Stefan Hild,

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Advanced Virgo optical designArm cavities with
adjustable Finesse

• Stefan Hild,
• Andreas Freise, Simon Chelkowski
• University of Birmingham
• Roland Schilling, Jerome Degallaix
• AEI Hannover
• Maddalena Mantovani
• EGO, Cascina
• March 2008, GEO-simulation WS

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Overview

• Requirements for Advanced Virgo arm cavities
  Etalon effect vs wedges.
• New concept for advanced GW detectors that
  combines wedges and etalon effect.
• Performance of an ideal etalon
• Example of optical system design Influence of
  etalon imperfections
• Numerical simulations
• Analytical approximations
• Influence onto alignment signals
• Higher-order mode buildup

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Motivation Input mirror without wedge

• Initial Virgo has no wedges in the input mirrors
• The etalon effect could be used for adjusting the
  cavity finesse (compensating for differential
  losses)
• If etalon effect is not controlled it might cause
  problems

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Motivation Input mirror featuring a wedge

• Used by initial LIGO
• Reflected beams from AR coating can be separated
  from main beam gt pick-off beams provide
  additional ports for generation of control
  signals.
• No etalon effect available.

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What to use for Advanced VIRGO?Etalon or Wedges
??

• For AdV possibility to adjust cavity finesse gets
  more important (higher cavity finesse,
  DC-readout).
• For AdV possibility to create more and better
  control signals seem desirable.

Is there a possibilty to have both for Advanced
Virgo ??
Fortunately YES !
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Advanced Virgo symmetric beam geometry

• Increase beam size at mirrors gt reduce thermal
  noise contribution of the test masses.
• Move beam waist away from input test mass

Is there still an etalon effect in the
(flat/curved) input mirror ?
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Etalon effectflat/flat vs curved/flat

• Flat/flat etalon
• Perfect overlap of wavefronts

• Fortunately mirror curvature of a few km is not
  so far from flat.
• Simulations show a reduced etalon effect in
  curved/flat input mirror is still present

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Etalon effectflat/flat vs curved/flat

• Flat/flat etalon
• Perfect overlap of wavefronts

Still we have to choose either wegde in input
mirror (Pick-off beams available) or no wedge in
input mirror (Etalon effect available)

• Curved/flat etalon
• Mismatch of wavefront curvature

• Fortunately mirror curvature of a few km are not
  so far flat.
• Simulations show a reduced etalon effect in
  curved/flat input mirror is still present

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Overview

• Requirements for Advanced Virgo arm cavities
  Etalon effect vs wedges.
• New concept for advanced GW detectors that
  combines wedges and etalon effect.
• Performance of an ideal etalon
• Example of optical system design Influence of
  etalon imperfections
• Numerical simulations
• Analytical approximations
• Influence onto alignment signals
• Higher order mode buildup

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IDEA Wedges at input mirrors and etalon effect
at end mirrors

• Wedge at input mirrors
• Allows for additional pick-off beams
• (Concentrate on compensating thermal lensing in
  input mirror)
• Use etalon effect at end test mass
• Replace AR-coating by a coating of about 10
  reflectivity.
• Ideally use a curved back surface (same curvature
  as front).
• End mirror behaves similarly to flat/flat etalon.

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Now lets have a lookat numbers for Advanced
Virgo
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Overview

• Requirements for Advanced Virgo arm cavities
  Etalon effect vs wedges.
• New concept for advanced GW detectors that
  combines wedges and etalon effect.
• Performance of an ideal etalon
• Example of optical system design Influence of
  etalon imperfections
• Numerical simulations
• Analytical approximations
• Influence onto alignment signals
• Higher order mode buildup

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Starting with a single AdV arm cavity

• Using a single AdV arm cavity (no IFO).
• Parameters used
• IM trans 0.007
• IM loss 50 ppm
• EM trans 50 ppm
• EM loss 50 ppm
• AR coatings 0ppm
• IM curvature 1910m
• EM curvature 1910m
• Input 1W
• Figure of merrit intra cavity power, i.e. loss
  compensation.

Parameters taken from these 2 documents
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Influence of losses inside the cavity

• Imperfection of optics (surface coatings) might
  cause different losses in the arm cavities
  differential losses.

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End mirror as curved etalon (optimal solution)

• Simulation done with Finesse.
• Back surface of end mirror curved (1910m).
• AR coating replaced by coating of 10 or 20
  reflectivity.
• R0.1 allows adjustment range of 10W (?65ppm)
• R0.2 allows adjustment range of 16W (?95ppm)

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Optimal solution curved Etalon

• Alternative figures of merrit
• Transmittance of end mirror (etalon)
• Finesse of arm cavity

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Etalon changes optical phase

• When changing the etalon tuning the optical-phase
  changes as well. (noise!)
• The two etalon surfaces build a compound mirror,
  whose apparent position depends on the etalon
  tuning.

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Requirement for temperature stability of etalon
substrate

• Can calculate require-ment for temperature
  stability for Advanced Virgo etalon
• Using worst case 1.22pm/deg
• dn/dT 1.09e-5/K
• Substrate thickness 10cm

Example _at_100Hz 4e-11K/sqrt(Hz)
This requirement is still 2 orders of magnitude
above (safer) than temperature stability required
from dL/dT of the substrates.
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Everything fine as long Etalon matches the
specs but what if not ??gt need to check !!
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Overview

• Requirements for Advanced Virgo arm cavities
  Etalon effect vs wedges.
• New concept for advanced GW detectors that
  combines wedges and etalon effect.
• Performance of an ideal etalon
• Example of optical system design Influence of
  etalon imperfections
• Numerical simulations
• Analytical approximations
• Influence onto alignment signals
• Higher order mode buildup

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Optical design Check system integrity for
deviations from specs

• A deviation in the reflectivity of the etalon
  coating
• Only changes tuning range (no problem)

• A deviation in the relative misalignment
  (parallelism) and relative curvature of the two
  etalon surfaces
• Imperfect wave front overlap
• Reduces tuning range
• Beam shape distortions

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FFT-simulation of a non-perfect etalon

• Using R. Schillings WaveProp, (http//www.rzg.mpg
  .de/ros/WaveProp/)
• Parameters
• Field 256x256
• Computing 3000 roundtrips
• End mirror front
• 50ppm transmission
• R_c 1910m
• End mirror back
• Varying three parameters
• Reflectance
• Misalignment (parallelism)
• Curvature

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Analytic Approximations using Higher-Order Modes

• Reflection at a (slightly) misaligned component
  can be characterised by scattering into higher
  order TEM modes
• This model is valid for misalignments below half
  the diffraction angle (paraxial approximation)
• The amplitude in the outgoing fields is given by
  coupling coefficients knmnm

• For small misalignments the coupling coefficients
  knmnm can be approximated. The amount of light
  which remains in a TEM00 mode is given by
• (q is the Gaussian beam parameter of the
  light at the mirror)

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Misalignment of etalon back surface

• Strong influence of relative alignment of etalon
  surfaces.
• Question What accuracy can state of the art
  manufacturing provide?
• Example Initial Virgo input mirrors (flat/flat)
  1urad

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Curvature deviation of etalon back surface

• Curvature mismatch has only moderate influence to
  tuning range of the etalon.

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!!! KEEP IN MIND !!!For this example

• Numerical simulations and analytical
  approximation
• Can used to understand optics
• Are used to derive specifications
• Both do not necessarily represent the reality in
  all cases
• Optimal solution (if feasible)
• Test concept in a prototype experiment

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Investigating alignment signals for Advanced
Virgo with etalons

• Aim Checking influence of perfect and
  non-perfect etalon to alignment signals
• Performed FINESSE simulation
• Investigating Ward and Anderson techniques

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Alignment signals for perfect etalon
Signal in reflection Ward technique
Signal in transmission Anderson technique
10 variation
150 variation
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Non perfect etalon TEM01-buildup in the arm
cavity

• Misalignment of etalon back surface induces 1st
  order modes inside the arm cavities.
• TEM01 from etalon imperfection is negligible
  compared to misalignment of the whole end test
  mass.

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Summary

• Advanced Virgo CAN feature wedges in the input
  mirrors AND use the etalon effect at the end
  mirrors.
• Proposed concept allows us to build arm cavities
  with adjustable losses.
• A curved/curved etalon would be ideal.
• Evaluated and quantified the influence of etalon
  imperfections using numerical simulations and
  analytical approximations (tuning range,
  alignment signals)

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Outlook

• Potential issues to be investigated
• Need a control system for etalon tuning (error
  signal actuator).
• Need a value for the expected differential losses
  in Advanced Virgo in order to choose the
  reflectivity of the etalon.

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