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

2. A bit of nomenclature LASER SRM ITM ETM PRM E in0 E sr E in1 E in2 E circ1 E circ2 E sig1 E sig2 E re1 E re2 EsEs E ar EaEa E out 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

3. 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 cavity With very high power circulating  possibly relaxing the power on PRC SRM ITM PRM E in0 E out BS ANTIRESONANT HIGH FINESSE  Adv = 5 ms  P = 0.65 ms 800 KW (Adv Ligo Estimation)

4. 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 Virgo from Laval/Marque/Punturo simulations and measurements  l = 1  m/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

5. Loss of SNR due to ITM common defocus Loss of SNR as a function Of Guoy phase for common Defocus. The Huge SNR loss happens when the Guoy phase of HOMs cancels the SRC detuning so that the HOMs of both the carrier and the signal light are resonant in The SRC while the fundamental modes are detuned The loss is proportional to the square of mirror’s aberrations Yi Pan_2006

6. Power Loss in Long cavities and Power Gain in SRC for non degenerate SRC Loss of power (KW) in long cavities As a function of Guoy phase The power inside ideal cavity is 835 KW The left side part of the figure Correspond to degenerate case. The Power loss is about 3 KW Power Gain in SRC: the carrier Power rises from 1 W to about 7 W This power is spread on varius modes

7. Rayleigh and Guoy phase of VIRGO present cavities The Guoy phase for the cavity eigenmode is: If the curvature of mirrors are R1 and R2 The Guoy phase of the Hermite-Gauss fundamental modes is: Rayleigh Lenght R ETM = 3580 m (North End) R ITM = 74 Km (North Input) R PRM = flat Z 0 = 120 m (Close to zero) L ARM = 3 Km L prc = 12 m

8. Degeneracy of present cavities 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 fall Inside the resonance peak of TM00

9. Proposals for remove PRC and SRC degeneracies Reduce beam size and/or increase path length ITM ETM LASER PRM E circ1 E sig1 BS E out 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

10. K-metric SRC cavity ITM ETM LASER PRM E circ1 E sig1 BS E out 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

11. 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