Transcript Advanced Virgo: Arm cavities with adjustable finesse

Update on the Advanced Virgo Arm
Cavity Design
Stefan Hild,
Andreas Freise, Simon Chelkowski
University of Birmingham
Roland Schilling, Jerome Degallaix
AEI Hannover
Maddalena Mantovani
EGO, Cascina
April 2008, Virgo R&D Review
Overview
 At January’s Virgo week we
presented a new concept for arm
cavity design of advanced Virgo
(www.sr.bham.ac.uk/~hild/presentations/etalon_vs_wedges.ppt)
 The new concept combines
advantages of wedges and etalon
effect.
 What is new since last talk?
 Numerical simulations and Analytical
approximations
 Quantitative evaluation of etalon
imperfection
 Temperature stability requirement
 Influence onto alignment signals
See Maddalenas talks
 Higher order mode buildup
Stefan Hild
VIRGO R&D review, April 2008
Slide 2
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
Stefan Hild
VIRGO R&D review, April 2008
Slide 3
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.
Stefan Hild
VIRGO R&D review, April 2008
Slide 4
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.
Stefan Hild
VIRGO R&D review, April 2008
Slide 5
What can we gain by using the
proposed arm cavity design?
 Experience from current detectors: Reflectivities of coatings
accurate, but unexplained losses.
 We concentrate on the differential losses => Optimal
solution: adjusting end mirror transmittance. (Changing the input
mirror would also change the amount of directly reflected light)
 Several technical noises (such as laser frequency and laser
intensity noise) couple proportional to the asymmetry of
the arms.
 Illustrating example:
 30 ppm differential losses
 Using the etalon effect it should be possible to reduce the
differential losses to 1 ppm
 Reduce the noise coupling by a factor of 30 !!
Stefan Hild
VIRGO R&D review, April 2008
Slide 6
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
Parameters taken from these 2 documents:
 Figure of merrits = intra cavity
power or loss compensation or
cavity finesse or transmittance
of EM.
Stefan Hild
VIRGO R&D review, April 2008
Slide 7
Optimal solution: curved Etalon
 Examples of figures of merrit:
 Transmittance of end mirror (etalon)
 Finesse of arm cavity
Stefan Hild
VIRGO R&D review, April 2008
Slide 8
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.
Stefan Hild
VIRGO R&D review, April 2008
Slide 9
Requirement for temperature
stability of etalon substrate
 Can calculate requirement 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.
Stefan Hild
VIRGO R&D review, April 2008
Slide 10
Stefan Hild
VIRGO R&D review, April 2008
Slide 11
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 …
Stefan Hild
VIRGO R&D review, April 2008
Slide 12
FFT-simulation of a nonperfect etalon
 Using R. Schilling’s WaveProp,
(http://www.rzg.mpg.de/~ros/WaveProp/)
 Cross checking with DarkF.
 Parameters:
 Field: 256x256
 Computing 3000 roundtrips
 End mirror front:
 50ppm transmission
 R_c = 1910m
 End mirror back:
 Varying three parameters
 Reflectance
 Misalignment (parallelism)
 Curvature
Stefan Hild
VIRGO R&D review, April 2008
Slide 13
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)
Stefan Hild
VIRGO R&D review, April 2008
Slide 14
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
Stefan Hild
VIRGO R&D review, April 2008
Slide 15
Curvature deviation of etalon back
surface
 Curvature mismatch has only moderate influence to tuning
range of the etalon.
Stefan Hild
VIRGO R&D review, April 2008
Slide 16
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.
 Investigations of influence onto alignment signals and higher
order mode buildup: See Maddalena’s talk.
Stefan Hild
VIRGO R&D review, April 2008
Slide 17
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.
More details can soon
be found in …
Stefan Hild
VIRGO R&D review, April 2008
Slide 18
END
Stefan Hild
VIRGO R&D review, April 2008
Slide 19
Common Mode Rejection Factor
Finesse assymetry
Differential losses
Flaminio et al, VIR-NOT-LAP-1390-313
 Finesse and losses are coupled.
 Probably the differential losses will be the driving element.
Stefan Hild
VIRGO R&D review, April 2008
Slide 20