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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 R L laser: λ=1064nm, 100% right-handed e- -beam: 1.3Gev Left-handed polarized gamma-rays dominate in the high energy region High polarization of laser light →High polarization of gamma-rays 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 General description on Quarter-wave stack mirror y A periodic dielectric multilayer mirror d1 d 2 d1 d 2 n0 0 n1 n2 n1 n2 cos i Mi ipi sin i 2 1 1 i ······ sin i pi cos i 2 i cos sin i i Mi q i······ iq sin cos i i i pair N pair 1 pair 2 i 2 ni d i cos i s-wave 0 i=1,2 pi ni cos i S z 2 i ni d i cos i 0 p-wave Substrate n s cos i i=1,2 q i ni Each layer has different characteristic matrix for s-wave and p-wave Using specified layer thickness corresponding to λ0 and θ0 ni d i cos i 0 4 i 2 Quarter-wave stack General description on Quarter-wave stack mirror In an ideal case, means no fabrication error on layer’s thickness and refraction index: n1d1 cos 1 n2 d 2 cos 2 For a s-wave: 0 M1 ip1 i 0 M p1 2 0 ip2 i p2 0 ps p1 2 N ( ) p0 p 2 rs p p 1 s ( 1 )2 N p0 p 2 1 S 0 4 M Np P Reflection coefficient is real number: 1 2 2 p2 N ( p ) 1 ( M 1M 2 ) N 0 p1 N ( ) p2 qs q1 2 N ( ) q0 q 2 rp q q 1 s ( 1 )2 N q0 q 2 1 arg(rp ) 0, arg(rs ) 0 0 General description on Quarter-wave stack mirror Rs rs 2 R p rp 2 A General 45º Mirror N , 2 rp 1, rs 1 2 arg(rp ) arg(rs ) 0 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: arg(rp ) 0, arg(rs ) 0 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 5º 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. 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 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 strong A mechanical solution: Four mirrors cavity A 4-mirror Fabry-perot Cavity 4-mirror Ring Cavity R≈L R R waist laser L L R≈L W0 0 when RL 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. A 4-mirror Fabry-perot Cavity Polarization preserving in a 4-mirror cavity: ◆All the reflection on the mirror is oblique Circular polarized degree (S3) ◆Oblique incidence has different reflection coefficients for s and p wave ◆Fabrication error of stacked quarter-wave layer has effect on polarization: argrp ≠ argrs 0.32 rad To keep at least 95% circular polarization: The different phase shift between s and p should be smaller than 0.32rad Difference phase shift between s and p A 2D 4-mirror Fabry-perot Cavity Considering the easy mechanical design, first a 2D 4-mirror cavity. ◆Assume all the 4 mirrors are perfectly aligned ◆Gain: 10000 laser 0.32rad arg(r p ) arg(r s ) 0.8 10 5 rad 4 10000 Blue: d: 0.02% n: 0.02% Red: d: 0.01% n: 0.01% Green: 0.005% 0.005% 0.8×10-5 rad A model of 37 layers Ta2O5/SiO2 p s 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 Not safety for 2D 4-mirror cavity to preserve polarization at a so high gain 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 by Araki 2D Cavity 3D Cavity 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 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. 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. Possibility of fast switching polarization of Compton source Assume a cavity has a Finesse F=30000, and Cavity length L=2m. The decay time: FL c 6.4 105 Power of stacking laser in cavity I I 0 exp( t ) L-handed Polarization R-handed Polarization I I 0 [1 exp( t )] ms Possibility of fast switching polarization of Compton source Roughly estimate on the average polarization depends on the switching frequency: RL P RL To get about 90% polarization at a fast switching frequency 1kHz Summary 1. 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!!