Transcript Slides - Indico LAL

FOUR MIRRORS Fabry Perot
resonator at LAL-Orsay
Y. Fedala
With help of
F. Zomer, R.Cizeron
25/05/2007
POSIPOL 2007
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Outline of the talk
• Introduction
• 2D four mirrors cavity
– theoretical and experimental results of:
• Eigen modes
• Astigmatism
• Minimum waist size
• 3D four mirrors cavity
– theoretical and experimental results of:
• Eigen modes
• Minimum waist size
• Reduction of astigmatism
– Waist size stability
• mechanical design of final four mirrors cavity (R. Cizeron)
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Introduction
Reduction of the laser beam waist with 2 mirrors
 Concentric cavity
R ≈ >L/2
R ≈ > L/2
R
0 when
→ →
ω0
L/2
w0≈200mm
10 mrad
optical axis
R = 1m
c
10 mrad
c
laser
1mm
10 mm
•2m long concentric cavity: IF w0=50mm, l=800nm
for an axial and angular mirror misalignment of 1mm and 1mrad.
spot size shift of 30mm on the mirrors !!!
Mechanical constraints very strong …
A mechanical solution: Four mirrors cavity
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Four mirrors 2D or 3D cavities
plane mirror
Y
X
Y
X
φ
w00
when Z
RL
V2
R
laser
spherical mirror
2D Ring cavity
R
S2
spherical mirror
L
φ=0  2D cavity.
φ0  3D cavity
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P2
V1
P1
S1
plane mirror
Non planar cavity advantages :
•reduction of astigmatism
•Circular polarisation much
less sensitive to mirror
misalignment
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Mechanical tolerances for 4 mirrors cavity
Max. beam movement on mirrors (K. Moenig & F.Zomer)
•
for w0 0: with 4m optical path, 6cm between 2
adjacent mirror centres
– Dxi=±0.1mm; Daxi=±0.1mrad [=2. 1020
configurations for a 3D cavity]
max displacement on:
• plane mirrors: 0.6mm
• on spherical mirrors: 1.1mm
• At beam waist: 0.3mm: 0.5mrad
 High mechanical stability
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2D cavity
1 cylinder which allows to position the
mirror holders
1 point of rotation on the table
The axis passes in the
center of the entrance
mirror
2 platines supports adjacent
mirrors
Cw laser diode in
extended cavity config
(Littrow configuration)
1 fixed in Z and the other
adjustable
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2D cavity modes
TEM20
TEM10
TEM00
LG11
Exp.
modes
Calculated modes
Similar to usual modes of
2 mirrors FP cavity
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2D cavity waist size
CCD
R
laser
R
L
Fm=2R=1000mm
F=200mm
D
Equivalent
scheme
W0s
W0e
ws²=f(Z)
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Quadratic fit
Z
Waist after the
end mirror(W0s)
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Transport
matrix
Waist in the cavi
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Astigmatism of 2D cavity
Variation of TEM00 profile
with respect to L
L>R
elliptic fit
LR
Diffraction on
mirror edges
Astigmatism increases with the
focusing strength
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Astigmatism of 2D cavity
Calculated contour view of the intensity profile of the 00 mode versus the distance Z (F. Zomer)
[see J.A. Arnaud 'Nonorthogonal optical waveguides and resonators‘, Bell Syst. Tech. J.49 (1970)2311]
After the lens
Limited with
mirrors width
End mirror
of the cavity
Effect seen
experimentally
Inside the cavity
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2D cavity waist size
The ellipse turns
calculation
Mesured waist size
WX 40µm
Wy 12µm
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Limited by
mirror size
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End mirror
of the cavity
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3D cavity
plane mirror
Y
X
P1
Y
V1
V2
plane mirror
P2
f
X
Z
S1
S2
spherical mirror
spherical mirror
f0  3D cavity
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3D cavity modes
Exp.
Higher order
Modes
Th. results
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Z
3D cavity eigen modes
Z
Propagation of the
modes outside the
cavity
Fundamental mode
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3D cavity Waist size
Exp.data
measurements
good
agreement of
theory & exp.
Th. calculation
Wx 54µm
Wy 56µm
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To be verified
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beam size
calculations
A shift of ~1.5mm
Same phenomenon outside
the cavity
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Reduction of the astigmatism
Result of calculation
After the lens
End mirror
of the cavity
Inside the
cavity
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Comparison of astigmatism in 2D & 3D
config.
Zoom around the waist position
(calculations) 2D
Strong astigmatism
3D
2 waist positions
inside the cavity
Third position circular
beam with small waist
compensated in 3D
config.
POSIPOL
2007results reproduced with
measured data .
astigmatism
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Effect of laser wave length
Variation of the
waist for l=800nm
& l=820nm
for ∆l=20nm
small variation of the
waist and no effect on
its position
For 1ps, ∆l=0.49nm  the effect is negligible
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Stability of the beam size
5µm
< 5µm
There is ~ three populations
 ~ 3 modes
•The beam is stable in time without any isolation of the setup
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drift of beam size outside is only ~3% in 2 hours.
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Design Study of a four mirror
cavity implementable around
electron beam
R. Cizeron
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Confocal non planar 4 mirrors cavity
scheme
2 flat mirrors
e- beam tube
1m
100 mm
laser
entrance
IP
2 spherical mirrors
- Laser
• 75 MHz
•Optical path de 4m
- Distance between the mirrors 1m & 100 mm
- Radius of curvature of spherical mirrors 1 m
- Angle of Compton interaction 8°
- Laser injection & the axis of the 2 spherical mirrors is parallel to the optical
table
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Degrees of freedom needed to align
the cavity
∆Z
θy
θx
qx et qy for all the mirrors
Dz = ± 1 mm on the 2 spherical mirrors to approach the confocal
config.
Dz = ± 1 mm on the 2 flat mirrors to remain the optical length of
cavity constant
Challenge  insure all the adjustments with
keeping the stability of the set up
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System isolation
Vacuum
chamber
beam
Optical Table
Keep UHV  Mirrors aligned with actuators
put the actuators in capsules to avoid vacuum contamination
3 degrees of freedom for each mirror  12 actuators
Avoid the transport of environmental noise and vibrations via the isolation
 the system set on an independent beam
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Length 1.5m
tube diameter : 420 mm
e- beam
tube
Vacuum
chamber
Support
beam
Support
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e- beam
Interaction
point
beam
e- beam tube
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Flat mirrors
Spherical
mirrors
Invar ( Fe-Ni alloy)
3 Beam
supports
Flat mirror
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Holders to align the
mirrors
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Mirrors holders
Cardan
θx & θy
actuator θy
Z displacement
actuator θx
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Z DisplacementFlex
All the parts are
related to the flex
// Displacement
Negligible variation on height
∆Z=1mm  12 µm
0.5mm  3µm
0,1mm  0.1 µm
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Actuators
Micro-Controle DC actuators of mini increment
0,05 µm (0.5 µrad) with a coder
bidirectional repeatability 2 µm
Axial charge Capacity de 120 N
Course 25 mm
Course after encapsulage ± 2 mm
Useful Course ± 1 mm  ± 10 mrad  ± 20mm
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Cardan (gimble)
Ø 1 inch
membrane to
support mirror
piezo
3 piezos
at 120°
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summary
• 4 mirrors cavity is a good solution to
provide a very small beam waist with high
mechanical stability.
• 3D configuration allows the reduction of
astigmatism effects
– Experimental results well described by
‘Nonorthogonal resonators’ theory of Arnaud
– But : 2 waist positions inside the cavity
• To be done :
– measurement of the polarisation eigen modes
• Need for a very high finesse cavity
– Study of the Compton e-laser beam interaction
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