update on the advanced virgo arm cavity design

Stefan Hild, Andreas Freise, Simon ChelkowskiUniversity of Birmingham

Roland Schilling, Jerome DegallaixAEI Hannover

Maddalena MantovaniEGO, Cascina

April 2008, Virgo R&D Review

Update on the Advanced Virgo Arm Cavity Design

Stefan Hild VIRGO R&D review, April 2008 Slide 2

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 Higher order mode buildup See Maddalenas talks


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


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.


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.


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 !!


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 merrits = intra cavity power or loss compensation or cavity finesse or transmittance of EM.

Parameters taken from these 2 documents:


Optimal solution: curved Etalon

Examples of figures of merrit: Transmittance of end mirror (etalon) Finesse of arm cavity


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.


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.


Everything fine as long

Etalon matches the

specs…

… but what if not ??

=> need to check !!


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 …


FFT-simulation of a non-perfect 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

http://www.rzg.mpg.de/~ros/WaveProp/





Analytic Approximations using Higher-Order Modes

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)

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


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


Curvature deviation of etalon back surface

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


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.


OutlookPotential 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 …


E N D


Common Mode Rejection Factor

Finesse and losses are coupled. Probably the differential losses will be the driving element.

Flaminio et al, VIR-NOT-LAP-1390-313

Finesse assymetry Differential losses

update on the advanced virgo arm cavity design

Documents

etalon tuning

input mirroruse etalon

etalon surfaces

input mirrorsthe etalon

flatflat etalon

etalon effect available

end mirror transmittance

proposed arm cavity