polarization-preserving of laser beam in fabry perot cavity accelerator center, ihep li xiaoping

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:

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


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

qq

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


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


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


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


◆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


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


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


)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


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.

Thank you!!

polarization-preserving of laser beam in fabry perot cavity accelerator center, ihep li xiaoping

Documents