Design of the Advanced LIGO recycling cavities

The current LIGO detectors will undergo an upgrade which is expected to improve their sensitivity and bandwidth significantly. These advanced gravitational-wave detectors will employ stable recycling cavities to better confine their spatial eigenmodes instead of the currently installed marginally stable power recycling cavity. In this letter we describe the general layout of the recycling cavities and give specific values for a first possible design. We also address the issue of mode mismatch due to manufacturing tolerance of optical elements and present a passive compensation scheme based upon optimizing the distances between optical elements.