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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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Presentation Transcript
slide2

Introduction of Polarization preserving

An important factor of the generated polarized gamma-rays:

◆ Polarized degree

Energy dependent cross section

laser:

λ=1064nm, 100% right-handed

e- -beam: 1.3Gev

R

L

Left-handed polarized gamma-rays dominate in the high energy region

High polarization of laser light →High polarization of gamma-rays

slide3

Polarization preserving in cavity

◆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

slide4

General description on Quarter-wave stack mirror

y

A periodic dielectric multilayer mirror

······

s-wave i=1,2

z

······

p-wave i=1,2

Substrate

pair 2

pair N

pair 1

Each layerhas different characteristic matrix for s-wave and p-wave

Using specified layer thicknesscorresponding to λ0 and θ0

Quarter-wave stack

slide5

General description on Quarter-wave stack mirror

In an ideal case, means no fabrication error on layer’s thickness and refraction index:

For a s-wave:

P

S

Reflection coefficient is real number:

slide6

General description on Quarter-wave stack mirror

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:

slide7

General description on Quarter-wave stack mirror

Assume all the layers have same fabrication errors:

Thickness error: 0.01% Refraction Index error: 0.01%

20º

15º

10º

Mirror

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.

slide8

A 2-mirror Fabry-perot Cavity

Polarization preserving in 2-mirror cavity:

R ≈ > L/2

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

slide9

Difficulty of 2-mirror cavity

Difficulty of 2-mirror cavity:

Δ=0.001º

optical axis

c

laser

c

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

slide10

A 4-mirror Fabry-perot Cavity

4-mirror Ring Cavity

R≈L

R≈L

L

R

R

W0  0

whenRL

waist

L

laser

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.

slide11

A 4-mirror Fabry-perot Cavity

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

polarization: argrp≠argrs

To keep at least 95% circular polarization:

The different phase shift between s and p should be smaller than 0.32rad

0.32 rad

Circular polarized degree (S3)

Difference phase shift between s and p

slide12

A 2D 4-mirror Fabry-perot Cavity

Considering the easy mechanical design, first a 2D 4-mirror cavity.

p

s

◆Assume all the 4 mirrors are

perfectly aligned

◆Gain: 10000

laser

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

0.8×10-5 rad

Not safety for 2D 4-mirror cavity to preserve polarization at a so high gain

A model of 37 layers Ta2O5/SiO2

slide13

A 3D 4-mirror Fabry-perot 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 Cavity

3D Cavity

by Araki

slide14

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

slide15

Possibility of fast switching polarization of Compton source

A high repetition frequency Pockels Cellcould be used to get fast switching on the polarization state of Compton source.

Pockels cell

Laser

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.

Cavity

slide16

Possibility of fast switching polarization of Compton source

Assume a cavity has a Finesse F=30000, and Cavity length L=2m.

The decay time:

Power of stacking laser in cavity

L-handed Polarization

R-handed Polarization

ms

slide17

Possibility of fast switching polarization of Compton source

Roughly estimate on the average polarization depends on the switching frequency:

To get about 90% polarization at a fast switching frequency 1kHz

slide18

Summary

  • The importance of laser polarization preserving
  • A general description on ideal quarter-wave stack dielectric mirror
  • A 2-mirror cavity: a good capability to preserve polarization even there is fabrication error but it has a high sensitivity to misalignment
  • 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
  • A 3D 4-mirror seems to be the best choice, but it needs a complicated mechanical design.
  • Fast switching on polarization. A very high finesse(30000) was assumed, and a higher frequency could be achieved at low finesse.