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

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 structure2. 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

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

Optical scheme of the nonplanar cavity

2 plan mirrors

2 spherical mirrors

WAIST

.

Injection laser

e-Interaction

point

Electron pipe

Fundamental mode of the nonplanar cavity

Distance between the curve mirrors: 502.8mm

Transverse scale: 0.1mm =

Longitudinal stepbetween two successive images : ~ 8mm

Fundamental mode of the nonplanar cavitydictorted by abberations

Distance between the curve mirrors: 502mm

Transverse scale : 0.1mm =

Longitudinal stepbetween two successive images: ~ 8mm

Cavity construction for ATF

Compact construction operated under high vacuum and remotely adjusted

PZT

Cavity mirrors actuators

θx

θy

PZT

Flexible support

Mirror

Step motorin vacuum housing

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

CEREPn ffn

2_CCEFP

n nFSR

Pulse laser – cavity locking through the one-parameter

F_ce lockingF_rep ramping

F_rep lockingF_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

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PHIce/(2 pi) (without unit)

no

rma

lized

tra

ns

mit

ted

po

wer

Fabry-Perot cavity transmision power sensitivity over PHIce, Tau = 2ps

Requirements on the electronics: noise level inside the bandwidth of the actuators smaller than noise necessary for the tight lock.

L

F

f

One-parameter locking

F-cavity finessefL- laser frequency

Scheme of the pulse laser locking on the optical cavity

grep

vf

L

gceo

v vf

1. Ramping frep – motor M1

2. Locking frep -PZT

1. Ramping fceo – starter (wedges)

2. Locking fceo – AOM1+AOM2

PumpLaser

U=0U=δ

Digital Feedback (1)

PH REFLEXION

DPDHDPDH

command

command

command

PH TRANS

DDSDDS

ADC

ADC

ADC

DPDHDPDH

FPGA

PZT

AOM

VHS-ADAC

EOM

DAC

DAC

DAC

DAC

PH REFLEXION

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-ADAC8 inputs - 8 outputsparallel ADC, DAC, 14bits Latency : 60ns (ADC) + (0.3-1)µs + 40ns (DAC)

Frep phase noise

PDH voltage noise power densityin closed loop Sv(f)

Estimation ofPhase noise in closed loop

and in open loop

ΔFrep RMS ~ 1 mHz (@ f<100kHz) in CL

For coupling 90% of the powerOne needs ΔFrep RMS ~ 0.1 mHz

Detection noise floorPDH noise floor

Unity gain frequency ~ 10 kHz

0 0

0

( )6

0.16

Frepf n n Frep

FrepFrep mHz

n

F

F

Frep frequency noise

101

102

103

104

105

106

107

108

-80

-60

-40

-20

0

20

40

60

Frequency (Hz)

Nois

e P

ow

er

(dB

c/H

z)

100

102

104

106

108

10-1

100

101

102

103

104

105

Frequency (Hz)

Estimation of theFrequency noise power density

of the carrier in closed loop

Estimation of theIntegrated Frequency noise power

of the carrier in closed loop

0( ) 5006

Frepf n Hz

F

Detectionnoise floor

~5 kHz