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Waveguide Mirrors: Coupling of Transverse intoLongitudinal Motion

Sean Leavey Bryan Barr Angus Bell Neil Gordon Stefan HildSabina Huttner John Macarthur Borja Sorazu Kenneth Strain

Institute for Gravitational ResearchUniversity of Glasgow

UK

August 2014

Thermal noise in the advanced detectors

101

102

103

104

10−24

10−23

10−22

Frequency [Hz]

Str

ain

[1/√

Hz]

(1) Quantum noise

(2) Seismic noise

(3) Gravity Gradients

(4) Suspension thermal noise

(5) Coating Brownian noise

(6) Coating Thermo−optic noise

(7) Substrate Brownian noise

(8) Excess Gas

(9) Total noise

(9)

(1)

(4)(3)

(2)

(8)

(6)

(7)

(5)

Sean Leavey Waveguide Mirrors: Coupling of Transverse into Longitudinal Motion 2 / 18

Future thermal noise reduction

Potential reductions to mirror thermal noise (note that this is Stefan Hild’spersonal opinion, and not something approved/agreed by the GW community)

Image taken from Stefan Hild’s talk given at GWADW, Elba, May 2013.


https://dcc.ligo.org/LIGO-G1300584

Grating Mirrors

Periodic, high refractive index structuredmaterial embedded on a low refractive indexsubstrate

Only need one coating with thickness oforder λ (or none, if using silicon)

Highly wavelength dependent


Grating MirrorsLittrow Gratings

Littrow gratings previouslyconsidered as arm cavityinput couplers

Suffer from additional noiseeffect due to transversemotion coupling arisingfrom many alloweddiffraction orders

Δx

ΔΦ ≠ 0

ΔΦ = 0


Grating MirrorsSidemotion Noise

𝚡

z

𝛂 𝛃m

𝛇A𝛇B

𝚫𝚡

Figure : Freise et al, 2007.

Extra phase shift

∆φ λ2π = ζA + ζB = ∆x (sinα + sinβm)

(Freise et al).

Is this a problem? Yes.

The effect has been known byshort-pulse laser physicists for yearsbut did not come to light ininterferometry physics until recently

In gratings, this effect canswamp savings in thermal noise


http://dx.doi.org/10.1088/1367-2630/9/12/433

http://dx.doi.org/10.1088/1367-2630/9/12/433

Grating MirrorsSolution to Sidemotion Noise

Can potentially fix this problem

Constrain grating period

Light is forced into a single reflectivediffraction order, the zeroeth

In transmission, only the zeroeth and firstdiffraction orders are allowed

Add waveguide below grating to allowwaveguide modes inside material

Light exists waveguide with a π phase shiftcompared to the zeroeth order light

Phase shift invariant of sidemotion

Constraint

λ

nH< grating period <

λ

nL

waveguide (nhigh)

substrate (nlow)

destructive interference

constructive interference

grating structure


Waveguide Grating Mirrors

Heinert et al calculation ofthermal noise in waveguidegrating mirrors

For the geometriesconsidered at 1064 nm androom temperature, no clearimprovement in thermalnoise

Cryogenic temperatures at1550 nm looks verydifferent, offering aBrownian thermal noisereduction of around afactor of 10

Figure : Room temperature 1064 nm silica/tantalabilayers vs cryogenic 1550 nm waveguide gratingmirror at 100Hz. Heinert et al, 2013.


http://dx.doi.org/10.1103/PhysRevD.88.042001

http://dx.doi.org/10.1103/PhysRevD.88.042001

Waveguide Grating Mirrors

Brown et al showed in simulations that sidemotion noise in waveguide gratingmirrors is reduced by 5 orders of magnitude over conventional gratings

Grating mirrors

Susceptible to sidemotion noise

Waveguide grating mirrors

Potentially cancel sidemotion noise

Need experimental verification of waveguide grating mirror sidemotioncancellation!


http://dx.doi.org/10.1364/OL.38.001844

Determining a Waveguide Mirror’s Sidemotion CouplingFabrication

Collaboration with Jenaand the AEI

Tantala grating layer ontop of a tantalawaveguide layer,mounted on a fusedsilica substrate

Parameter ValueDesign λ 1064 nmGrating depth 390 nmWaveguide depth 80 nmEtch stop depth 20 nmGrating period 688 nmFill factor 0.38

Figure : Friedrich et al, 2011.


http://dx.doi.org/10.1364/OE.19.014955

Determining a Waveguide Mirror’s Sidemotion CouplingExperimental Setup

We created a 10 mFabry-Perot cavity withwaveguide mirror as ITMand silica ETM

ETM rotated to producesidemotion

The cavity length changes(where sidemotion effectswould show up) were readout using an RF photodiode

Tank 2Tank 1

Tank 3

Tank 4

Tank 5

10m Fabry-Perot

cavity

Photodiode

CCDcamera

EOM

10 MHzsource

Mixer

70 Hzsource

Fast feedback

Frequencystabilisation

servo

Modecleaningfibre

Mid feedback(PZT)

Slow feedback(temperature)

1064 nmlaser

Dataacquisition

system

Coildriver


Determining a Waveguide Mirror’s Sidemotion CouplingUnderstanding Mirror Phase Effects

All (near-)planar mirrors have longitudinal phaseeffects during rotation:

Reflection from front surface on a mirror ofdepth d :

d

4θ2 (for small θ)

Displacement of light beam from centre:

xd tan θ ≈ xdθ

Current and proposed future gravitational wavedetectors can tolerate these noise sources as theyare lower than the dominating sources.

θ

d


Determining a Waveguide Mirror’s Sidemotion Coupling

Expect to see notch due to phase interaction between waveguide couplingand mirror rotationCan imply waveguide mirror coupling from known rotation effects

0.04 0.02 0.00 0.02 0.04Spot position on ETM [m]

10-11

10-10

10-9

10-8

Cav

ity le

ngth

cha

nge

[m]

ETM rotation effectTotal effect 1Total effect 2Total effect 3WGM coupling 1WGM coupling 2WGM coupling 3



Measurements taken with cavity aligned to 4 different spot positionsCan compare to simulation of coupling to determine couplingError on spot positions defines coupling level upper limit, i.e. worst fitthrough the data

0.015 0.010 0.005 0.000 0.005 0.010 0.015Spot position on ETM [m]

10-11

10-10

10-9

Cav

ity le

ngth

cha

nge

[m]

Coupling = 1/30000Coupling = 1/15000No couplingMeasurements



Model simulates effect of ‘beam smearing’ by assuming the spot moves in aGaussian distribution across the waveguide grating mirror

Cavity length signal (y-axis) scaling is arbitrary

Fitting the model to the data therefore not straightforward since fit must fitscaling, spot movement standard deviation and coupling level

A Bayesian approach is beneficial



Can marginalise over threeparameters:

sidemotion couplingsignal (y-axis) scaling‘spot movement’ standarddeviation

Markov-chain Monte-Carloalgorithm

Produces three probability densitydistributions

Coupling

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10−4

0

0.5

1

1.5

2

2.5x 10

4

Coupling

Pro

babili

ty D

ensity

Scaling

0 0.2 0.4 0.6 0.8 1

0

5

10

15

Scaling

Pro

babili

ty D

ensity

Std. Deviation

0 0.5 1 1.5

x 10−3

0

500

1000

1500

2000

2500

Standard Deviation

Pro

babili

ty D

ensity



Probability distribution of coupling level allows us to determine an upper limit.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10−4

0

0.5

1

1.5

2

2.5x 10

4

Coupling

Pro

ba

bili

ty D

en

sity

1 sigmacoupling = 1 : 24000





Standard Deviation Side-to-Longitudinal Coupling1 1 : 240002 1 : 90003 1 : 6000

Within 3 standard deviations, the coupling level is at worst 1 : 6000

This represents a longitudinal phase shift comparable to the effect due torotation at the centre (the d

4 θ2 effect).

Contrast this to the sidemotion coupling of the Littrow grating measured byBarr et al, which was of order 1 : 100.

Waveguide grating mirrors can still be considered for future interferometerapplications

End


http://dx.doi.org/10.1364/OL.36.002746

Extra Slides


Waveguide Reflectivity

−4 −2 0 2 4

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Refl

ecti

vit

y

Angle [deg]

Waveguide reflectivity angular dependence


The MichelsonsETM Masses

Figure : Courtesy of Jumpei Kato


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