Spectra-Physics Tsunami - Calculating Pulse Broadening

Pulse Width Measurement
B-7
For an initial setup based on your Tsunami and a Model 409-08 autocorre-
lator, set the prisms approximately 30 cm apart at Brewster's angle to the
beam with the high reflector a few cm from the second prism. With this
spacing, the prism pair should start with excess negative GVD. By moving
the prism tips into the beam, we can balance the GVD for minimum pulse
width. To do this, place the first prism on a translation stage that moves the
prism in the direction of the bisector of the apex. This way, more glass can
be pushed into the beam path without displacing the beam or changing its
angular direction. This allows the negative GVD of the prism system to bal-
ance the positive GVD created by all the glass. By moving the prism into
the beam path and monitoring the output from a Model 409-08, the pulse
should get narrower as the dispersion is balanced. If a minimum cannot be
found, adjust the prism spacing and search for the minimum again.
Calculating Pulse Broadening
Below are some simple formulae for calculating the effects of GVD and
compensation. B (broadening), is defined as the ratio of the output pulse
width to the input pulse width where B = t
out
/ t
in
. Consequently, knowing
the input pulse width, B can be calculated and then t
out
= B•t
in
.
A simple formula for calculating the broadening of a transform-limited
Gaussian pulse by dispersive elements is:
[1]
where t
in
is the input pulse width in femtoseconds, and D
ω
is a dispersion
value normalized for a given length and wavelength. Table B-3 gives values
for different materials at 800 nm. Also given in Table B-4 are the values for
some negative dispersion setups, prisms, and grating pairs for compensa-
tion at 800 nm. Using these values, B is calculated directly; we define S as:
Table B-3: Positive Dispersion Values @ 800 nm
Material
Dω (fs
2
/cm)
Fused Silica 300
BK-7 450
Ti:sapphire 580
SF-10 1590
Table B-4: Negative Dispersion Values @ 800 nm
System
Dω (fs
2
/cm)
SF-10 Brewster Prism pair, double pass –80.2
BK-7 Brewster Prism pair, double pass –12.8
Grating pair, 400 lines/cm
@ 30° incidence angle, double pass
–1500
Grating pair, 1000 lines/cm
@ 30° incidence angle, double pass
–10,000
Bt
out
t
in
⁄ 1 7 68 D
ω
Lt
in
2
⁄⋅()
2
⋅⋅[]+



1
2
---
==