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Tsunami - Beckman Institute Laser Resource Center

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<strong>Tsunami</strong><br />

Signal Interpretation<br />

In order to determine the actual pulse width from the displayed autocorrelation<br />

function, it is necessary to make an assumption about the pulse<br />

shape. Table B-1 shows the relationship between pulse width, A$, and the<br />

autocorrelation function, At,,, for several pulse shapes. It also shows the<br />

time-bandwidth product, A tp Av, for transform-limited pulses.<br />

d<br />

Table B-1: Second-order Autocorrelation functions and Time - Bandwidth Products for<br />

Various Pulse Shape Models.<br />

Function<br />

Square<br />

Diffraction Function<br />

Gaussian<br />

Hyperbolic Secant<br />

Lorentzian<br />

Symmetric twosided<br />

exponential<br />

10)<br />

I(t) = 1; ltl 5 td2<br />

0; Itl >td2<br />

I(t) = sin2 (ffAtp)<br />

(tlAtp)<br />

I(t) = exp -(41n2) t2<br />

At2,<br />

I(t) = sech2 11.76t)<br />

Atp<br />

I(t) = 1<br />

1 + (4t2/At2,)<br />

I (t) = exp - (ln2)t<br />

Atp<br />

* At, (sec) is FWHM of intensity envelope of the pulse.<br />

** AhC (sec) is FWHM of autocorrelatorfunction of the pulse.<br />

***At,, (Hertz) is FWHM of the spectrum of the pulse.<br />

**<br />

Atp*/~tAC<br />

1<br />

0.751<br />

0.707<br />

0.648<br />

0.500<br />

0.41 3<br />

A~,Av***<br />

1<br />

0.886<br />

0.441<br />

0.31 5<br />

0.221<br />

0.142

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