Chirped-pulse amplification (CPA)

Chirped-pulse amplification (CPA) raises the energy of femtosecond and picosecond pulses without letting their peak intensity damage the amplifier. A short pulse from an oscillator is first stretched in time by a dispersive element that gives it a strong frequency chirp, typically from tens of femtoseconds to a few hundred picoseconds. The stretched pulse is amplified, often by a factor of 10⁶ or more, and a pulse compressor with the opposite dispersion then restores the short duration. Because the intensity in the amplifier is lower by the stretch factor, a 10 mJ pulse that would self-focus and damage a sapphire crystal at 100 fs passes it safely when stretched to 300 ps. Donna Strickland and Gérard Mourou demonstrated the method in 1985, and it earned them half of the 2018 Nobel Prize in Physics.

Stretcher, amplifier and compressor

The stretcher adds a large positive group-delay dispersion (GDD), so that red frequencies lead and blue frequencies trail. For a Gaussian pulse of transform-limited width $\tau_0$, stretched far beyond it, the width grows approximately as

$$\tau \approx \frac{4\ln 2\;\mathrm{GDD}}{\tau_0}.$$

Stretching a 30 fs pulse to 300 ps, a factor of 10⁴, therefore needs a GDD of about 3.25 × 10⁶ fs² (3.25 ps²). Such values come from grating stretchers, usually a Martinez arrangement, in which a telescope between two diffraction gratings reverses the sign of the grating-pair dispersion, or its all-reflective Öffner variant with a single grating, or from long lengths of fiber or chirped fiber Bragg gratings in fiber systems.

The amplifier is commonly a regenerative amplifier for the first factor of 10⁶, followed by multipass stages. Ti:sapphire dominates at 800 nm for pulses of 20–50 fs; ytterbium-doped crystals, thin disks and fibers dominate at 1030 nm for pulses of a few hundred femtoseconds and higher average power. The compressor is normally a grating pair with negative GDD matched to the stretcher; with 1200 lines/mm gratings at 30° incidence and 800 nm, a double-passed pair needs a perpendicular separation of about 87 cm to cancel 3.25 ps². The last compressor grating sees the full energy at the short duration, so its damage threshold and size set the output limit of large systems.

Peak power and the B-integral

The gain in peak power is set by the compressed duration. A 1 J pulse compressed to 30 fs with a Gaussian shape has a peak power of 0.939 × 1 J / 30 fs, about 31 TW. Petawatt-class systems deliver tens of joules in similar durations, and the most powerful facilities have reached about 10 PW.

Damage is one reason to stretch; nonlinear phase is the other. The optical Kerr effect adds a phase proportional to intensity, and the accumulated on-axis value through the amplifier chain is the B-integral,

$$B = \frac{2\pi}{\lambda}\int n_2\,I(z)\,dz .$$

Consider 10 mJ at 800 nm in a Gaussian beam of 2.5 mm radius passing 2 cm of sapphire, with $n_2 \approx 3 \times 10^{-20}$ m²/W. At 100 fs the peak intensity is about 9.6 × 10¹¹ W/cm² and $B \approx 45$ rad. Stretched to 300 ps, the intensity falls to 3.2 × 10⁸ W/cm² and $B \approx 0.015$ rad. Large B-integral causes self-phase modulation that the compressor cannot remove and, across the beam, small-scale self-focusing that breaks the beam into filaments. Designers commonly keep the total B below a few radians.

Where it is used

CPA systems drive high-harmonic and attosecond-pulse generation, laser-plasma particle acceleration, and strong-field physics at focused intensities above 10¹⁹ W/cm². At lower energies, fiber CPA systems at 1030 nm provide the microjoule pulses used in ultrafast micromachining and ophthalmic surgery. Optical parametric CPA applies the same stretching to a parametric amplifier, which supports broader bandwidth and deposits little heat in the gain medium.

Pitfalls

Stretcher and compressor must cancel to higher orders. A residual third-order dispersion, from material in the amplifier chain that the gratings do not fully compensate, leaves a pulse with a pedestal or satellite pulses and a longer duration than the bandwidth permits. Gain narrowing in high-gain amplifiers narrows the spectrum and lengthens the compressed pulse. Amplified spontaneous emission and leakage of prepulses through the switching optics set the temporal contrast, which matters at high intensity because light arriving picoseconds early can ionize a target before the main pulse. Compressor transmission is modest: four grating reflections at 90–95 % efficiency each pass 66–81 % of the energy.

Common questions

Why can the pulse not be amplified directly?

At femtosecond durations the intensity of a millijoule pulse in a beam of a few millimetres exceeds 10¹¹ W/cm²; the nonlinear phase reaches several radians per pass through a 2 cm crystal and tens of radians over a multipass chain, and the beam self-focuses to intensities that damage the optics. Enlarging the beam to compensate would require impractically large crystals.

Who invented chirped-pulse amplification?

Strickland and Mourou at the University of Rochester, published in Optics Communications in 1985. The idea of stretching and compressing a chirped signal came from radar, where it had been used since the 1950s.

What limits the shortest pulse from a CPA system?

The gain bandwidth after gain narrowing, and how completely the compressor cancels the dispersion of the stretcher and amplifier materials to third and fourth order.

References: D. Strickland, G. Mourou, Opt. Commun. 56, 219 (1985); J.-C. Diels, W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic Press, 2006); W. Koechner, Solid-State Laser Engineering 6th ed. (Springer, 2006); A. E. Siegman, Lasers (University Science Books, 1986).