Spectra-Physics Tsunami - Signal Interpretation and Analysis

Tsunami Mode-Locked Ti:sapphire Laser
B-4
Signal Interpretation
In order to determine the actual pulse width from the displayed autocorre-
lation function, it is necessary to make an assumption about the pulse
shape. Table B-1 shows the relationship between pulse width, ∆t
p
, and the
autocorrelation function, ∆t
ac
, for several pulse shapes. It also shows the
time-bandwidth product, ∆tp ∆n, for transform-limited pulses.
* ∆t
p
(sec) is FWHM of intensity envelope of the pulse.
**∆t
AC
(sec) is FWHM of autocorrelator function of the pulse.
***∆t
n
(Hertz) is FWHM of the spectrum of the pulse.
Table B-1: Second-order Autocorrelation functions and Time-Bandwidth Products for Various
Pulse Shape Models
Function I(t) ∆t
p
*/∆t
AC
** ∆t
p
∆υ***
Square 1 1
Diffraction Function 0.751 0.886
Gaussian 0.707 0.441
Hyperbolic Secant 0.648 0.315
Lorentzian 0.500 0.221
Symmetric two-
sided exponential
0.413 0.142
It()
1t; t
p
2⁄≤
0 t; t
p
2⁄>
=
I
t()
sin
2
t ∆tp⁄(
)
t ∆tp⁄()
---------------------------------
--
=
It
()
exp 4In2()t
2
–
∆t
2
p
--------------------------------
=
It
() h
2
sec
1.76t()
∆tp
-------------------
=
It()
1
14t
2
∆t
2
p
⁄()+
--------------------------------=
It()
In2()t–
∆tp
-------------------
exp=