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A mode-locked laser maintains definite relative wave phases among many longitudinal resonator modes. Their coherent sum forms a repeating train of short optical pulses, rather than merely producing a broad optical spectrum.

For an ordinary linear resonator, the repetition interval is approximately the round-trip travel time. More phase-aligned spectral bandwidth permits shorter pulses, subject to the time-bandwidth product and spectral shape. A photodetector can measure pulse-train timing, while an intensity autocorrelation estimates much shorter pulse durations under a stated model. Neither a broad spectrum nor a fast periodic intensity signal alone uniquely reconstructs the pulse's complex electric field.

An optical postpulse is a secondary optical pulse arriving after the chosen main pulse. Specify the delay, relative peak radiant power, duration and collected laser pulse energy: a relative peak alone does not determine the energy of a differently shaped replica. It is distinct from an extended optical pulse pedestal and from electronic ringing from a photodetector.

A transparent plate provides a concrete mechanism. At normal incidence, a transmitted replica that makes one additional internal round trip has approximate delaywhere $\ell$ is plate thickness and $n_g$ is its group refractive index. Neglect absorption, dispersion and overlap, and let each internal reflection retain power fraction $R$. The first delayed replica then has approximately $R^2$ times the directly transmitted energy. This etalon round-trip delay can create a physical optical echo.

For an original chosen $\ell =1.2\mathrm{mm}$, $n_g=1.5$ and $R=0.04$, the delay is about $12\mathrm{ps}$ and the energy ratio is $0.0016$. A $2.0\mathrm{mJ}$ main pulse would be followed by a $3.2\mu \mathrm{J}$ replica under that model. The historical single-shot correlator experiment deliberately inserted a BK7 etalon to generate and detect such a delayed pulse.^[ref]

Changing the plate thickness tests the delay prediction; changing optical alignment tests whether a stray reflection is involved. A third-order intensity autocorrelation can distinguish temporal sides under its model, while a symmetric second-order intensity autocorrelation cannot alone assign a feature to a prepulse or postpulse. An opposite-delay correlation feature may instead be a third-order pulse correlation ghost; it need not identify another physical pulse.

A detector too slow to resolve a femtosecond field can measure its integrated nonlinear response instead. Split the pulse, delay one replica, overlap both in a thin phase-matched crystal, and select the sum-frequency signal. For negligible depletion and sufficiently broad phase matching, the cross-generated field is proportional to $A(t)A(t-\tau )$; integrated signal gives the second-harmonic intensity autocorrelationA noncollinear geometry can reject each replica's individual second harmonic. The optical response supplies the fast gate while the detector integrates slowly. Crystal thickness, group-velocity mismatch, spectral acceptance, beam overlap and delay calibration limit resolution.

For a Gaussian pulse specified by its intensity profile, the autocorrelation's full width at half maximum is $\sqrt{2}$ times the intensity full width at half maximum. For a sech-squared intensity profile the ratio is about $1.543$. These are model-dependent conversion factors. An intensity autocorrelation is symmetric in delay and loses phase information; different pulses can share it. An interferometric autocorrelation retains rapid carrier fringes but still does not generally reconstruct an arbitrary complex field uniquely.

frequency-resolved optical gating also resolves the gated signal's spectrum, giving a two-dimensional delay-frequency record. For second-harmonic frequency-resolved optical gating,where $\omega$ is measured relative to the signal's carrier. An iterative retrieval seeks an envelope whose predicted record matches the measurement. Alternatively, polarization-gating frequency-resolved optical gating uses the optical Kerr effect to gate the probe by a delayed replica's intensity, with signal envelope proportional to $A(t)|A(t-\tau ){|}^2$. The original FROG work introduced nonlinear optical gating plus spectral resolution to characterize arbitrary femtosecond pulses.^[ref]

Absolute wave phase and absolute time origin remain undetermined by these intensity records. The SHG record also cannot distinguish $A(t)$ from $A^{\ast }(-t)$, so its time-direction ambiguity remains. Retrieval agreement, an independently measured spectrum, adequate signal dynamic range and gate-response calibration are practical consistency checks. A pulse train that changes between shots can yield an averaged record that no single pulse faithfully represents. Thus nonlinear gating solves the detector-speed problem but does not remove inverse problem ambiguities or experimental limitations.

The gain bandwidth must be expressed as a frequency range:The gain bandwidth limit on a laser pulse then givesThe numerical coefficient depends on the pulse shape and width definition. For example a Gaussian pulse whose intensity spectral FWHM actually filled this width would have a transform-limited intensity duration about $6.2\mathrm{fs}$. A hard gain interval does not by itself specify such a FWHM. Reaching the estimated scale requires coherent mode locking and control of group velocity dispersion; the cavity round-trip time determines the pulse separation. An intensity autocorrelation measurement can estimate the pulse duration once its shape is specified.

The self-gated second-harmonic spectrogram has the displayed ideal form. Its delay marginal is proportional to the intensity autocorrelation by the Parseval identity. Absolute time and wave phase are undetermined; $A(t)$ and $A^{\ast }(-t)$ also give the same record. Finite crystal acceptance and spatial walk-off modify the ideal gate.

The 1985 experiment launched $150\mathrm{ps}$ pulses from a mode-locked laser into $1.4\mathrm{km}$ of optical fiber. Dispersion and self-phase modulation produced a broader spectrum and approximately $300\mathrm{ps}$ pulses. A Pockels cell selected a pulse for repeated amplification in neodymium glass, giving approximately $2\mathrm{mJ}$ before the double-pass diffraction grating compressor. Its transmission was 50 percent. The amplified output was reported as $1\mathrm{mJ}$ with a $2\mathrm{ps}$ width limited by the streak camera response. The compressor was adjusted on fiber-output pulses using intensity autocorrelation; that measurement gave $1.5\mathrm{ps}$. Steve Williamson was acknowledged for help developing the concept, and Philippe Bado and Marcel Bouvier for technical support.^[ref]

The crucial comparison is compression before and after amplification. It asks whether enough usable spectral phase structure survives the amplifier, rather than merely whether its output is bright. A response-limited trace cannot establish the true width below the detector's resolution or prove that every higher-order phase coefficient vanished. An intensity autocorrelation is also not a direct unique measurement of the complex electric field. These are limits on the inference, not extra controls attributed to the experiment.

Donna Strickland's 2018 lecture describes setting the compressor with the high-repetition oscillator pulses and making the amplified-pulse measurement with Steve Williamson's streak camera. It explicitly notes imperfect chirp matching.^[ref] The first apparatus therefore illustrates the strategy without establishing a universal lossless or exactly phase-matched amplifier.

Donna Strickland leads an ultrafast laser group at Waterloo investigating intense laser interactions and nonlinear optics.^[ref] Gérard Mourou's later work includes coherent combination of laser beams in the XCAN project at École polytechnique.^[ref] Their complementary research settings connect the original short-pulse experiment with the continuing problems of producing useful energy, peak power and average power together.

A third-order intensity autocorrelation measures the delay-dependent intensity productThe name counts three intensity factors. A physical implementation can use two second-order nonlinear processes: second-harmonic generation creates a gate proportional to $I^2$, and sum-frequency generation mixes it with a delayed fundamental replica. It therefore need not use a third-order material susceptibility. The historical device spatially encoded delay in crossing beams and imaged the sum-frequency signal onto a charge-coupled device.^[ref]

An original Gaussian calculation illustrates response width. Set $I(t)=I_0{e}^{-t^2/(2{\sigma }^2)}$. Completing the square in the integral givesHence the third-order correlation width of a Gaussian pulse obeys ${\tau }_3=\sqrt{3/2}{\tau }_I$ for intensity full widths at half maximum. A $90\mathrm{fs}$ correlation width would imply ${\tau }_I\approx 73.5\mathrm{fs}$ within this ideal Gaussian model. The square-root-of-two conversion appropriate to second-order Gaussian intensity autocorrelation would be different.

For a general pulse, $A_3(\tau )$ need not equal $A_3(-\tau )$; this asymmetry can distinguish a delayed feature from an earlier one. It is still a cross-correlation with a finite-width nonlinear gate, rather than a direct reading of $I(\tau )$. The existing optical pulse temporal contrast derivation shows how a delayed weak replica also produces an opposite-delay third-order pulse correlation ghost.

Characterize phase matching, beam overlap, spatial uniformity and the temporal response before interpreting a narrow feature. Scaling the input intensity by $k$ scales this ideal signal by $k^3$, so input fluctuations also matter. The measured trace does not uniquely reconstruct an arbitrary complex optical electric field.