Optical Autocorrelation - Intensity Autocorrelation

Intensity Autocorrelation

To a complex electric field corresponds an intensity and an intensity autocorrelation function defined by

The optical implementation of the intensity autocorrelation is not as straightforward as for the field autocorrelation. Similarly to the previous setup, two parallel beams with a variable delay are generated, then focused into a second-harmonic-generation crystal (see nonlinear optics) to obtain a signal proportional to . Only the beam propagating on the optical axis, proportional to the cross-product, is retained. This signal is then recorded by a slow detector, which measures

is exactly the intensity autocorrelation .

The generation of the second harmonic in crystals is a nonlinear process that requires high peak power, unlike the previous setup. However, such high peak power can be obtained from a limited amount of energy by ultrashort pulses, and as a result their intensity autocorrelation is often measured experimentally. Another difficulty with this setup is that both beams must be focused at the same point inside the crystal as the delay is scanned in order for the second harmonic to be generated.

It can be shown that the intensity autocorrelation width of a pulse is related to the intensity width. For a Gaussian time profile, the autocorrelation width is longer than the width of the intensity, and it is 1.54 longer in the case of an hyperbolic secant squared (sech2) pulse. This numerical factor, which depends on the shape of the pulse, is sometimes called the deconvolution factor. If this factor is known, or assumed, the time duration (intensity width) of a pulse can be measured using an intensity autocorrelation. However, the phase cannot be measured.