Ultrashort pulse chirping
The same 150 fs pulse measured three ways — bare, chirped by 100 mm of dense flint, and recompressed — each on its own autocorrelator.
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A transform-limited pulse is the shortest envelope its spectrum allows: every frequency component arrives in phase. Glass takes that away. Because the refractive index varies with wavelength, the blue components travel slower than the red ones, so the pulse leaves the glass chirped — its colours strung out in time — and therefore longer, even though nothing about its spectrum has changed and its ray still runs dead straight.
The quantity that governs this is the group delay dispersion, the second derivative of spectral phase. It accumulates along the path, adds up over every piece of glass, and can be undone by anything supplying the opposite sign.
What this setup demonstrates
Three identical 150 fs, 532 nm Gaussian sources, each measured by its own autocorrelator wired to a detector screen.
The first arm has nothing in the beam and reads 150 fs — the reference. The second passes through 100 mm of N-SF11, a dense flint whose GVD at 532 nm is about 387 fs²/mm: roughly +38 680 fs² in total, stretching the pulse to about 731 fs, nearly five times longer. The third adds a compressor set to −38 680 fs², which cancels the glass exactly and returns the measurement to 150 fs.
Each screen shows what an autocorrelator actually produces: delay on the horizontal axis rather than laboratory time, the self-convolution of the pulse envelope, the half-maximum chord that constitutes the measurement, and the duration inferred by dividing out the shape factor (√2 for a Gaussian). Change the assumed shape on any autocorrelator and it will tell you how far wrong that assumption puts the answer.
Wavelength matters as much as path length here: the same rod at 800 nm contributes only about 18 750 fs², because N-SF11's GVD falls steeply toward the infrared. Retune the sources and watch all three traces change together.
Only second-order dispersion is modelled. Real glass also has third-order and higher terms that reshape a pulse asymmetrically rather than simply widening it, and a real compressor is a grating, prism, or chirped-mirror assembly with its own higher-order dispersion, loss, and alignment sensitivity rather than a single signed number. The pulse is assumed to enter transform-limited; an input chirp would add to or subtract from the glass instead of simply being stretched by it. The autocorrelation curve is drawn from the inferred duration, not from a simulated scanning measurement, and absorption in the glass is not modelled at all.