is not given
BK7 replica spacing	equal, about 11.5 ps	11.63 ps = 2 n_g d / c	agrees	none
replica I (1.1 mm BK7 plate in the sampling arm)	about 6e-4	1.9e-3 (R^2)	does not (0.5 decade)	A: plate angle, coating, polarisation, attenuator calibration not given
replica II	about 2.7e-6	3.7e-6	agrees (0.14 decade)	none
replica III	about 8e-10 / "about 1e-9"	7.2e-9	does not (0.9 decade)	A as for I, and U: the read-off sits among 1e-9 background fluctuations
pre-pulse position and height (time to space)	Fig. 1 principle	exact to 1e-5 pixel / 1e-9	agrees	engine self-consistency (analytic by construction), not a test of the paper
dynamic range 1e10 / 3e10	detector specification	input of the model	not tested	L: fibre array, PMT, air scatter, stripe filter not simulated
air scatter 1e-8 to 1e-6; crystal-face spikes at 15 ps	measured / Fig. 6a	spike delay implies L = 1.33 mm only	not tested	L: no beam propagation in the crystal, no scatter, no face reflections in singleShotCorrelator

Overall. The geometry of the instrument (eqs. 1 and 2, the position-to-delay mapping, the area law) and the replica ladder of a plate in the gate arm are now reproduced with engine instruments, the former to 1e-6 against the analytic formulas. The two replica levels that disagree with the paper come from a plate whose angle and coating the paper does not state; Fresnel for bare BK7 is what the engine gives. The paper's second half (dynamic range, scatter, reflections, the fibre-array read-out) is about the instrument's artefacts and electronics and is not simulated. To close the gap one would need a spatial model of the crossing beams in the crystal (efficiency, depletion, walk-off, face reflections) and the plate and attenuator data of the experiment.