3f Locking for the 2009 40m Upgrade
Introduction
3f locking usually refers to a technique to lock an optical cavity of the interferometer which involves the error signal obtained by demodulating the signal from the reflection photodiode at 3 times the modulation frequency of the sideband.
In the classical Pound-Drever-Hall locking technique the signal from the reflection photodiode are demodulated at the same frequency as that used to generate the sidebands. In that way the obtained signals are proportional to the amplitude of the beat between the first order sidebands and the carrier.
--put here picture illustrating how the PDH signals originate--
In the 3f locking, the main component extracted by the triple frequency demodulation is proportional to the beating between the first and the second order sidebands.
--put here picture illustrating how the 3f signals originate--
3f signals to lock the central part of the interferometer
In the old configuration of the 40m (2001-2009), the lock acquisition of the interferometer starts by locking the Dual Recycling Michelson (DRM) with the arm cavities out of resonance. At this stage the classical PDH error signals are used. Then to complete the locking of the full IFO, the CARM offset is reduced and the arms are slowly brought into resonance.
The process affects the carrier light and it cannot provide anymore suitable error signals to lock the central part of the IFO. Other signals become necessary if the short cavities are to be locked.
Before the CARM offset is completely reduced, the controls signals for the central part are replaced with the double demodulation signals, which are less affected by the carrier state in the arms.
However suitable double demodulation signals are available only in the IFO narrow-band configuration, that is with a detuned SRM. For the broadband configuration, as it is going to be used for the 40m Upgrade and in Advanced LIGO, the 3f signals are planned to be the alternative.
3f locking scheme for the 40m upgraded interferometer
--inserthere simulated sensing matrix and plots--