Chirped Pulse Amplification (CPA)

Chirped pulse amplification: transform-limited duration of a bandwidth, stretcher GDD for a stretch ratio, Treacy grating-compressor separation, recompressed duration against a separation error, and peak powers.

Model: Textbook approximation

Centre wavelength (nm)Spectral bandwidth, FWHM (nm)Stretch ratio τ_s/τ₀Amplified pulse energy (mJ)Compressor grating (lines/mm)Incidence angle (°)Compressor separation offset ΔG (mm)

Transform-limited duration τ₀

94.21 fs

Gaussian, Δν = 4.684 THz, τ₀ = 0.4413/Δν

Stretched duration

94.21 ps

stretcher GDD +3.201 ps²; peak in the amplifier 9.972 MW

Matched grating separation G

225.6 mm

double pass, β = 43.23°, -1.419e4 fs²/mm; TOD 1.140e7 fs³

Recompressed duration

125.9 fs

residual GDD -2838 fs²; peak 7.461 GW, assuming a lossless compressor (real four-reflection grating compressors pass ≈ 60–70 %)

A Gaussian spectrum of FWHM Δν supports a pulse no shorter than τ₀ = 0.4413/Δν. A GDD φ₂ stretches it to τ₀√(1 + (4 ln2 φ₂/τ₀²)²), so the stretcher needs φ₂ = (τ₀²/4 ln2)√(r² − 1) for a stretch ratio r. The amplifier sees the lower stretched peak power. A Treacy grating pair, passed twice, gives φ₂ = −2Gλ³/(2πc²d²cos³β) with sin β = λ/d − sin α, and the separation G that cancels the stretcher returns the pulse to τ₀. Moving the grating by ΔG leaves a residual GDD and a longer pulse; no setting gives less than τ₀. The stretcher is assumed to cancel the compressor TOD as well.

Recompressed duration against grating separation

Output FWHM
Set offset

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Gaussian pulses with quadratic spectral phase: τ = τ₀√(1 + (4 ln2 φ₂/τ₀²)²), τ₀ = 0.4413/Δν. Treacy double-pass grating-pair GDD and TOD in the first order; the stretcher is assumed to cancel the compressor TOD, and the compressor is lossless. Gain narrowing, the B-integral and material dispersion are not modelled.

Treacy E. B. (1969). Optical pulse compression with diffraction gratings. IEEE J. Quantum Electron. 5, 454–458. doi:10.1109/JQE.1969.1076303
Strickland D., Mourou G. (1985). Compression of amplified chirped optical pulses. Opt. Commun. 56, 219–221. doi:10.1016/0030-4018(85)90120-8
Diels J.-C., Rudolph W. (2006). Ultrashort Laser Pulse Phenomena, 2nd ed., ch. 1. Academic Press.

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