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 RL 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 ······ pair 1 pair 2pair N z y Each layer has different characteristic matrix for s-wave and p-wave A periodic dielectric multilayer mirror s-wave i=1,2 p-wave i=1,2 Quarter-wave stack Using specified layer thickness corresponding to λ 0 and θ 0

General description on Quarter-wave stack mirror In an ideal case, means no fabrication error on layer’s thickness and refraction index: For a s-wave: Reflection coefficient is real number: S P

General description on Quarter-wave stack mirror 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: A General 45 º Mirror

General description on Quarter-wave stack mirror Assume all the layers have same fabrication errors: 20 º 5º5º 10 º 15 º 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/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: argr p =argr s In theory, a 2-mirror cavity has a good capability to keep polarization

Difficulty of 2-mirror cavity c c laser Δ=0.001 º Difficulty of 2-mirror cavity: optical axis A concentric cavity has a high sensitivity to misalignment: In the case of: σ 0 =30um R=210.5mm L=420mm Assume a angle misalignment of one mirror is º, a misalignment of optical axis is ≈0.2 º and spot position shift on mirror is ≈0.7mm Mechanical constraint is very strong A mechanical solution: Four mirrors cavity A Concentric Cavity

A 4-mirror Fabry-perot Cavity laser waist L R R W 0  0 when R  L 4-mirror Ring Cavity R≈L L A Confocal Cavity A confocal cavity has a low sensitivity to misalignment: Assume a angle misalignment of one spherical mirror is º, 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 A 4-mirror Fabry-perot Cavity ◆ Fabrication error of stacked quarter-wave layer has effect on ≠ polarization: argr p ≠ argr s Difference phase shift between s and p Circular polarized degree (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. 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 Ta 2 O 5 /SiO 2 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: 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

A 3D 4-mirror Fabry-perot Cavity 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 Cavity by Araki

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 (5.7 º ), 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. Laser Pockels cell Cavity

Possibility of fast switching polarization of Compton source L-handed Polarization R-handed Polarization Assume a cavity has a Finesse F=30000, and Cavity length L=2m. The decay time: ms Power of stacking laser in cavity

Possibility of fast switching polarization of Compton source Roughly estimate on the average polarization depends on the switching frequency: 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.

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