#### 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 1 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) 25/05/2007 POSIPOL 2007 2 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 25/05/2007 POSIPOL 2007 3 Four mirrors 2D or 3D cavities plane mirror Y X Y X φ w00 when Z RL V2 R laser spherical mirror 2D Ring cavity R S2 spherical mirror L φ=0 2D cavity. φ0 3D cavity 25/05/2007 P2 V1 P1 S1 plane mirror Non planar cavity advantages : •reduction of astigmatism •Circular polarisation much less sensitive to mirror misalignment POSIPOL 2007 4 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 25/05/2007 POSIPOL 2007 5 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 25/05/2007 POSIPOL 2007 6 2D cavity modes TEM20 TEM10 TEM00 LG11 Exp. modes Calculated modes Similar to usual modes of 2 mirrors FP cavity 25/05/2007 POSIPOL 2007 7 2D cavity waist size CCD R laser R L Fm=2R=1000mm F=200mm D Equivalent scheme W0s W0e ws²=f(Z) 25/05/2007 Quadratic fit Z Waist after the end mirror(W0s) POSIPOL 2007 Transport matrix Waist in the cavi 8 Astigmatism of 2D cavity Variation of TEM00 profile with respect to L L>R elliptic fit LR Diffraction on mirror edges Astigmatism increases with the focusing strength 25/05/2007 POSIPOL 2007 9 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 25/05/2007 POSIPOL 2007 10 2D cavity waist size The ellipse turns calculation Mesured waist size WX 40µm Wy 12µm 25/05/2007 Limited by mirror size POSIPOL 2007 End mirror of the cavity 11 3D cavity plane mirror Y X P1 Y V1 V2 plane mirror P2 f X Z S1 S2 spherical mirror spherical mirror f0 3D cavity 25/05/2007 POSIPOL 2007 12 3D cavity modes Exp. Higher order Modes Th. results 25/05/2007 POSIPOL 2007 13 Z 3D cavity eigen modes Z Propagation of the modes outside the cavity Fundamental mode 25/05/2007 POSIPOL 2007 14 3D cavity Waist size Exp.data measurements good agreement of theory & exp. Th. calculation Wx 54µm Wy 56µm 25/05/2007 To be verified POSIPOL 2007 15 beam size calculations A shift of ~1.5mm Same phenomenon outside the cavity 25/05/2007 POSIPOL 2007 16 Reduction of the astigmatism Result of calculation After the lens End mirror of the cavity Inside the cavity 25/05/2007 POSIPOL 2007 17 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 2007results reproduced with measured data . astigmatism 25/05/2007 18 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 25/05/2007 POSIPOL 2007 19 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 25/05/2007 POSIPOL 2007 drift of beam size outside is only ~3% in 2 hours. 20 Design Study of a four mirror cavity implementable around electron beam R. Cizeron 25/05/2007 POSIPOL 2007 21 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 25/05/2007 POSIPOL 2007 22 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 25/05/2007 POSIPOL 2007 23 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 25/05/2007 POSIPOL 2007 24 Length 1.5m tube diameter : 420 mm e- beam tube Vacuum chamber Support beam Support 25/05/2007 POSIPOL 2007 25 e- beam Interaction point beam e- beam tube 25/05/2007 POSIPOL 2007 26 Flat mirrors Spherical mirrors Invar ( Fe-Ni alloy) 3 Beam supports Flat mirror 25/05/2007 POSIPOL 2007 27 Holders to align the mirrors 25/05/2007 POSIPOL 2007 28 Mirrors holders Cardan θx & θy actuator θy Z displacement actuator θx 25/05/2007 POSIPOL 2007 29 Z DisplacementFlex 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 25/05/2007 POSIPOL 2007 30 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 25/05/2007 POSIPOL 2007 31 Cardan (gimble) Ø 1 inch membrane to support mirror piezo 3 piezos at 120° 25/05/2007 POSIPOL 2007 32 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 25/05/2007 POSIPOL 2007 33