1. 25/05/2007POSIPOL 20071 FOUR MIRRORS Fabry Perot resonator at LAL-Orsay Y. Fedala With help of F. Zomer, R.Cizeron

2. 25/05/2007POSIPOL 20072 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)

3. 25/05/2007POSIPOL 20073 Introduction Reduction of the laser beam waist with 2 mirrors  Concentric cavity R ≈ > L/2 2m long concentric cavity: IF  0 =50  m, =800nm for an axial and angular mirror misalignment of 1  m and 1  rad.  spot size shift of 30mm on the mirrors !!!  Mechanical constraints very strong … A mechanical solution: Four mirrors cavity optical axis c c 1mm 10 mm 10  rad R = 1m laser  0 ≈200  m

4. 25/05/2007POSIPOL 20074 Four mirrors 2D or 3D cavities Non planar cavity advantages : reduction of astigmatism Circular polarisation much less sensitive to mirror misalignment φ X Y Y X Z P1P1 P2P2 S1S1 S2S2 plane mirror spherical mirror plane mirror spherical mirror φ=0  2D cavity. φ  0  3D cavity V1V1 V2V2 laser w 0  0 when R  L 2D Ring cavity L R R

5. 25/05/2007POSIPOL 20075 for  0  0: with 4m optical path, 6cm between 2 adjacent mirror centres –  x i =±0.1mm;  xi =±0.1mrad [ =2. 10 20 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 Mechanical tolerances for 4 mirrors cavity  Max. beam movement on mirrors (K. Moenig & F.Zomer)

6. 25/05/2007POSIPOL 20076 2D cavity The axis passes in the center of the entrance mirror 2 platines supports adjacent mirrors 1 fixed in Z and the other adjustable 1 cylinder which allows to position the mirror holders 1 point of rotation on the table Cw laser diode in extended cavity config (Littrow configuration)

7. 25/05/2007POSIPOL 20077 2D cavity modes Exp. modes Calculated modes Similar to usual modes of 2 mirrors FP cavity TEM20 TEM10 TEM00 LG11

8. 25/05/2007POSIPOL 20078 2D cavity waist size laser L R R D Z Fm=2R=1000mmF=200mm W 0e W 0s CCD w s ²=f(Z) Quadratic fit Waist after the end mirror(W 0s ) Waist in the cavity Transport matrix Equivalent scheme

9. 25/05/2007POSIPOL 20079 Astigmatism of 2D cavity Astigmatism increases with the focusing strength Variation of TEM00 profile with respect to L Diffraction on mirror edges elliptic fit L>R LRLR

10. 25/05/2007POSIPOL 200710 Astigmatism of 2D cavity Calculated contour view of the intensity profile of the 00 mode versus the distance Z (F. Zomer) Inside the cavity After the lens End mirror of the cavity Limited with mirrors width Effect seen experimentally [see J.A. Arnaud 'Nonorthogonal optical waveguides and resonators‘, Bell Syst. Tech. J.49 (1970)2311]

11. 25/05/2007POSIPOL 200711 2D cavity waist size Mesured waist size WX  40µm Wy  12µm The ellipse turns Limited by mirror size calculation End mirror of the cavity

12. 25/05/2007POSIPOL 200712 3D cavity  X Y Y X Z 11 22 11 22 plane mirror spherical mirror plane mirror spherical mirror   0  3D cavity V1V1 V2V2

13. 25/05/2007POSIPOL 200713 3D cavity modes Exp. Higher order Modes Th. results

14. 25/05/2007POSIPOL 200714 3D cavity eigen modes Z Z Propagation of the modes outside the cavity Fundamental mode

15. 25/05/2007POSIPOL 200715 3D cavity Waist size Wx  54µm Wy  56µm To be verified Exp.data Th. calculation good agreement of theory & exp. measurements

16. 25/05/2007POSIPOL 200716 beam size A shift of ~1.5mm Same phenomenon outside the cavity calculations

17. 25/05/2007POSIPOL 200717 Reduction of the astigmatism Inside the cavity End mirror of the cavity After the lens Result of calculation

18. 25/05/2007POSIPOL 200718 Comparison of astigmatism in 2D & 3D config. 2 waist positions inside the cavity Third position  circular beam with small waist Strong astigmatism 2D 3D Zoom around the waist position (calculations) astigmatism compensated in 3D config.  results reproduced with measured data.

19. 25/05/2007POSIPOL 200719 Effect of laser wave length Variation of the waist for =800nm & =820nm for ∆ =20nm small variation of the waist and no effect on its position For 1ps, ∆ =0.49nm  the effect is negligible

20. 25/05/2007POSIPOL 200720 Stability of the beam size There is ~ three populations  ~ 3 modes 5µm < 5µm The beam is stable in time without any isolation of the setup  drift of beam size outside is only ~3% in 2 hours.

21. 25/05/2007POSIPOL 200721 Design Study of a four mirror cavity implementable around electron beam R. Cizeron

22. 25/05/2007POSIPOL 200722 Confocal non planar 4 mirrors cavity scheme laser entrance 2 flat mirrors 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 100 mm 1 m e- beam tube IP

23. 25/05/2007POSIPOL 200723 Degrees of freedom needed to align the cavity  x et  y for all the mirrors  z = ± 1 mm on the 2 spherical mirrors to approach the confocal config.  z = ± 1 mm on the 2 flat mirrors to remain the optical length of cavity constant θy θy θxθx ∆Z Challenge  insure all the adjustments with keeping the stability of the set up

24. 25/05/2007POSIPOL 200724 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 System isolation beam Optical Table Vacuum chamber

25. 25/05/2007POSIPOL 200725 e- beam tube Vacuum chamber Support beam Support Length 1.5m tube diameter : 420 mm

26. 25/05/2007POSIPOL 200726 e- beam tube beam Interaction point e- beam

27. 25/05/2007POSIPOL 200727 Spherical mirrors 3 Beam supports Flat mirrors Flat mirror Invar ( Fe-Ni alloy)

28. 25/05/2007POSIPOL 200728 Holders to align the mirrors

29. 25/05/2007POSIPOL 200729 Mirrors holders actuator θx Cardan θx & θy actuator θy Z displacement

30. 25/05/2007POSIPOL 200730 Z Displacement  Flex // Displacement Negligible variation on height ∆Z=1mm  12 µm 0.5mm  3µm 0,1mm  0.1 µm All the parts are related to the flex

31. 25/05/2007POSIPOL 200731 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

32. 25/05/2007POSIPOL 200732 3 piezos at 120° membrane to support mirror piezo Cardan (gimble) Ø 1 inch

33. 25/05/2007POSIPOL 200733 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