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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
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