Pickoff

Pre-StabilizedLaser

BeamSplitterInnolight

PROMETHEUS

Aso configuration for LCGT green locking2011-11-04

Arm CavityL=3000m

ServoFilterfor PLL

ResonantEOM

AOMfor freq. shift

Pickoff

PD forIRarm lockPD for

PLL

LO forgreen

arm lock

testmass

actuator

PD forgreenarm lock

LO forIRarm lock

PickoffPR2orSR2

InputTestMass

EndTestMass

IR=1064nm

Green=532nm

Ctrloffsetfreq.

1

2

3

45 phase

comparator

6

7

Figure 1: Green Lock configuration for LCGT

SHGNoise

+-

+-

FGR

AAOM

AMASS

AOMfor freq. shift

End testmass actuator

Green Lock

FMASSlow freq.

+-

CGR DGR

Demod_GRArm cavity Pole

feedback point

feedback point

GreenShotNoise

PDH_GR

+-

foffset f->phi

FPZTAPZT

Volt->Hz

FTHRATHR

Volt->Hz

PLL for PSL

PLLShotNoise

Beam combiner

x2

SHG

feedback point

+-

Arm cavity for IR

ArmShotNoise

comparator

f->phi

f->phi

fcav

fPSL

fcav_FR

arm cavityseismic noise

fPSL

Pre-StabilizedLaser

phasecomparator

fGR

DPLL

Hz->m

low freq.

high freq.

fIR err

fPLL_err

fGR_s

fGR_err

fcav

+-

InnolightPROMETHEUS

fIR_FR

--+

fcav_GR

x2

fcav

fIR

1064nmFree Run

VoltageContorl

Oscillator

VCOPhaseNoise

AVCO

fVCO

FGR_1high freq.

fIR

Hz2m

3 2

1.f_IR

phasecomparator

gain

-K-

phasecomparator

feedbackpointof PLL

f->phi 3

2*pi

s

f->phi 2

2*pi

s

f->phi 1

2*pi

s

add 2

add 1F_PZT

zeros(s)

s 2

Beamcombiber

A_PZT

-K-

5

4

3

2.f_IR_FR

1.f_PSL

f_IR

f_IR

f_PSL

f_IR_FR

Simulink Model of PLL part

foffset

fPSL

fIR FR

fIR

[[ Each components ]]

Phase comparator

= 1 V /rad(see LCGT wiki : http://gwwiki.icrr.u-tokyo.ac.jp/JGWwiki/LCGT/subgroup/ifo/ISC/TaskList/LockAcquisition)

Innolight PROMTHEUS: PZT actuator

= 2 MHz /V** catalogue spec.

Servo filter for PZT loop (One zero version)

servo gain @DC = 0.01

zero freq. (1) = 10 kHz

zero freq. (2) = 0 Hz

Servo filter for PZT loop (Two zero version)

servo gain @DC = 0.01

zero freq. (1) = 5 kHz

zero freq. (2) = 5 kHz

100

105

1010

1015

Mag(dB)

PLL - Open Loop TF

10-1

100

101

102

103

104

105

106

-180

-135

-90

-45

0

45

90

135

180

Frequency (Hz)

Phase(deg)

UGF = 20kHz

f-3

f-2

G = 5e+11

G = 2e+8

Phase margin= 60 deg.

Two zero version

One zero version

[[ Noise Response to fIR ]]

OTF = openloop transfer function

* f_{IR FR} In(2) --> Out(1)

OTF = 1 / (1+G)f < UGF OTF = 1/Gf > UGF OTF = 1

* f_{offset} In(5) --> Out(1)

OTF = G / (1+G)f < UGF OTF = 1f > UGF OTF = G

* f_{PSL} In(1) --> Out(1)

same as LO, but the sign is flopped.

* Shot noise (PLL) In(4) --> Out(1)

LO "f-->phi"OTF = G / (1+G) * f

* Servo Electronics Noise (PLL) In(3) --> Out(1)

Shot noise "phase comparator gain", "phase comparator gain" = 1 shot noise OTF

10

10

10

10

10

10

10

-6

-4

-2

0

2

4

6

Magnitude

Freq noise coupling to fIR

10 10 10 10 10 10 10 10-1 0 1 2 3 4 5 6-180

-135

-90

-45

0

45

90

135

180

Frequency (Hz)

Phase(deg)

Shot noise

Servo Elec.

f PSL

f+1

UGF = 20kHz

1Hz

1+G1 1+G

Gf+3

f-1

1+GG

x f

f IR FRf offset

[[ Amount of noise source estimation ]]

* Shot noise of the phase comparator

= 2.5e-8 rad/sqrt(Hz)Wiki =>

* Servo Electric noise

= 100 nV/sqrt(Hz)

PZT loop UGF = 20 kHz

100 nV worst case

* Frequency noise of the laser free-run

= 1.0e+4 / f Hz/sqrt(Hz)

* Local Oscillator freq. noise

** Agilent E8663D-UNX catalogue spec.

= 5e-5 / f^2 Hz/sqrt(Hz) --> freq. noise = 5e-5 / f Hz/sqrt(Hz)

10 10 10 10 10 10 10 10-1 0 1 2 3 4 5 610

10

10

10

10

10

10

10

10

10

10

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

Frequency (Hz)

Mag(Hz/sqrt(Hz))

fIR

Shot noise

Servo Elec.

fIR FR

foffset

fIR

pendulum

num(s)den(s)

noiseinjection

point2

noiseinjection

point1

inverted_pend

w_IP*w_IPden(s)

feedbackpointof GR

feedbackpoint

o f_cav

SHG

PDH_GR

IR->GR

2

F_MASS

F_GR1 F_GR

Demod_GRCavity Pole

wCav

(s+wCav)

A_VCO (V->Hz)

A_MASS

A_AOM

7

6 5

4

3

2

1

2

-K-

-K-

6

5

4

3

2

1

zeros(s)poles(s)

zeros(s)poles(s)

zeros(s)poles(s)

num(s)den(s)

Simulink model of Green Laser PDH Locking

fcav

fcav FR

= Seis

SHGinducednoise

fIR

ShotGrPDH

VCOnoise

[[ Each components of Green PDH ]]

Cavity pole for green laser

= c / 4 / L / (Finesse for green laser)

= 2.5 kHz

Finesse for green laser = 10

Demodulation gain for GrPDH

Resonant width in freq. of the arm cavity

= fFSR / (Finesse for green laser)

1 Volt

Demod Gain for GrPDH = (Finesse for Gr) / fFSR

= 2e-4 V/Hz

fFSR = c /2 /L = 50 kHz

Servo filter (F_GR)

servo gain = 0.1

pole freq. (1) = 0 Hz

zero freq. (1) = 2.5 kHz

Servo filter (F_GR1)

servo gain @DC = 1

zero freq. (1) = 0 Hz

pole freq. (1) = 10 Hz

Servo filter (F_MASS)

servo gain @DC = -2e+2pole zero

0 10

0 10

100 10

500

500

Mass Actuator (A_MASS)

servo gain @DC = 5e-6 um/V * m2Hz

= 4.7e+5 Hz/V

pole freq. = 1 Hz

Q favtor = 10

m2Hz = 2/lambda * c/2/L

= 9.3e+10

10-5

100

105

1010

Magnitude

Green PDH - Open Loop TF

OverallMass OnlyAO Only

10-2 10-1 100 101 102 103 104 105 106-180

-135

-90

-45

0

45

90

135

180

Frequency (Hz)

Phase(deg)

Cross-overfreq. = 10 Hz

OverallUGF= 40 kHz

-140 deg.

+135 deg.

135-(-140)= 275 - 180= 95 deg.

[[ GrPDH noise TF ]]

* cross-over freq. mass servo

10 Hz

* SHG noise, VCO noise, f_{IR} 10 Hz

* Shot noise GrPDH SHG, VCO, f_{IR} cavity pole

cavity pole freq. = 2.5 kHz --> pole zero

* fIR -> fcav

10-10

10-8

10-6

10-4

10-2

100

102Magnitude

Green laser freq noise coupling to fIR

SHGSeis+MassShot GrPDHVCOfIRMass servoSeis Att.

10-2 10-1 100 101 102 103 104 105 106-180

-135

-90

-45

0

45

90

135

180

Frequency (Hz)

Phase(deg)

Cross-overfreq. = 10 Hz

[[ Amount of noise source estimation ]]

* SHG induced noise

1e-5 (phase noise, f>10 Hz) --> 1e-5 * f (freq. noise)

** measured spectrum at Caltech 40m: LIGO G1000311-v2

* Seismic motion

= 1e-9 / f^2 m/sqrt(Hz)

* Shot noise of Green PDH

= 8e-6 Hz/sqrt(Hz)

???

* VCO freq. noise

** Agilent E8663D-UNX catalogue spec.

= 5e-5 / f^2 Hz/sqrt(Hz) --> freq. noise = 5e-5 / f Hz/sqrt(Hz)

fcav

10-2 10-1 100 101 102 103 10410-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Magnitude

(Hz/sqrt(Hz))

Frequency (Hz)

SHGSeisShotVCO

fcav

IR Error

fIR

fIR

fPSL

fIR FR

foffset

Shot PLL

SHGinducednoise

VCOfreq.noise

ShotGrPDH

fCAV FR= Seis

ShotIR PDH

Elec. PLL

phasecomparator

gain

phasecomparator

pendulum

num(s)den(s)

noiseinjection

point3

noiseinjection

point2

noiseinjection

point1

noiseinjection

point

inverted_pend

w_IP*w_IPden(s)

feedbackpointof PLL

feedbackpointof GR

feedbackpoint

of f_cav

f->phi 3

2*pis

f->phi 2

2*pis

f->phi 1

2*pi

add 1

SW_THR

SHG

PDH_IR

PDH_GRIR->GR

Hz->m

F_THR

zeros(s)s 2

F_PZT

zeros(s)s 2

F_MASS

zeros(s)poles(s)

F_GR1

zeros(s)poles(s)

F_GR

zeros(s)poles(s)

Demod_GRCavity Pole

wCav

(s+wCav)

Beamcombiber

A_VCO (V->Hz)

A_THR

A_PZT

A_MASS

num(s)den(s)

A_AOM

11

10

9

8 7

6

5

4

3 2

1

-K-

-K-

2

2

-K-

-K-

-K-

-K-

-K-

10

9

87

6

5 4

3

2

1

s

Shot PLL

10-5

100

105Magnitude

Freq noise coupling to IR Error

Shot PLLElec. PLLfIR GRfoffset

10-2 10-1 100 101 102 103 104 105 106-180

-135

-90

-45

0

45

90

135

180

Frequency (Hz)

Phase(deg)

Cross Over= 10 Hz

10-3 10-2 10-1 100 101 102 103 10410-22

10-20

10-18

10-16

10-14

10-12

10-10

Frequency (Hz)

Mag(m/sqrt(Hz))

Displacement noises at IR Errorwithout PSL noise

Shot PLLElec. PLLfIR FRfoffsetSHGSeisShot GrVCOShot IR

cumulative spectrum

0.02 pm

10-10

10-5

100

Magnitude

PSL noise to IR Error

10-3 10-2 10-1 100 101 102 103 104-180

-135

-90

-45

0

45

90

135

180

Frequency (Hz)

Phase(deg)

Cross-OverFreq. = 10 Hz

fPSL

Free-run: frequency noise

1e+4 / f Hz/sqrt(Hz)

10-3 10-2 10-1 100 101 102 103 10410-20

10-18

10-16

10-14

10-12

10-10

10-8

Frequency (Hz)

Mag(m/sqrt(Hz))

PSL noises at IR Error

Total w/o PSLFree Run Laser1e-7 Hz/sqrt(Hz)1e-3 /f Hz/sqrt(Hz)toy model