Ultrashort Laser Pulse Phenomena, 2nd Edition

458 Diagnostic Techniques

9.1. INTENSITY CORRELATIONS

9.1.1. General Properties

The temporal profile I

s

(t) of an optical signal can be easily determined, if

a shorter (reference) pulse of known shape I

r

(t) is available. The method is to

measure the intensity cross correlation:

A

c

(τ) =



∞

−∞

I

s

(t)I

r

(t − τ) dt. (9.1)

Let us define the Fourier transforms of the intensity profiles as:

I

j

() =



∞

−∞

I

j

(t)e

−it

dt, (9.2)

where the subscript j indicates either the reference (r) or signal (s) pulse.

The Fourier transform of Eq. (9.2) should not be confused with the spectral

intensity (proportional to |

˜

E()|

2

). The Fourier transform of the correlation (9.1)

is A

c

(), related to the Fourier transforms of the intensities by:

A

c

() = I

r

()I

∗

s

(). (9.3)

The shape of the signal ...