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Shimoda TomofumiAndo lab. seminar on 22 Dec. 2017
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2C B• Wearedevelopinganimprovedangularsensor• sensitivityofwavefrontsensor(WFS)canbeimprovedbyusingauxiliarycavityforHG10 moderesonance• itgivesusmanymeritsandafewdemeritscomparedwithconventionalangularsensors
rf rm re
frontmirror
midmirror
endmirror
QPD
auxiliary cavity
ra,10 = ra,00 eiφa
main cavity
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)? C• principle• merits&demerits• technicalissues• designforTOBA• summary
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B
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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))
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C = B ? -• sensitivityofconventionalWFSisinthesameorderasMichelsoninterferometerwhosearmseparationisbeamdiameter• because10modesignalisnotamplifiedbythecavity
beamdiameter
� lowsensitivity
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= 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
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C = B ? -• sensitivityofimprovedsensor isinthesameorderasFabry-PerotMichelsoninterferometerwhosearmseparationisbeamdiameter
beamdiameter
� highsensitivity
HG00
HG10
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• 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)
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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)
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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)
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? ? 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
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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
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?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
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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)
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?CC 2 ? B ? C• testmasscanbeputanywhere
TM
@frontmirror
TM
@mid mirror
TM
insertedincavity
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= B C = B C
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?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
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• 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
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?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
![Page 21: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/21.jpg)
? ?G B A I ? C• nofrequencynoiseinwavefrontsensor
• (spatialnonuniformityoffrequencyfluctuationcan benoise...?)
HG00
HG10
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C= B C ? &• makingflatnessiseasierinsmallerscale• especiallythisisgoodpointforlargebars(L>50cm)whicharedifficulttomakeflatnessbetweenbothends
~barsize(~m) ~beamsize(~mm)
thanMichelsoninterferometers
Michelsoninterferometer
Lθ
WFS
w
![Page 23: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/23.jpg)
B B= 2B?G• higherby(barlength)/(beamdiameter)
thanMichelsoninterferometers
Michelsoninterferometer
L
WFS
w
noise~(fluctuation)/L noise~(fluctuation)/w
![Page 24: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/24.jpg)
C == BI ? = B C = B C• newsensoristhebest!!
conventionalWFS
Michelsoninterferometer
newWFS
shotnoise
linearrange
beamjitter
frequencynoise
trans-coupling
thermalnoise
?
← notdominantinTOBA
![Page 25: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/25.jpg)
CC C
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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
![Page 27: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/27.jpg)
= F I C• auxiliarycavityisdetunedfromHG00 resonance
→ auxiliarycavityworksaswellassinglemidmirrorforHG00� reflPDHsiganalmainlycontainsmaincavitylengthsignal
auxiliarycavity
mid� under-coupledcavitygivesbettersignalseparation(main-auxiliary)
![Page 28: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/28.jpg)
BI F I C• reflectivityofauxiliarycavityabs(ra) dependsonauxiliarycavitylength� trans/reflDCpowerchanges
auxiliarycavity
ra
ra
transDCreflDC
transDCreflDC
![Page 29: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/29.jpg)
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
![Page 30: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/30.jpg)
? 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)
![Page 31: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/31.jpg)
? ? 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?
![Page 32: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/32.jpg)
O ?• cavitylengthcontrol(mid,endmirror)
• shakemirrorangle
• appearinsignal
(notevaluatedindetailyet)
actuatorasymmetry
signalcoupling
�10-9 m/[email protected]
�10-10 rad/[email protected]
�10-12 rad/[email protected]
(veryroughestimation)
front mid
feedbacktolength
coupletoangle
vibrate
readinminimumcouplingquadrature
large
0.1rad/m
![Page 33: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/33.jpg)
P? B CC C• Dononexplicitcouplingroutesexist?from...• frequencyfluctuation• polarizationfluctuation• intensityfluctuation• andsoon... ?
![Page 34: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/34.jpg)
C ?B (
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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)
![Page 36: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/36.jpg)
? ? 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
![Page 37: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/37.jpg)
: B C B CC ?• QPDnoise:~10-7 V/[email protected]• 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
![Page 38: Shimoda Tomofumi Ando lab. seminar on 22 Dec. 2017 · 2C'B ' •We are developing an improved angular sensor •sensitivity of wave front sensor(WFS) can be improved by using auxiliary](https://reader036.vdocuments.mx/reader036/viewer/2022071107/5fe19722540b3079a170c70c/html5/thumbnails/38.jpg)
C C?B ? C F• 4�10-14 rad/[email protected]
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
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C C?B ? C F• 4�10-14 rad/[email protected]
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
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C == BI
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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
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B = CC C• measureorestimateangularfluctuationof(semi-)monolithicoptics
• calculatelength-anglecouplingindetailandthinkhowtoreduceit
front mid
feedbacktolength
coupletoangle
vibratelength-anglecoupling
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