1. Nonplanar Cavity Construction and Locking Technique for High Finesse Cavity Soskov V., Chiche R., Cizeron R., Jehanno D., Zomer F. Laboratoire de l’Accélérateur Linéaire, Orsay, France

2. Outline Why a nonplanar cavity 1.Compact size(mechanical stability, vacuum) 2.No reverse beam 3.Easy adapt to the different frequencies 4. Elliptic particle beam  astigmatic eigen mode of the cavity = nonplanar cavity Cavity for ATF (KEK) 1. Mode structure 2. Construction Requirements for laser to cavity tight locking - requirements for electronics - requirements for actuators Digital Feedback for locking a pulse laser to the optical cavity

3. Nonplanar cavity Why a nonplanar cavity 1.Compact size(mechanical stability, vacuum) 2.No reverse beam 3.Easy adapt to the different frequencies 4. Elliptic particle beam  astigmatic eigen mode of the cavity = nonplanar cavity Eigen modes of such cavities = gaussian beam with general astigmatism e ph IP

4. Optical scheme of the nonplanar cavity 2 plan mirrors 2 spherical mirrors WAIST. Injection laser e-e- Interaction point Electron pipe

5. Fundamental mode of the nonplanar cavity Distance between the curve mirrors: 502.8mm Transverse scale: 0.1mm = Longitudinal step between two successive images : ~ 8mm

6. Fundamental mode of the nonplanar cavity dictorted by abberations Distance between the curve mirrors: 502mm Transverse scale : 0.1mm = Longitudinal step between two successive images: ~ 8mm

7. Cavity construction for ATF Compact construction operated under high vacuum and remotely adjusted

8. PZT Cavity mirrors actuators θx θy PZT Flexible support Mirror Step motor in vacuum housing

9. Pulse laser locking to the optical cavity Principle : coherent combinig of the successive laser pulses inside the optical cavity : --> mutual coherence of pulse laser cavity --> two parameters locking carrier envelope Fabry-Perot Cavity FSR Laser spectrum Cavity eigen modes

10. Pulse laser – cavity locking through the one-parameter F_ce locking F_rep ramping F_rep locking F_ce ramping Two parameters have to be locked Requirements on the actuators: 1.big dynamic range (ramping) 2. min noise (tight lock) Two actuators for each paramaters: one for the ramping another for locking Requirements on the electronics: noise level inside the bandwidth of the actuators smaller than noise necessary for the tight lock. One-parameter locking F-cavity finesse f L - laser frequency

11. Scheme of the pulse laser locking on the optical cavity 1.Ramping f rep – motor M 1 2.Locking f rep -PZT 1.Ramping f ceo – starter (wedges) 2.Locking f ceo – AOM1+AOM2 Pump Laser U=0 U=δ

12. Front-end TRANSMISSION Digital Feedback (1) PH REFLEXION DPDH command Error Signal PDH PH TRANS Front-end TRANSMISSION Front-end REFLEXION Front-end REFLEXION DDS ADC DPDH Driver PZT Driver AOM FPGA PZT AOM VHS-ADAC Driver EOM DAC PH REFLEXION

13. Digital feedback (2) 1.2 inputs + 4 outputs parameters = MIMO 2. Nonstationary response of F-P cavity 3. Nonlinear reaction of the feedback system: ramping + triggering + filtering (linear and nonlinear) 4. Simple communication with the another digital systems Lyrtech: VHS-ADAC 8 inputs - 8 outputs parallel ADC, DAC, 14bits Latency : 60ns (ADC) + (0.3-1)µs + 40ns (DAC)

14. Frep phase noise PDH voltage noise power density in closed loop S v (f) Estimation of Phase noise in closed loop and in open loop ΔFrep RMS ~ 1 mHz (@ f<100kHz) in CL For coupling 90% of the power One needs Δ Frep RMS ~ 0.1 mHz Detection noise floor PDH noise floor Unity gain frequency ~ 10 kHz

15. Frep frequency noise Estimation of the Frequency noise power density of the carrier in closed loop Estimation of the Integrated Frequency noise power of the carrier in closed loop Detection noise floor ~5 kHz