Nonplanar Cavity Construction and Locking Technique for High Finesse Cavity

1. Nonplanar Cavity Construction andLocking 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 IP ph e

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

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

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 Fabry-Perot Cavity carrier envelope Laser spectrum Cavity eigen modes FSR

10. Pulse laser – cavity locking through the one-parameter Two parameters have to be locked F_ce locking F_rep ramping F_rep locking F_ce ramping 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 One-parameter locking F-cavity finesse fL- laser frequency Requirements on the electronics: noise level inside the bandwidth of the actuators smaller than noise necessary for the tight lock.

11. Scheme of the pulse laser locking on the optical cavity Pump Laser Ramping frep – motor M1 Locking frep -PZT Ramping fceo – starter (wedges) Locking fceo – AOM1+AOM2 U=0 U=δ

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

13. Digital feedback (2) • 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 Estimation of Phase noise in closed loop and in open loop PDH voltage noise power density in closed loop Sv(f) ΔFrep RMS ~ 1 mHz (@ f<100kHz) in CL Detection noise floor PDH noise floor For coupling 90% of the power One needs ΔFrep RMS ~ 0.1 mHz 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 ~5 kHz Detection noise floor