advanced virgo optical design: arm cavities with adjustable finesse

Stefan Hild, Andreas Freise, Simon ChelkowskiUniversity of Birmingham

Roland Schilling, Jerome DegallaixAEI Hannover

Maddalena MantovaniEGO, Cascina

March 2008, GEO-simulation WS

Advanced Virgo optical design:Arm cavities with adjustable Finesse

Stefan Hild GEO Simulation WS, March 2008 Slide 2

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


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.


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 ??


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 ?


Etalon effect:flat/flat vs curved/flat

Flat/flat etalon: Perfect overlap of wavefronts

Curved/flat etalon: Mismatch of wavefront curvature 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


Etalon effect:flat/flat vs curved/flat

Flat/flat etalon: Perfect overlap of wavefronts

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 presentStill

we have to choose:

either wegde in input m

irror (P

ick-off beams available)

or no wedge in input mirro

r (Etalon effect available)


Overview




Example of optical system design: Influence of etalon imperfections Numerical simulations Analytical approximations Influence onto alignment signals Higher order mode buildup


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.


Now let’s have a look

at numbers for

Advanced Virgo


Overview






Starting with a single AdV arm cavity

Using a single AdV arm cavity (no IFO).

Parameters used:IM trans = 0.007IM loss = 50 ppmEM trans = 50 ppmEM loss = 50 ppmAR coatings = 0ppmIM curvature = 1910mEM curvature = 1910mInput = 1W

Figure of merrit = intra cavity power, i.e. loss compensation.

Parameters taken from these 2 documents:


Influence of losses inside the cavity

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

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.


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)


Optimal solution: curved Etalon

Alternative 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 !!


Overview






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/)

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.


!!! 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


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


Alignment signals for perfect etalon

Sig

nal i

n tr

ansm

issi

on:

An

der

son

tec

hniq

ue

Sig

nal i

n re

flect

ion:

War

d t

echn

ique

150 %variation

10 %variation


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.


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)


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 …


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advanced virgo optical design: arm cavities with adjustable finesse

Documents

reduced etalon effect

etalon effect vs wedges

input mirroruse etalon

input mirrorsthe etalon

presentetalon effect

curvedflat input mirror

flatcurved input mirror

advanced virgo arm cavities