DAZZLER
TM
system manual Part I : installation & operation
2.2
2.2.2
Spectral resolution
We now assume a perfect phase-matching for a set of frequencies and directions. If the in-
put optical frequency is varied while all the other parameters are kept constant (directions,
polarizations, acoustic frequency) then ∆
k L
6
= 0 and the diffraction efficiency drops (sinc
2
function).
For
P < P
0
δλ
1
/
2
=
0
.
8
·
λ
2
δn
·
L
≈
8
.
9
·
λ
2
L
(2.16)
δn
being the index difference between ordinary and extraordinary waves on the propagation
axis in the crystal. For HR Dazzler
TM
systems,
•
For
L
= 25 mm,
λ
= 800 nm,
δλ
1
/
2
= 0
.
23 nm
•
For
L
= 45 mm,
λ
= 1
µ
m,
δλ
1
/
2
= 0
.
20 nm
2.2.3
Number of independent programming points
If ∆
λ
is the bandwidth of input optical signal in wavelengths, the number of independent
programming points of the AOPDF is:
N
=
∆
λ
δλ
1
/
2
= 1
.
25
·
δn
·
L
·
∆
λ
λ
2
≈
L
8
.
9
·
∆
λ
λ
2
(2.17)
•
For
L
= 25 mm, ∆
λ
= 100 nm@800 nm,
N
= 439
•
For
L
= 25 mm, ∆
λ
= 300 nm@800 nm,
N
= 1318
•
For
L
= 45 mm, ∆
λ
= 20 nm@1
µ
m,
N
= 101
2.2.4
Input beam angular aperture (divergence)
With a WB crystal cut, the divergence of the input beam must be inferior to:
δθ
1
/
2
=
n
0
·
(
δθ
0
)
1
/
2
= 2
.
47
·
(
δλ
λ
)
1
/
2
= 22
·
λ
L
(2.18)
•
For
L
= 25 mm,
λ
= 800 nm,
δθ
1
/
2
= 0
.
04
◦
•
For
L
= 45 mm,
λ
= 1
µ
m,
δθ
1
/
2
= 0
.
028
◦
The input beam divergence degrades the resolution.
2.2.5
Acoustic power density to drive n points
The acoustic power density needed to drive the
N
independent spectral points of
for a total diffraction of these points is:
P
N
=
N
·
P
0
= 4
.
15
·
10
5
·
∆
λ
L
in W/mm
2
(2.19)
•
For
L
= 25 mm and ∆
λ
= 100 nm,
P
N
= 1
.
66 W/mm
2
•
For
L
= 45 mm and ∆
λ
= 20 nm,
P
N
= 0
.
18 W/mm
2
V3.00 - 8
th
April 2019
