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A chirp is an oscillation whose instantaneous frequency changes with time. For $s(t)=A\cos \varphi (t)$, with a smoothly increasing wave phase $\varphi$, the instantaneous frequency is $f(t)={\varphi }^{\prime }(t)/(2\pi )$. A linear chirp hasThe chirp rate $\alpha$ has units of hertz per second; positive and negative values give increasing and decreasing frequency over intervals where the stated interpretation applies.

A swept tone can probe the response of a coupled oscillator over a band, although a rapid sweep need not reproduce the steady response at each frequency. In radar or sonar, comparing a returned chirp with the transmitted signal supports pulse compression: a long transmitted signal can be processed into a narrow delay peak. A finite-duration chirp occupies a range of frequencies, even though its local wave phase supplies a well-defined instantaneous rate.

Chirped pulse amplification increases an optical pulse's energy while keeping its peak power lower during amplification: stretch the pulse, amplify it, then compress it. A chirp is a changing instantaneous frequency. Stretching separates the arrival times of different frequencies; pulse compression brings their contributions back together. The gain medium supplies energy, whereas the compressor concentrates the surviving energy into a shorter time.

Donna Strickland and Gérard Mourou demonstrated chirped pulse amplification at Rochester in 1985. Their experiment used an optical fiber, a regenerative amplifier and a diffraction grating compressor.^[ref]

The useful idea is to arrange where the large peak power occurs. Lower light intensity in the amplifier reduces unwanted self-focusing and self-phase modulation; the compressed output can still drive strong nonlinear optics. Stretching does not remove every damage mechanism, and compression does not manufacture energy.

Optical parametric chirped pulse amplification combines the stretch–amplify–compress sequence of chirped pulse amplification with an optical parametric amplifier. A stretched signal pulse overlaps a strong pump pulse in a nonlinear crystal. Three-wave mixing transfers pump energy into the signal and an idler; subsequent pulse compression brings the amplified signal's frequencies back together. The pump supplies the added energy, rather than a stored population inversion.^[ref]

A. Dubietis, G. Jonušauskas and A. Piskarskas reported chirped and stretched pulse parametric amplification in beta barium borate in 1992. Their paper establishes a concrete early implementation of the parametric route; its published title identifies the nonlinear crystal.^[ref]

For pump, signal and idler angular frequencies, the conversion obeysEfficient amplification also requires phase matching, so contributions generated along the crystal reinforce. For collinear propagation the corresponding wave-vector relation is $k_p=k_s+k_i$; a noncollinear geometry requires the vector relation. Crystal dispersion and the chosen geometry determine which signal bandwidth is efficiently amplified.

An original energy-accounting example uses a 515-nanometre pump and an 800-nanometre signal. Their vacuum wavelengths giveSuppose 40 percent of a 2-millijoule pump is converted into signal–idler pairs, with negligible seed energy and other losses in this chosen model. Each conversion divides photon energy according to frequency, so the added signal energy isThe idler receives the remaining 0.285 millijoule. Assigning all depleted pump energy to the signal would violate this accounting.

If a compressor transmits 80 percent of that signal energy into a 50-femtosecond Gaussian pulse, the surviving energy is 0.412 millijoule. The chirped pulse amplification energy budget givesThese are stipulated teaching values, not a reconstruction of the 1992 experiment. Stretching lowers peak power during amplification; it does not remove the need to manage pump intensity or optical damage.

A useful apparatus check varies pump–signal delay while recording signal and idler spectra and energies. This tests temporal overlap and the frequency-conversion relation. Measuring the compressed pulse separately checks whether amplified bandwidth and residual spectral phase support the claimed pulse duration. Gain alone does not demonstrate successful compression, and an energy measurement alone does not establish peak power.