Introduction of Polarization preserving
An important factor of the generated polarized gamma-rays:
High polarization of laser light →High polarization of gamma-rays
R L
Left-handed polarized gamma-rays dominate in the high energy region
◆ Polarized degree
Energy dependent
cross section
laser:λ=1064nm, 100% right-handed e- -beam: 1.3Gev
A high gain Fabry-Perot cavity
Laser light will go back-and-forth many times in the cavity:
◆ High reflectivity →High gain
◆ No phase shift on reflection →Keep high polarization
Polarization preserving in cavity
quarter-wave-stack dielectric mirror
◆ High power of laser →Large number of gamma photons
Enhanced pulse laser
General description on Quarter-wave stack mirror
Substrate
······
······
0n 1n 1n2n 2n
sn
1d 1d2d 2d
pair 1 pair 2 pair N
z
y
0 S1
12 2
Each layer has different characteristic matrix for s-wave and p-wave
i
ii
iiii
iii
ii
ii
nq
dn
iqq
iM
cos
cos2
cossin
sincos0
A periodic dielectric multilayer mirror
s-wave i=1,2
iii
iiii
iii
ii
ii
np
dn
ipp
iM
cos
cos2
cossin
sincos0
p-wave i=1,2
24cos 0 iiiidn Quarter-wave stack
Using specified layer thickness corresponding to λ0 and θ0
General description on Quarter-wave stack mirror
In an ideal case, means no fabrication error on layer’s thickness and
refraction index:
4coscos 0
222111
dndn221
For a s-wave:
0
0
0
0
2
22
1
11
ipp
iM
ipp
iM
N
N
NNp
p
pp
p
MMM)(0
0)()(
2
1
1
2
21
Ns
Ns
s
pp
pp
pp
pp
r2
2
1
0
2
2
1
0
)(1
)(1
Ns
Ns
p
q
qqq
q
q
r2
2
1
0
2
2
1
0
)(1
)(1
Reflection coefficient is real number: 0)arg(,0)arg( sp rr
S P
General description on Quarter-wave stack mirror
0)arg()arg( sp rr
1,1,22 sp rrN A quarter-wave stack dielectric mirror:
◆ a very high reflectivity ◆0 phase shift for both s and p
In real case, it always has fabrication error: 0)arg(,0)arg( sp rr
A General 45º Mirror
2
2
pp
ss
rR
rR
General description on Quarter-wave stack mirror
Assume all the layers have same fabrication errors:
20º
5º
10º
15º
Thickness error: 0.01% Refraction Index error: 0.01%
If N is big enough (N>10) there will be no change on the different phase shift between p and s wave with the increase of N. But, with the increase of incidence angle, the phase shift difference increase.
Mirror
A 2-mirror Fabry-perot Cavity
Polarization preserving in 2-mirror cavity:
R ≈ > L/2R ≈ >L/2
A Concentric Cavity
In a perfectly aligned 2-mirror cavity:
◆ Laser light takes a normal incidence on the mirror
◆ Axial symmetry: no difference between s-wave and p-wave
◆ Fabrication error of stacked quarter-wave layer has no effect on polarization: argrp=argrs
In theory, a 2-mirror cavity has a good capability to keep polarization
Difficulty of 2-mirror cavity
c
claser
Δ=0.001º
Difficulty of 2-mirror cavity:
optical axis
A concentric cavity has a high sensitivity to misalignment:
In the case of: σ0 =30um R=210.5mm L=420mm
Assume a angle misalignment of one mirror is 0.001º, a misalignment of optical axis is ≈0.2º and spot position shift on mirror is ≈0.7mm
Mechanical constraint is very strong
A mechanical solution: Four
mirrors cavity
A Concentric Cavity
A 4-mirror Fabry-perot Cavity
laser
waist
L
R RW0 0
when RL
4-mirror Ring Cavity
R≈LL
A Confocal Cavity
A confocal cavity has a low sensitivity to misalignment:
Assume a angle misalignment of one spherical mirror is 0.001º, spot position shift on the other is ≈0.007mm
R≈L
4-mirror ring cavity can reduce 2 orders of magnitude of the sensitivity
to the misalignment of the mirror compared with 2-mirror case.
Polarization preserving in a 4-mirror cavity:
◆All the reflection on the mirror is oblique
◆Oblique incidence has different reflection coefficients for s and p wave
A 4-mirror Fabry-perot Cavity
◆Fabrication error of stacked quarter-wave layer has effect on
polarization: argrp ≠≠ argrs
Difference phase shift between s and p
Circ
ular
pol
ariz
ed d
egre
e (S
3)
0.32 rad To keep at least 95% circular polarization:
The different phase shift between s and p should be smaller than 0.32rad
Considering the easy mechanical design, first a 2D 4-mirror cavity.
rad100.8100004
0.32rad)arg(r)arg(r 5
sp
A 2D 4-mirror Fabry-perot Cavity
laser
p
s
0.8×10-5 rad
◆Assume all the 4 mirrors are
A model of 37 layers Ta2O5/SiO2
perfectly aligned
Blue: d: 0.02% n: 0.02%Red: d: 0.01% n: 0.01%Green: 0.005% 0.005%
Not safety for 2D 4-mirror cavity to preserve polarization at a so high gain
◆Gain: 10000
a planar cavity
◆Minimum error is about 0.01% for both d and n (from company)
◆Perfectly aligned is not possible, mechanical error always there
◆Typical incidence angle is 5.7º
A 3D 4-mirror Fabry-perot Cavity
3D Cavity
To reduce the degradation of the circular polarization
◆ Considering a non-planar cavity such that planes of incidence
are two by two orthogonal
◆ s and p wave are exchanged reflection after reflection
◆ phase shift difference cancelled by two consecutive reflection
2D Cavityby Araki
A 3D 4-mirror Fabry-perot Cavity
As we know, two exactly orthogonal
incidence plane could cancel phase
difference completely. However, in
geometry, two pairs exactly
orthogonal planes of incidence is not
possible to close a 4-mirror ring.
◆ No detailed calculation results. Considering the small incidence
angle (5.7º), the two incidence planes are almost orthogonal, so it
should be much better than 2D cavity to preserve polarization.
◆ Complicated mechanical design
Possibility of fast switching polarization of Compton source
A high repetition frequency Pockels Cell could be used to get fast
switching on the polarization state of Compton source.
Locate Pockels cell just before the cavity, then the
polarization of laser beam in cavity could be
switched by applying high voltage on the Pockels
cell.
LaserPockels cell
Cavity
Possibility of fast switching polarization of Compton source
)exp(0 tII
5104.6 cFL
L-handed Polarization
R-handed Polarization
Assume a cavity has a Finesse F=30000, and Cavity length L=2m.
The decay time:
ms
)]exp(1[0 tII
Power of stacking laser in cavity
Possibility of fast switching polarization of Compton source
Roughly estimate on the average polarization depends on the
switching frequency:
LR
LRP
To get about 90%
polarization at a
fast switching
frequency 1kHz
Summary1. The importance of laser polarization preserving
2. A general description on ideal quarter-wave stack dielectric mirror
3. A 2-mirror cavity: a good capability to preserve polarization even there
is fabrication error but it has a high sensitivity to misalignment
4. A 2D 4-mirror cavity: low sensitivity to misalignment. But the phase
shift difference between s and p wave will limit it to preserve
polarization at a very high gain
5. A 3D 4-mirror seems to be the best choice, but it needs a complicated
mechanical design.
6. Fast switching on polarization. A very high finesse(30000) was
assumed, and a higher frequency could be achieved at low finesse.
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