DAZZLER
TM
system manual Part I : installation & operation 2.2
2.2.6 Convolution with an acoustical linear chirp
If ∆ν is the frequency bandwidth of the linear chirp, the acoustic power density needed to
transfer totally the optical signal input to the optical signal output in a crystal of length L is
given by:
P
N
= 4.15 · 10
5
·
λ
L
·
∆ν
ν
in W/mm
2
(2.20)
If β is the slope (∆ν/T ) of the linear chirp, T being the acoustic time duration of the chirp,
P
N
can be written as:
P
N
= 3.7 · 10
4
·
β
ν
2
in W/mm
2
(2.21)
For λ = 800 nm, L = 25 mm, ν = 85.93 MHz, β = 0.1 MHz/µs, P = 0.5 W/mm
2
.
2.2.7 Maximal pulse shaping capability
The maximal pulse shaping capability corresponds to the maximal group delay variation that
can be introduced. Using Equation 2.4, the maximal pulse shaping capability ∆τ
max
can be
expressed by:
∆τ
max
=
[n
ge
(ω) − n
go
(ω)]ωL
c
(2.22)
This relation can be written to first order in ∆n/no
2
:
∆τ
max
=
∆n
g
(ω) cos
2
θ
o
ωL
c
(2.23)
where ∆n
g
3
is the group birefringence of the crystal.
For HR25 Dazzler
TM
systems, the maximal pulse shaping capability is 8.5 ps at 800 nm.
2.2.8 Crystal dispersion compensation
The Dazzler
TM
crystal introduces an optical dispersion on the incident pulse corresponding to
the propagation along the ordinary axis of a crystal with length L. The introduced group delay
τ
crystal
is:
τ
crystal
(ω) =
n
go
(ω)ωL
c
(2.24)
This dispersion can be compensated by programming an acoustic wave inducing an inverse
group delay variation in the diffracted beam (SelfC button in the Dazzler
TM
software, section
5.1.3).
2
∆n is the crystal birefringence, not the ordinary index.
3
∆n
g
= n
g e0
− n
g o
V3.00 - 8
th
April 2019 (ContentsTable) (FiguresTable) 12/94
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