Degeneracy for power-recycling and signal recycling cavities in Advanced Virgo

A bit of nomenclature

LASER

SRM

ITM ITM

ETM

ETM

PRM

Ein0Esr

Ein1

Ein2 Ecirc1

Ecirc2

Esig1

Esig2

Ere1

Ere2

Es

Ear

Ea

Eout

BS

SRC = Signal Recycling Cavity

PRC = Power Recycling Cavity

The signal recycling cavity is defined by the recycling mirror (SRM) and the Input mirrors (ITM) – the SRC lenght is the mean distance SRM to ITMs

VIRGO SIGNAL RECYCLING SCHEME

• Later, by changing the SMR parameters (reflectivity and position) the detector could operate

in narrowband configuration to optimize the search for GWs in specific frequency regions.

We have still not written in Virgo White Paper what will be the signal recycling scheme

LIGO will use the (broadband) resonant-signal-recycling (RSE): the SRC is anti-resonant for GW signal the GW signal is extracted from the arm cavities thus lowering the bandwidth for GW signal allow to use high finesse arm cavityWith very high power circulating possibly relaxing the power on PRC

SRM

ITM

PRM

Ein0

Eout

BS

ANTIRESONANT

HIGH FINESSEAdv = 5 ms

P= 0.65 ms

800 KW(Adv Ligo Estimation)

Some constraints on High Order Modes

0) At the present we do not have simulations on Signal Recycled ITF Laborious to implement SRC in DarkF M. Laval Finesse: possible to simulate SRC

Present estimation in Virgofrom Laval/Marque/Punturo simulationsand measurements

l = 1m/Watt-Absorbed

l = 75 nm (North ITM – Virgo)

1) K. Thorne - geometric optics

peak-to-valley in SRC < 2nm in broadband and <1nm in narrowband configuration to reduce the contribution of mode mixing to less than 1% of SNR

2) Yi Pan – static simulation of high order modes propagation (confirms Thorne results): ITM radius error of 5 m 2 nm peak-to-valle produce a

4% loss in SNR if common and 0.4% if differential

Loss of SNR due to ITM common defocus

Loss of SNR as a functionOf Guoy phase for commonDefocus.

The Huge SNR loss happens when the Guoy phase of HOMs cancels the SRCdetuning so that the HOMs of both the carrier and the signal light are resonant inThe SRC while the fundamental modes are detuned

The loss is proportional to the square of mirror’s aberrations

Yi Pan_2006

Power Loss in Long cavities and Power Gain in SRC for non degenerate SRC

Loss of power (KW) in long cavitiesAs a function of Guoy phaseThe power inside ideal cavity is 835 KWThe left side part of the figureCorrespond to degenerate case. The Power loss is about 3 KW

Power Gain in SRC: the carrierPower rises from 1 W to about 7 WThis power is spread on varius modes

Rayleigh and Guoy phase of VIRGO present cavities

?PRC

41.1ARM

The Guoy phase for the cavity eigenmode is:

If the curvature of mirrors areR1 and R2

The Guoy phase of the Hermite-Gauss fundamental modes is:

Rayleigh Lenght

RETM = 3580 m (North End)

RITM = 74 Km (North Input)

RPRM = flat

Z0 = 120 m

(Close to zero)

LARM = 3 Km

Lprc = 12 m

Degeneracy of present cavities

ARMARM fkHzL

c 2.18

2

kHzfL

cPRCPRC

PRC

200(?)2

The arm cavities are well non defenerate

Power recycling is degenerate because even if the Guoy phase is eventually non zero - it is sufficiently small to let high order modes frequencies fallInside the resonance peak of TM00

Proposals for remove PRC and SRC degeneracies• Reduce beam size and/or increase path length

ITM ITM

ETM

ETM

LASER

PRM

Ecirc1

Esig1BS

Eout

Not feasible a single lens to obtain a

reasonable Guoy phase the beam must be

focused to a waist size of few tens of

microns with a too high power density of 10GW/m2

-Multiple Optics(reflective): insert injection and detection telescopes inside the ITF

K-metric SRC cavity

ITM ITM

ETM

ETM

LASER

PRM

Ecirc1

Esig1BS

Eout

SRC: 3 Km long SRC cavity this would allow to collect power in both signal sidebands and increase the SNR by a factor 2

SRC2

Conclusion

• Degenerates PRC and SRC Interferometers seems to be more vulnerable to high input power

• Short cavities with telescope inserted could be a solution• Long SRC cavity could be also of theoretical interest • Simulations/theoretical investigations are a bit lacking in Virgo in this

moment