ET filter cavities for third generation detectors

Albert-Einstein-InstituteHannover

ET filter cavitiesfor third generation detectors

Keiko KokeyamaAndre Thüring


Contents

• Introduction of Filter cavities for ET

Part1. Filter-cavity-length requirement

- Frequency dependant squeezing

- Filter cavity length and the resulting squeezing level

Part2. Layout requirement from the scattering light analysis

• SummaryK. Kokeyama and Andre Thüring 17 May 2010, GWADW


Contents








Design sensitivity for ET-C

Lets focus on the ET-C LF

part.

ET-C : Xylophone consists ofET-LF and ET-HF

ET-C LF• Low frequency part of the xylophone• Detuned RSE• Cryogenic• Silicon test mass & 1550nm laser• HG00 mode

1/20

S. Hild et al. CQG 27 (2010) 015003

K. Kokeyama and Andre Thüring 17 May 2010, GWADW


To reach the targeted sensitivity, we have to utilize squeezed states of light

We dream of a broadband

QN-reduction by 10dB

A broadband quantum noise reduction requires the frequency dependent squeezing,

therefore filter cavities are necessary

2/20K. Kokeyama and Andre Thüring 17 May 2010, GWADW


Contents








Contents








Quantum noise in a Michelson interferometer

X1

X2

X1

X2

Quantum noise reduction with squeezed light

X1

X2

Filter cavities can optimize the squessing angles



ET-C LF bases on detuned signal-recycling

Optical spring resonance

Optical resonance

Two filter cavities are required for an optimum generation of frequency dependent squeezing

In this talk we consider the two input filter

cavities



Contents








Requirements defined by the interferometer set-up:

The bandwidths and detunings of the filter cavities

What we can choose

The lengths of the filter cavities

Limitations

Infrastructure, optical loss (e.g. scattering) , phase noise, ...

...And the optical layout (Part2)



Degrading of squeezing due to optical loss

A cavity reflectance R<1 means loss . The degrading of squeezing is then frequency dependent

At every open (lossy) port vacuum noise couples in

couplingmirror



The impact of intra-cavity loss

There exists a lower limit Lmin. For L < Lmin the filter cavity is under-coupled and the compensation of the phase-space rotation fails!

The filter‘s coupling mirror reflectance Rc needs to be chosen with respect to

1. the required bandwidth gaccounting for

2. the round-trip loss lRT 3. a given length L



The impact of shortening the cavity length

Example for ET-C LFdetuning = 7.1 Hz 100 ppm round-trip loss,bandwidth = 2.1 Hz

If L < Lmin ~ 1136 m the filter is under-coupled and the filtering does not work

For L < 568m Rc needs to be >1

The filter cavity must be as long as possible for ET-LF



Narrow bandwidths filter are more challenging

Assumptions:L = 10 km, 100 ppm round-trip loss,Detuning = 2x bandwidth

Filter cavities with a bandwidth greater than 10 Hz are comparatively easy to realize



Exemplary considerations for ET-C LF

Filter I:g = 2.1 Hzfres = 7.1 Hz

Filter II:g = 12.4 Hzfres = 25.1 Hz

Filter I:L = 2 kmF = 17845Rc = 99.9748%

Filter I:L = 5 kmF = 7138Rc = 99.9220%

Filter I:L = 10 kmF = 3569Rc = 99.8341%

Filter II:L = 2 kmF = 3022Rc = 99.8023%

Filter II:L = 5 kmF = 1209Rc = 99.4915%

Filter II:L = 10 kmF = 604Rc = 98.9757%

15dB squeezing100ppm RT - loss7% propagation loss



Contents








Stray light analysis for four designs

Which design is suitable for ET cavitiesfrom the point of view of the loss

due to stray lights?

Triangular - ConventionalLinear

Rectangular Bow-tie



Scattering Angle and Fields

TriangularLinear

Rectangular Bow-tie



# f0 f Scat field Scat power

Counter-propagating

1 Small 0 Rigorous field Large

2 Large 0 Rigorous field Small

3 Small Gauss tail small?

4 Large Spherical wave approx.

Small

Normal-propagating



Small

Scattering Field Category




Counter-propagating





Small

Normal-propagating



Small




#1

Counter-Propagating, Small f0, f~0

C1 =A<ETEM00•m(x,y) •E*TEM00>

Coupling factor




Counter-propagating





Small

Normal-propagating



Small




#2

Counter-Propagating, Large f0, f=0

Coupling factor

C2= A<ETEM00•m(x,y) •E*TEM00>




Counter-propagating





Small

Normal-propagating



Small




#3Counter-Propagating,Large f (at 2nd scat)

C3=<ETEM00tail •E*TEM00> C4 =<ESphe •E*TEM00>

#4Counter-Propagating,Small f (at 2nd scat)




Counter-propagating





Small

Normal-propagating



Small




#5Normal-Propagating,Large f (at 2nd scat)

#6Normal-Propagating,Small f (at 2nd scat)

C5=<ETEM00tail •E*#TEM00> C6 =<ESphe •E*#

TEM00>



K. Kokeyama and Andre Thüring 17 May 2010, GWADW

Liner Cavity

TriangularCavity

Rectangular Cavity

Bow-tie Cavity

#1 (big scat) 0 A•C1 0 4A•C1

#2 (small scat) 0 2A•C2 4A•C2 0

#3 (Gauss tail. cp) 0 0 2•C3 Negligible

#4 (sphe. cp) 0 0 2•C4 Negligible

#5 (Gauss tail. np) 0 0 2•C5 Negligible

#6 (sphe, np) 0 0 2•C6 Negligible

Total

-----=

18/20


Liner Cavity

TriangularCavity

Rectangular Cavity

Bow-tie Cavity

#1 (big scat) 0 A•C1 0 4A•C1

#2 (small scat) 0 2A•C2 4A•C2 0

#3 (Gauss tail. cp) 0 0 2•C3 Negligible

#4 (sphe. cp) 0 0 2•C4 Negligible

#5 (Gauss tail. np) 0 0 2•C5 Negligible

#6 (sphe, np) 0 0 2•C6 Negligible

Total

Preliminary Results



• We have shown that the requirement of the filter-cavity length which can accomplish the necessary level of squeezing

• We have evaluated the amount of scattered light from the geometry alone to select the cavity geometries for arm and filter cavities for ET.

• As a next step coupling factors between each fields and the main beam should be calculated quantitatively so that total loss and coupling can be estimated.

• At the same time the cavity geometries will be compared with respect to astigmatism, length & alignment control method

Summary


ET filter cavities for third generation detectors

Documents

et part1

frequency dependent

lisa et filter cavitiesfor

ethf etc lf low frequency

layout requirement

etlf yellow

etclets focus

socalled etc design