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Polarization-preserving of laser beam in Fabry Perot Cavity. Accelerator center, IHEP. Li Xiaoping. Introduction of Polarization preserving. An important factor of the generated polarized gamma-rays:. ◆ Polarized degree. Energy dependent cross section. laser:
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Accelerator center, IHEP
An important factor of the generated polarized gamma-rays:
◆ Polarized degree
Energy dependent cross section
λ=1064nm, 100% right-handed
e- -beam: 1.3Gev
Left-handed polarized gamma-rays dominate in the high energy region
High polarization of laser light →High polarization of gamma-rays
◆High power of laser→Large number of gamma photons
Enhanced pulse laser
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
quarter-wave-stack dielectric mirror
A periodic dielectric multilayer mirror
Each layerhas different characteristic matrix for s-wave and p-wave
Using specified layer thicknesscorresponding to λ0 and θ0
In an ideal case, means no fabrication error on layer’s thickness and refraction index:
For a s-wave:
Reflection coefficient is real number:
A General 45º Mirror
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:
Assume all the layers have same fabrication errors:
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.
Polarization preserving in 2-mirror cavity:
R ≈ > 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:
A Concentric Cavity
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 strongA mechanical solution:Four mirrors cavity
4-mirror Ring Cavity
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
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
◆Fabrication error of stacked quarter-wave layer has effect on
To keep at least 95% circular polarization:
The different phase shift between s and p should be smaller than 0.32rad
Circular polarized degree (S3)
Difference phase shift between s and p
Considering the easy mechanical design, first a 2D 4-mirror cavity.
◆Assume all the 4 mirrors are
a planar cavity
Blue: d: 0.02% n: 0.02%
Red: d: 0.01% n: 0.01%
Green: 0.005% 0.005%
◆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
Not safety for 2D 4-mirror cavity to preserve polarization at a so high gain
A model of 37 layers Ta2O5/SiO2
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
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
A high repetition frequency Pockels Cellcould 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.
Assume a cavity has a Finesse F=30000, and Cavity length L=2m.
The decay time:
Power of stacking laser in cavity
Roughly estimate on the average polarization depends on the switching frequency:
To get about 90% polarization at a fast switching frequency 1kHz