Documentation

More details can be found in the following notes:

G. Vajente - Note on signal recycling I: Field equations VIR-030B-08

G. Vajente - Note on signal recycling II: Lengths and modulations VIR-032A-08

G. Vajente - Possible sets of lengths and modulation frequencies for Advanced Virgo  VIR-049A-08

Basic requirements

The requirements on lengths and modulation frequencies are mainly linked to the necessity of decoupling as much as possible the signal recycling cavity length SRCL degree of freedom from the other ones, both during lock acquisition and in steady state.

Three modulation frequencies are needed, corresponding to three pairs of RF sidebands. The requirements (assuming the carrier on resonance and dark fringe) are:

• SB1: should be reflected by the arm cavities, resonant inside the power recycling cavity and not transmitted to the signal recycling one
• SB2: should be reflected by the arm cavities, transmitted to the signal recycling cavity and resonant there-in for zero detuning (resonant signal extraction RSE regime)
• SB3: should be reflected by the entire interferometer, or in other words not resonant inside the power recycling cavity

The first requirement (SB1 not transmitted to SRC) allows a simplification of the lock acquisition procedure:

• Initially the signal recycling mirror (SRM) is largely mis-aligned (hundreds of microradians). The control reduces to a power-recycled interferometer, which can be brought to dark fringe (without DC offset) with a relatively simple extension of the variable finesse technique used in Virgo
• The power recycled interferometer must be controlled using signals extracted from carrier, SB1 and SB3. When in dark fringe, all these fields are not present with relevant amplitude inside the SRC
• The SRM can be re-aligned without perturbing the lock of the power recycled ITF. Therefore the SRC can be locked using a signal extracted from SB2 (for example single demodulation at the beam splitter pick-off port)

Three possible sets of parameters have been selected to meet the above requirements:

• Small Schnupp asymmetry - SB2 resonant in both PRC and SRC
  

• Small Schnupp asymmetry - SB2 resonant only in SRC
  

• Large Schnupp asymmetry