Small Schnupp asymmetry - SB2 resonant in both PRC and SRC

This page summarize the results of a Finesse simulation of the optical matrix, including all pick-off ports.

The five degrees of freedom are actuated using an extension of the present Virgo scheme:

• DARM and CARM to end mirrors
• PRCL to PRM only
• SRCL to SRM only
• MICH to BS, PRM, SRM according to the geometrical matrix

Herethe single demodulation scheme is used: all sidebands are generated by phasemodulation.

Demodulation phases have been optimized in order to maximize the following dofs in the phase signal:

• ASY_SB1: DARM
• ASY_SB2: DARM
• ASY_SB3: DARM
• SYM_SB1: PRCL
• SYM_SB2: PRCL
• SYM_SB3: CARM
• POBS_SB1: CARM
• POBS_SB2: SRCL
• POBS_SB3: nothing
• [X | Y]P_SB1: DARM
• [X | Y]P_SB2: DARM
• [X | Y]P_SB3: nothing
• PO[X | Y]_SB1: CARM
• PO[X | Y]_SB2: SRCL
• PO[X | Y]_SB3: CARM

The input file is available here.

Optical transfer functions

All transfer function plots can be found in a single PDF file here. Solid lines refer to phase signal, dotted one to quadrature.

DC optical matrix

The transfer function values at DC (to be precise at 10 mHz) are summarized in the following table. This must be considered with care, since the response of many signals is not at all flat with frequency.

Signal	DARM	CARM	PRCL	MICH	SRCL
ASY_SB1_P	+4.17e+10	-8.19e+07	+1.12e+05	+5.22e+07	-8.11e+01
ASY_SB1_Q	-4.87e+08	+9.57e+05	-1.59e+03	+1.34e+05	-4.75e+02
ASY_SB2_P	+6.53e+12	-1.28e+10	-8.56e+06	+8.18e+09	+7.43e+06
ASY_SB2_Q	+9.12e+09	-1.79e+07	+1.32e+05	+1.64e+07	-2.03e+05
ASY_SB3_P	-2.16e+09	+4.24e+06	+5.29e+03	-2.71e+06	+3.63e+00
ASY_SB3_Q	+3.28e+06	-6.45e+03	-3.60e+02	+3.30e+04	+7.68e+01
SYM_SB1_P	+9.60e+09	+4.08e+14	+6.27e+11	-2.08e+07	+8.20e+05
SYM_SB1_Q	+9.79e+06	+4.15e+11	+6.36e+08	+5.18e+06	+2.06e+04
SYM_SB2_P	-5.45e+09	-2.31e+14	-2.84e+11	-9.68e+08	-2.01e+10
SYM_SB2_Q	-2.72e+08	-1.21e+13	-1.46e+10	+1.08e+10	-1.44e+09
SYM_SB3_P	+9.77e+09	+4.15e+14	+5.20e+11	+1.42e+07	+1.48e+03
SYM_SB3_Q	-2.68e+06	-1.14e+11	-1.43e+08	-1.76e+04	-7.70e+01
POBS_SB1_P	-1.10e+10	-5.77e+11	+7.58e+08	-7.12e+05	+1.00e+04
POBS_SB1_Q	+1.29e+07	+6.72e+08	-2.80e+06	-1.64e+06	+7.08e+04
POBS_SB2_P	-4.16e+07	-2.18e+09	+1.56e+06	+1.45e+08	+2.81e+08
POBS_SB2_Q	-5.25e+09	-2.74e+11	-1.76e+08	+7.39e+07	-2.18e+05
POBS_SB3_P	-2.14e+08	-1.12e+10	-1.49e+07	+1.51e+05	+3.33e+03
POBS_SB3_Q	+3.44e+08	+1.80e+10	+2.07e+07	+1.05e+05	+2.00e+03
XP_SB1_P	+2.13e+07	+5.67e+10	-7.74e+07	+7.24e+04	-1.01e+03
XP_SB1_Q	-1.77e+04	-2.43e+07	-1.63e+05	-1.68e+05	+7.23e+03
XP_SB2_P	+1.01e+07	+2.69e+10	+1.80e+07	-7.60e+06	-7.56e+04
XP_SB2_Q	-2.20e+03	-1.23e+08	+2.21e+05	+1.48e+07	+2.87e+07
XP_SB3_P	+6.86e+03	+1.07e+08	-6.52e+04	+2.17e+04	+4.58e+02
XP_SB3_Q	+9.04e+05	+2.40e+09	+3.01e+06	+1.17e+02	-2.75e+01
YP_SB1_P	-1.85e+07	+5.67e+10	-7.74e+07	+1.91e+04	-1.08e+03
YP_SB1_Q	+1.82e+04	-2.94e+07	-1.56e+05	+1.62e+05	-7.28e+03
YP_SB2_P	+8.68e+06	-2.66e+10	-1.78e+07	-7.93e+06	-2.97e+05
YP_SB2_Q	+1.51e+06	-4.60e+09	-3.37e+06	-1.55e+07	+2.89e+07
YP_SB3_P	-1.50e+03	+1.07e+08	-6.55e+04	-2.19e+04	-4.64e+02
YP_SB3_Q	-7.85e+05	+2.40e+09	+3.00e+06	+6.89e+01	+2.77e+01
POX_SB1_P	-1.06e+10	+5.56e+11	-7.89e+08	+7.39e+05	-1.03e+04
POX_SB1_Q	-1.81e+06	+9.47e+07	-2.13e+06	-1.71e+06	+7.37e+04
POX_SB2_P	+3.58e+07	-1.87e+09	+1.80e+06	+1.51e+08	+2.93e+08
POX_SB2_Q	-5.05e+09	+2.64e+11	+1.84e+08	-7.71e+07	-3.91e+04
POX_SB3_P	-3.90e+08	+2.04e+10	+2.65e+07	+9.65e+03	-6.07e+01
POX_SB3_Q	-1.15e+05	+6.03e+06	+1.77e+06	-1.91e+05	-4.05e+03
POY_SB1_P	+1.07e+10	+5.57e+11	-7.90e+08	+1.94e+05	-1.09e+04
POY_SB1_Q	+8.66e+05	+4.51e+07	-2.06e+06	+1.65e+06	-7.43e+04
POY_SB2_P	+4.93e+07	+2.59e+09	-1.25e+06	-1.46e+08	+3.00e+08
POY_SB2_Q	+4.99e+09	+2.61e+11	+1.81e+08	+8.22e+07	+1.81e+05
POY_SB3_P	+3.90e+08	+2.04e+10	+2.64e+07	-8.07e+03	+6.04e+01
POY_SB3_Q	+1.84e+05	+9.59e+06	+1.77e+06	+1.93e+05	+4.09e+03