Reports until 17:15, Friday 11 March 2016
H1 ISC (ISC)
hang.yu@LIGO.ORG - posted 17:15, Friday 11 March 2016 - last comment - 20:48, Friday 11 March 2016(26028)
An idea of measuring SRC gouy phase

This is a small idea of measuring SRC gouy phase, following the recent ASC discussion (25999). 

The basic idea is that the propagation phase of an upper sideband HOM and a lower one moves in opposite direction, whereas the gouy phase goes in the same way. This will naturally lead to an unbalanced pair of sideband HOMs, whose ratio will be a function of gouy phase. By inverting this function, we can have a measure of gouy phase based on the ratio of sb. HOMs (which is independent of any absolute calibration).

We thus built a numerical simulation of DRMI only, with BS intentially misaligned. We computed the ratio of |E_usb|/|E_lsb| at the AS port as a function of SRC gouy phase, assuming a good prior knowledge of PRC gouy phase, cavity length, etc. The result was attched. It seemed that the |E_{+9M_10}| / |E_{-9M_10}| could be a good probe of gouy phase. 

We might want to do an OMC scan when the IFO was available, with DRMI locked. We could intentionally misalign BS (or the two ITMs) which would pump some +-9MHz 10 modes into the SRC cavity. With some clever stablization (e.g. using AS 18 as an error signal?), we could deduce the ratio of |E_{+9M_10}| / |E_{-9M_10}| from the OMC scan result. Comparing it with simulation, we could find out srcl gouy phase.

 

P.S. From the simulation we saw that the +-45M HOMs were pretty well balanced. However, this did not contradict with the observation of 25999, because the error signal for DC is <+45_10| +45_00> + <-45_10| -45_00>, and the error signal for 90 is <+45_10| -45_00> + <-45_10 | +45_00>.  Thus for the 90 MHz and DC seeing a different error signal, we only need the +/- 45 MHz 10 modes to have different phases relative to the +/- 45 MHz 00 modes. 

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daniel.sigg@LIGO.ORG - 20:48, Friday 11 March 2016 (26032)

Looking at the OMC scan here, this looks like a tough measurement. lsb1 is very close the USB0, whereas usb0 and lsb0 are very small.