UltrafastEngine

Tutorial 5 -- Contrast of an amplifier chain

Goal: follow a weak satellite pulse through a CPA chain and see how a nonlinear element turns a harmless post-pulse into a pre-pulse; measure it as a third-order cross-correlator would; scan the pulse energy with a parameter study and compare with the analytic estimate.

Files: docs/examples/LaserSystems/contrast-chain/ (chain.ufs, run.json, study.json). Run the commands from that folder.

1. The chain

"elements": [
  { "id": "stretcher",  "type": "dispersion", "gddFs2": 5.0e6 },
  { "id": "window",     "type": "plate", "material": "FusedSilica", "thicknessM": 3e-3,
                        "ghosts": { "orders": 1, "overlap": 1.0 } },
  { "id": "rod",        "type": "bulk", "material": "YAG", "lengthM": 0.02, "nonlinear": true,
                        "beam": { "kind": "constant", "radiusM": 0.5e-3 } },
  { "id": "compressor", "type": "dispersion", "gddFs2": -5.0e6 }
]

A 300 fs pulse is stretched to about 46 ps. It crosses an uncoated 3 mm window: the part reflected at the back surface and again at the front surface follows the main pulse by 2 n_g d / c = 29.3 ps with R² = 1.14·10⁻³ of its intensity (the window's note in summary.json says so). This ghost overlaps the stretched pulse. Then a 2 cm YAG rod (standing in for the amplifier crystal) adds a B-integral of about 1.9 rad, and the compressor removes the stretch. "overlap": 1.0 assumes the ghost stays on the main beam (normal incidence, no wedge); leave it out and the engine computes the overlap from the walk-off, the wedge and the beam size (components).

The run spec gives the input a weak exponential pedestal and measures the compressed pulse with a cross-correlator and the virtual contrast instrument:

"pulse": { "shape": "gaussian", "centerWavelengthM": 1.03e-6, "durationFwhmS": 300e-15, "energyJ": 5e-3,
           "pedestal": [ { "kind": "exponential", "level": 1e-6, "riseS": 2e-12, "fallS": 3e-12 } ] },
"instruments": [
  { "kind": "crossCorrelator", "name": "xc", "at": "end", "rangeS": [-60e-12, 60e-12], "stepS": 0.1e-12,
    "fineStepS": 20e-15, "fineRangeS": 2e-12, "dynamicRangeDb": 100, "probeDelaysS": [-29e-12, 29e-12] },
  { "kind": "contrast", "at": "end" }, { "kind": "pulseSummary" } ]

ultrafast run chain.ufs run.json -o results

The planner reports Estimated total B-integral (peak power after the dispersion before each element): 1.98 rad -- it applies the stretcher before estimating the rod's peak power -- and sizes the grid for the 84 ps group-delay spread plus the ghost (N = 32768, 15.6 fs steps, about one second).

The engine also warns that the peak power in the rod is 70 times the critical power for self-focusing. That is true of every mJ-class stretched pulse; whole-beam self-focusing needs a collapse length (here ~6 cm for a 0.5 mm beam) shorter than the crystal, so it is not an issue in 2 cm. Add "transverse": {"model": "radial"} to the rod to see it.

2. What the cross-correlator shows

summary.json → instruments → xc:

value meaning
postPulseContrastDb -26.6 dB at +29.1 ps the ghost: -29.4 dB from the window, raised by the Kerr effect
prePulseContrastDb -30.6 dB at -29.4 ps a pre-pulse that did not exist before the rod
fwhmS 0.51 ps the correlation width (gate and pulse convolved)

Plot it with ultrafast-plot results/ (xc_signal_db vs xc_delay_s), or in Python:

import ultrafast as uf, matplotlib.pyplot as plt
r = uf.load("results")
plt.plot(r["xc_delay_s"] * 1e12, r["xc_signal_db"]); plt.xlabel("delay (ps)"); plt.ylabel("signal (dB)")

Why the pre-pulse appears: in the stretched pulse every frequency arrives at a different time. The ghost is a delayed copy, so where it overlaps the main pulse the two beat at the frequency difference set by the 29 ps delay; the Kerr effect writes that beat as a phase modulation of the main pulse, which creates two sidebands -- after compression one at +29 ps (adding to the post-pulse) and one at -29 ps: a pre-pulse. Its relative intensity is approximately ε (B/2)² (Didenko et al., Opt. Express 16, 3178 (2008)), here 1.14·10⁻³ × 0.9 → -29.9 dB; the simulation gives -30.6 dB because the ghost sits where the stretched intensity, and so the local B, is lower than at the peak.

3. Scan the pulse energy

study.json runs the chain for nine energies between 0.1 and 10 mJ:

{ "format": "ultrafast-study", "system": "chain.ufs", "run": "run.json",
  "mode": "scan", "sampling": "grid", "parallel": 4,
  "parameters": [ { "path": "pulse/energyJ", "min": 0.1e-3, "max": 10e-3, "scale": "log", "points": 9 } ],
  "outputs": [ "record:rod/BIntegralRad", "instrument:xc/prePulseContrastDb",
               "instrument:xc/postPulseContrastDb", "pulse:end/fwhmS" ] }

ultrafast study study.json -o study-results        # 9 runs in ~5 s; study-results/study.csv
energy (mJ) B (rad) pre-pulse (dB) post-pulse (dB) FWHM (fs)
0.10 0.04 -58.1 -29.5 300
0.32 0.12 -54.0 -29.5 300
1.0 0.38 -45.4 -29.5 300
3.2 1.21 -35.3 -28.4 313
5.6 2.15 -29.3 -25.9 381
10 3.82 -24.4 -23.1 1068

Three regimes:

  • Low energy: the pre-pulse stays near -58 dB. That is not the pulse: a third-order correlator also shows a post-pulse ε at -T through its gate, with intensity ~ε² (1.3·10⁻⁶ → -59 dB). Real devices have this artefact too (the instrument's note says so) -- check signal_ideal or the contrast instrument to tell them apart.
  • Middle: the pre-pulse rises by 20 dB per decade of energy, i.e. as B² -- the signature of this mechanism.
  • High energy (B > 2): the SPM chirp is no longer removed by the compressor (the FWHM grows), and pre- and post-pulse approach each other.

The grid was frozen at the nominal run's plan, so all points are directly comparable; the stretcher and window are cached and only the rod and compressor are recomputed (Parameter studies).

4. Things to try

  • Wedge the window: "wedgeDeg": 0.1, "ghosts": { "orders": 1, "beamRadiusM": 0.5e-3 } (no fixed overlap). The ghost is tilted by 2 n α and no longer overlaps the beam (the note gives the overlap); the pre-pulse falls to the floor (-52 dB).
  • Move the window after the rod: the ghost is then created after the nonlinearity and stays a post-pulse.
  • Replace the window by an ndFilter ("kind": "reflective"): its ghost is much stronger.
  • Add { "kind": "prePulse", "delayS": 12e-12, "relativeIntensity": 1e-6 } to the pedestal and watch it in the cross-correlator, or a phaseNoise component for the coherent pedestal of a real stretcher.
  • Optimise instead of scanning: "mode": "optimize", "objective": {"output": "instrument:xc/prePulseContrastDb", "goal": "target", "target": -40} with the energy as the only parameter (no points) finds 1.88 mJ in 40 runs (analysis.optimum).