LIGO Document G0900558-v1

Optical Design of the Advanced LIGO Detectors with Stable Recycling Cavities

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The Advanced LIGO interferometers will employ dual recycling, i.e., both power and signal recycling cavities will be included in the optical configuration. The proposed optical design of Advanced LIGO detectors will incorporate stable geometries for power and signal recycling cavities in contrast with the marginally stable/degenerate power recycling cavity currently use in initial LIGO. In addition, it is likely that Advanced Virgo will utilize stable recycling cavities. A stable recycling cavity geometry is configured such that the RF sidebands maintain a well defined optical mode in the presence of thermal aberrations. This design ensures that the mode overlap between the carrier and any RF sidebands remains high, enabling a more robust interferometer sensing and control operation.
However, introducing stable cavities brings its own challenges. With a particular choice of the cavity stability factor g, an additional mode matching telescope is needed between the mode cleaner and the recycling cavity. In addition, the recycling cavity has to be flexible and tolerant enough to allow for radius of curvature tolerances and laser induced radius of curvature changes. Thermal effects play a major role in degradation of mode matching between various cavities. Our proposed design optimizes the mode matching to an intermediate power splitting the losses due to mode matching. Introduction of variable focal length lenses is used to keep the mode matching relatively good at all power levels.
In this paper, we will introduce the optical design parameters of the Advanced LIGO configuration. We will describe the rationale behind choosing particular values of stability factor and specific geometries of the various cavities. We will also address issues such as radius of curvature tolerances of mirrors, compensation of radius of curvature errors, compensation of thermal effects, and mode matching between various cavities. A proposed solution for compensating thermal effects in the Advanced LIGO cavities will also be addressed.
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