Shimoda TomofumiAndo lab. seminar on 22 Dec. 2017

2C B• Wearedevelopinganimprovedangularsensor• sensitivityofwavefrontsensor(WFS)canbeimprovedbyusingauxiliarycavityforHG10 moderesonance• itgivesusmanymeritsandafewdemeritscomparedwithconventionalangularsensors

rf rm re

frontmirror

midmirror

endmirror

QPD

auxiliary cavity

ra,10 = ra,00 eiφa

main cavity

)? C• principle• merits&demerits• technicalissues• designforTOBA• summary

B

B ? G F B? C C• tiltedmirrorconvertsHG00 toHG10

• HG10 modefromthecavityisdetectedasangularsignal• nocavityamplificationonHG10 modesignal (sameasopticallever)

input:HG00 E0

E0/t�θ

E0/t

�transmit&cavityamplification

� t�1/t2

outputHG10 signal

E0×θ

�converttoHG10� θ

�transmit� t

HG10

detectedwithQPD(interferencewithHG00)(orsinglePDwithjittermodulation(beatwithHG10 sideband))

C = B ? -• sensitivityofconventionalWFSisinthesameorderasMichelsoninterferometerwhosearmseparationisbeamdiameter• because10modesignalisnotamplifiedbythecavity

beamdiameter

� lowsensitivity

= B?F =• IfHG10 modecanresonateinsidethecavity,generatedsignalisamplified

input:HG00

E0

E0/t3�θ

E0/t

outputHG10 signal

E0 /t2×θ

�converttoHG10� θ

�transmit� t

HG10

�transmit&cavityamplification

� t�1/t2

�cavityamplification� 1/t2(�Finesse)

amplified

C = B ? -• sensitivityofimprovedsensor isinthesameorderasFabry-PerotMichelsoninterferometerwhosearmseparationisbeamdiameter

beamdiameter

� highsensitivity

HG00

HG10

• HG10 modegetsdifferentphasefromHG00 modebyΦGouy thereforetheycannotresonateatthesametimeinanormalcavity

input:HG00

E0

E0/t3�θ

E0/t

outputHG10 signal

E0 /t2×θ

�converttoHG10� θ

�transmit� t

HG10

�transmit&cavityamplification

� t�1/t2

�cavityamplification� 1/t2

?B= F I ? B C

φrt,10 = φrt,00 + ΦGouy

(round-tripphase)

BI F I ?B ? IC ?= C ?

• cavityhasdifferentreflectionphaseforeachmodes

-3

-2

-1

0

1

2

3

-0.1 -0.05 0 0.05 0.1 0.15

Ref

lect

ion

Phas

e [r

ad]

cavitylength[a.u.]

HG00 HG10 HG20 HG30

arg(

r a)

ra

(compoundmirror)

BI F I ?B ? IC ?= C ?

• reflectionphaseoftheauxiliarycavitycancompensateΦGouyinthemaincavity

φrt,10 = φrt,00 + ΦGouy+ arg(ra,10) - arg(ra,00)

= φrt,00 + 2nπ-3

-2

-1

0

1

2

3

-0.1 -0.05 0 0.05 0.1

Refle

ctio

n Ph

ase

[rad]

cavity length [a.u.]

φa

HG00 HG10

arg(

r a)

= - ΦGouy

or 2π - ΦGouy

ra

� resonateHG10 andHG00 atthesametime

round-tripphaseinthemaincavity

auxiliarycavity

ΦGouy

maincavity(compoundendmirror)

? ? C ? BI F I

-3

-2

-1

0

1

2

3

-0.1 -0.05 0 0.05 0.1

arg(ra,

10)-arg

(ra,00)

cavity length [a.u.]

-3

-2

-1

0

1

2

3

-0.1 -0.05 0 0.05 0.1

arg(

ra)

cavity length [a.u.]

HG00 HG10

HG10 - HG00

�changingHG00 phase�HG10 isanti-resonant

�HG00 isanti-resonant�changingHG10 phase

- ΦGouy

or

• detunedfromresonance• somesolutions

C? ? C ? G IC C• require...• enoughlargeΦGouy

• longcavity• smallbeam(thesearelimitedbychambersizeandthermalnoiserequirement)

• properreflectivityofauxiliarycavitymirrors

-3

-2

-1

0

1

2

3

-0.1 -0.05 0 0.05 0.1

arg(ra,

10)-arg

(ra,00)

cavity length [a.u.]

-3

-2

-1

0

1

2

3

-0.1 -0.05 0 0.05 0.1

arg(

ra)

cavity length [a.u.]

HG00 HG10

HG10 - HG00

- ΦGouy

?G B F I• cavitylength(10cm)&beamsize(0.8mm)arefixed

0.995 0.996 0.997 0.998 0.999 1Rmid

0.995

0.996

0.997

0.998

0.999

1

Rend

λ = 1064 nm / w0 = 0.8 mm

no solution

2 solutions

4 solutions

allowedregion

B BB B F I• enoughfinesseofthemaincavityisrequiredforangularsignalamplification

100

100

100

100100

100

200

200

200

200200

200

300

300

300

300

300300

300400

400

400

400

400

400

500

500

500

500600

600

0.995 0.996 0.997 0.998 0.999 1Rmid

0.995

0.996

0.997

0.998

0.999

1

Rend

Finesseofmaincavity(Rfront=99%(fixed))

nosolutionor

lowfinesse

(example)99.95%/99.9%→ F=360

(theseparametersarechoseninfollowingcalculations)

?CC 2 ? B ? C• testmasscanbeputanywhere

TM

@frontmirror

TM

@mid mirror

TM

insertedincavity

= B C = B C

?G C ? ? C•� highangularresponse(almostsameasMI)

• sameasMIshotnoiselevel� 10-15 rad/rtHz

Michelson

~#$%&' [W/rad]

~#$%/' 0[W/rad]

newWFSnewWFSwith1mmbeam

&finesse300� MIwith30cmbar

(w:beamradius,F:finesse)

(Pin:inputpower,L:barlength)

L

• roughlylargerby(barlength)/(beamdiamerer)

• less(no)angularcontrolisrequired� less(no)actuatornoise• (practically,rangeofPDshouldbeconsidered)

B B BthanMichelsoninterferometers

L

θ

θ<λ/L~1urad θ<λ/w~0.1mrad

w

?G 2 = : B ? C• suppressedbyfinesse

beamjitterθjitter :generateHG10 outsidethecavity� E10,jitter =E0 �θjitter � 1/t�t

cavitymirrortiltθmir :generateHG10 insidethecavity� E10,mirror =E0 �1/t� θmir� 1/t2 �t

(amplify) (transmit)

(amplify) (transmit)(amplify)

E10,jitter� t2� E10,mirror(�E10,mirror /F)

amplify(1/t)

HG10(jitter)

transmit(t)

tilt

HG10(mirror)HG10(jitter)

E0

amplify(1/t2)

convert

thanconventionalWFSs

? ?G B A I ? C• nofrequencynoiseinwavefrontsensor

• (spatialnonuniformityoffrequencyfluctuationcan benoise...?)

HG00

HG10

C= B C ? &• makingflatnessiseasierinsmallerscale• especiallythisisgoodpointforlargebars(L>50cm)whicharedifficulttomakeflatnessbetweenbothends

~barsize(~m) ~beamsize(~mm)

thanMichelsoninterferometers

Michelsoninterferometer

Lθ

WFS

w

B B= 2B?G• higherby(barlength)/(beamdiameter)

thanMichelsoninterferometers

Michelsoninterferometer

L

WFS

w

noise~(fluctuation)/L noise~(fluctuation)/w

C == BI ? = B C = B C• newsensoristhebest!!

conventionalWFS

Michelsoninterferometer

newWFS

shotnoise

linearrange

beamjitter

frequencynoise

trans-coupling

thermalnoise

?

← notdominantinTOBA

CC C

M C B ?• maincavity:ReflPDHsignal• auxiliarycavity:DCsignal(Trans– (const)�Refl)

tosetdcoffset0

42

PBS

REFL(PDH)

R=99.9%R=99.95%

15MHz

Test Mass

R=99%

TRANS(DC)

,DC)

main auxiliary

= F I C• auxiliarycavityisdetunedfromHG00 resonance

→ auxiliarycavityworksaswellassinglemidmirrorforHG00� reflPDHsiganalmainlycontainsmaincavitylengthsignal

auxiliarycavity

mid� under-coupledcavitygivesbettersignalseparation(main-auxiliary)

BI F I C• reflectivityofauxiliarycavityabs(ra) dependsonauxiliarycavitylength� trans/reflDCpowerchanges

auxiliarycavity

ra

ra

transDCreflDC

transDCreflDC

C C B ?• notbad(Rfront =99%,Rmid =99.95%,Rend =99.9%)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2cavity length [m] ×10-8

-0.015

-0.01

-0.005

0

0.005

0.01

sign

al [W

]REFL(I) (main)REFL(I) (auxiliary)REFL(DC)-TRANS(DC) (main)REFL(DC)-TRANS(DC) (auxiliary)

sensingmatrix main cavity auxiliarycavityPDH signal

(refl) 1 0.09DC signal(refl-trans) 0 1

? B?= ? B = BB?BC• everymirrorcangenerateHG10 mode

auxiliarycavitymaincavity

front mid end

-15 -10 -5 0 5 10 15Amplitude quadrature

-0.5

0

0.5

1

phas

e qu

adra

ture

front

mid

end

(samephaseasHG00 @frontmirror)

(90�

shiftfrom

HG 0

0@fron

tmirror)

generatedHG10 mode(example)

? ? 2 =• notenoughdegreesoffreedomtoseparatesignals• 2readoutquadraturevs 3mirrors

• (bychoosingreadoutdirection,couplingfromonlyonemirrorcanberemoved)

-15 -10 -5 0 5 10 15Amplitude quadrature

-0.5

0

0.5

1

phas

e qu

adra

ture

front

mid

end

readoutdirection

(semi-)monolithicmirrorsmaybenecessary� howmuchistheangularfluctuationofmirrors?

O ?• cavitylengthcontrol(mid,endmirror)

• shakemirrorangle

• appearinsignal

(notevaluatedindetailyet)

actuatorasymmetry

signalcoupling

�10-9 m/rtHz@0.1Hz

�10-10 rad/rtHz@0.1Hz

�10-12 rad/rtHz@0.1Hz

(veryroughestimation)

front mid

feedbacktolength

coupletoangle

vibrate

readinminimumcouplingquadrature

large

0.1rad/m

P? B CC C• Dononexplicitcouplingroutesexist?from...• frequencyfluctuation• polarizationfluctuation• intensityfluctuation• andsoon... ?

C ?B (

F I C• cavitylength:10cm(main)/7.5cm(auxiliary)• limitedbychambersize

• beamradius:0.8mm@frontmirror(waist)• fromthermalnoiserequirement

• Finesseofmaincavity:360

auxiliarycavity

HG00

HG10

R=99%flat

R=99.95%RoC=67m

R=99.9%RoC=28m

10cm 7.5cm

w=0.8mm

maincavity

sapphiremirrors(forcryogenic)

? ? B ? • putthefrontmirroronthetestmass• mid&endmirrorsare(semi-)monolithic• beamjitterissuppressedbycontrolwithtwoQPDs

42

PBS

REFL(PDH, DC)

R=99.9%R=99.95%

15MHz

Test Mass

R=99%

TRANS(DC)

jittersuppression wavelength:1064nmbeamradius:0.8mmcavitylength:10cmfinesse:360

: B C B CC ?• QPDnoise:~10-7 V/rtHz@0.1Hz• positionsensitivityofQPD(w=0.4mm):~30V/mm

→ positionsensingnoise:3�10-12 m/rtHz• measurebeamcenterattwopoints(separatedby30cm)

→ angularjitter:10-11 rad/rtHz• jitternoiseissuppressedbyfinesse(~300)

→ 3�10-14 rad/rtHz30cm

C C?B ? C F• 4�10-14 rad/rtHz@0.1Hz

10-3 10-2 10-1 100 101 102

Frequency [Hz]

10-16

10-15

10-14

10-13

10-12

Noi

se [r

ad/rt

Hz]

shot noisesubstrate browniancoating brownianbeam jittercircuit(QPD)circuit(AA filter)Total

wavelength:1064nmbeamradius:0.8mmcavitylength:10cmfinesse:360temperature:4Ksubstrate:sapphiresubstrateloss:10-8coatingloss:10-3

� target:5�10-14 rad/rtHz

�mirrorvibration&length-anglecouplingarenotincluded

C C?B ? C F• 4�10-14 rad/rtHz@0.1Hz

10-3 10-2 10-1 100 101 102

Frequency [Hz]

10-16

10-15

10-14

10-13

10-12

Noi

se [r

ad/rt

Hz]

shot noisesubstrate browniancoating brownianbeam jittercircuit(QPD)circuit(AA filter)Total

wavelength:1064nmbeamradius:0.8mmcavitylength:10cmfinesse:360temperature:4Ksubstrate:sapphiresubstrateloss:10-8coatingloss:10-3

� target:5�10-14 rad/rtHz

�mirrorvibration&length-anglecouplingarenotincluded

demonstrationexperimentisinpreparation

C == BI

C == BI• sensitivityofwavefrontsensorcanbeimprovedbyusingauxiliarycavityforHG10 moderesonance• improvedsensorhaslowshotnoise,jitternoise,frequencynoise,andlargelinearrange,buthighthermalbrowniannoise• opticaldesignforTOBAisfixed:(noise) 4�10-14 rad/rtHz(demonstrationexperimentisinpreparation)

designforTOBA auxiliarycavity

HG00

HG10

R=99% R=99.95% R=99.9%

10cm 7.5cm

w=0.8mm

maincavity

B = CC C• measureorestimateangularfluctuationof(semi-)monolithicoptics

• calculatelength-anglecouplingindetailandthinkhowtoreduceit

front mid

feedbacktolength

coupletoangle

vibratelength-anglecoupling