The Arm Cavities

Arm Cavity Finesse

In initial detectors such as Virgo and LIGO the choice of arm cavity finesse, and thus the arm cavity input mirror transmissivity, was a critical factor in determining the sensitivity of the detector: the finesse, in combination with the arm length, uniquely determined the detector bandwidth and frequency response.
For Advanced Virgo, which will use the signal recycling technique, the detector response will vary with the arm cavity input mirror transmissivity, the signal recycling mirror transmissivity, the signal recycling cavity length, and the circulating power. This combi- nation of factors means that the detector bandwidth depends only weakly on the specific choice of arm cavity finesse, since changes in the arm cavity input mirror transmissivity can be compensated by changing one of the other parameters.
Factors other than the ideal sensitivity curves thus drive the choice of arm cavity finesse. These factors include thermal loading in the central interferometer, length noise coupling from auxiliary degrees of freedom, and the relative impact of losses in the arm and signal recycling cavities.

Arm Cavity Radii of Curvature

The arm cavities have a bi-concave geometry, with each test mass mirror having a concave radius of curvature of slightly larger than half the arm cavity length. Such a near- concentric resonator configuration is chosen for two principle reasons: (1) to increase the beam size at the mirrors, thus averaging over a larger area of the mirror’s surface and reducing the relative contribution of mirror coating thermal noise, and (2) to limit the effect of radiation-pressure induced alignment instabilities [29].

This type of topology means that the cavity waist is near the middle of the arm cavity. Having different radii of curvature for the two cavity mirrors displaces the waist toward the mirror with the smaller radius of curvature, and the beam size on that mirror is also reduced. This can actually cause an increase in detector sensitivity, as the input mirror will have fewer coating layers and so its coating thermal noise contribution is actually slightly smaller for identical beam sizes on the two mirrors. We thus choose to have the ETM with a larger radius, and thus larger beam size, than the ITM.

See Choosing the Arm Cavity RoCs for more information.