Absolute Length Measurement

The auxiliary source is an additional NPRO laser that we have in the lab.
By means of an auxiliary laser beam it is possible to perform a particular set of experiments based on the interference with the main PSL beam.
One of these experiments that has been going on at the 40m is the Absolute Length Measurement (AbsL), by which it is possible to obtain information about the IFO's cavities such as length, g-factor, finesse and metrology of the optics.

Overview

It is possible to measure the absolute length of the interferometer's optical cavities by means of an auxiliary laser source.
While the cavity is held locked to the main PSL beam, a secondary beam at about the same frequency of the first is also injected. If both beams are resonant in the cavity, that is, their frequencies are multiple of the cavity Free Spectral Range (FSR), then they both get transmitted. There the two beams interfere and beat, resulting in a field with an amplitude modulated at a frequency equal to the difference of the two laser frequencies. The beat, which is observable on a photodetector, will have a frequency also multiple of the FSR.
The technique becomes a way to measure the cavity FSR and, from that, indirectly, the cavity optical length.

For the two beams to interfere and originate a beat at a fixed frequency, the relative frequency of the two lasers has to be constant. For this reason, part of the experiment is dedicated to lock the two lasers's frequencies to each other by means of a Phase Locked Loop (PLL) servo.

By a method similar to that used to measure the cavity FSR, it is also possible to measure the cavity Transverse Mode Spacing (TMS). In that case what is measured is the frequency of an Higher Order Mode (HOM) relative to that of the correspondent longitudinal mode. The way it is done is by locking the cavity to the fundamental mode (TEM00) of either one of the two beam and making one of the Higher Order Modes of the other beam resonant inside the cavity. This time the beat happens between an HOM and the TEM00 and its frequency is a multiple of the Transverse Mode Spacing.
From the TMS is then possible to calculate the cavity g-factor and so to extract information such as HOM distribution or mirror curvatures.

Status of the experiment at the 40m

So far (December 17, 2009), the technique has been applied to both arm cavities of the 40m (results on elog entry [http://131.215.115.52:8080/40m/1115 1115]).
A first attempt has also been done on the Power Recycling Cavity (preliminary results in a LIGO presentation [https://dcc.ligo.org/DocDB/0000/G0900060/003/AbsLpresentation.pdf LIGO-G0900060-v3]). A few problems arose when trying to meaasure the short cavities. Changes were necessary on part of the experimental setup (i.e., fast photodiodes needed, beam jitter).
The experiment has restarted nowadays and the plan is to fully measure the short cavity in the next weeks to come.