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Advanced Virgo optical design: Arm 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. Overview.

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advanced virgo optical design arm cavities with adjustable finesse

Advanced Virgo optical design:Arm 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

overview
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

GEO Simulation WS, March 2008

motivation input mirror without wedge
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

GEO Simulation WS, March 2008

motivation input mirror featuring a wedge
Motivation: Input mirror featuring a wedge
  • Used by initial LIGO
  • Reflected beams from AR coating can be separated from main beam => pick-off beams provide additional ports for generation of control signals.
  • No etalon effect available.

GEO Simulation WS, March 2008

what to use for advanced virgo etalon or wedges
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 !

GEO Simulation WS, March 2008

advanced virgo symmetric beam geometry
Advanced Virgo: symmetric beam geometry
  • Increase beam size at mirrors => 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 ?

GEO Simulation WS, March 2008

etalon effect flat flat vs curved flat

Curved/flat etalon:

    • Mismatch of wavefront curvature
Etalon effect:flat/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

GEO Simulation WS, March 2008

etalon effect flat flat vs curved flat1
Etalon effect:flat/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

GEO Simulation WS, March 2008

overview1
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

GEO Simulation WS, March 2008

idea wedges at input mirrors and etalon effect at end mirrors
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.

GEO Simulation WS, March 2008

overview2
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

GEO Simulation WS, March 2008

starting with a single adv arm cavity
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:

GEO Simulation WS, March 2008

influence of losses inside the cavity

What are the expected differential losses of AdV ? 5ppm? 50ppm?

  • A differential loss of 15ppm corresponds to a change of 2W intra cavity power in this example.
Influence of losses inside the cavity
  • Imperfection of optics (surface + coatings) might cause different losses in the arm cavities := differential losses.

GEO Simulation WS, March 2008

end mirror as curved etalon optimal solution
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.
  • R=0.1 allows adjustment range of 10W (65ppm)
  • R=0.2 allows adjustment range of 16W (95ppm)

GEO Simulation WS, March 2008

optimal solution curved etalon
Optimal solution: curved Etalon
  • Alternative figures of merrit:
    • Transmittance of end mirror (etalon)
    • Finesse of arm cavity

GEO Simulation WS, March 2008

etalon changes optical phase
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.

GEO Simulation WS, March 2008

requirement for temperature stability of etalon substrate
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 @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.

GEO Simulation WS, March 2008

everything fine as long etalon matches the specs but what if not need to check
Everything fine as long Etalon matches the specs…… but what if not ??=> need to check !!

GEO Simulation WS, March 2008

overview3
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

GEO Simulation WS, March 2008

optical design check system integrity for deviations from specs
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 …

GEO Simulation WS, March 2008

fft simulation of a non perfect etalon
FFT-simulation of a non-perfect etalon
  • Using R. Schilling’s 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

GEO Simulation WS, March 2008

analytic approximations using higher order modes
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)

GEO Simulation WS, March 2008

misalignment of etalon back surface
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

GEO Simulation WS, March 2008

curvature deviation of etalon back surface
Curvature deviation of etalon back surface
  • Curvature mismatch has only moderate influence to tuning range of the etalon.

GEO Simulation WS, March 2008

keep in mind for this example
!!! 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

GEO Simulation WS, March 2008

investigating alignment signals for advanced virgo with etalons
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

GEO Simulation WS, March 2008

alignment signals for perfect etalon
Alignment signals for perfect etalon

Signal in reflection:

Ward technique

Signal in transmission:

Anderson technique

10 %

variation

150 %

variation

GEO Simulation WS, March 2008

non perfect etalon tem01 buildup in the arm cavity
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.

GEO Simulation WS, March 2008

summary
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)

GEO Simulation WS, March 2008

outlook

More details can soon be found in …

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.

GEO Simulation WS, March 2008

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GEO Simulation WS, March 2008