Astigmatism free design for CE recycling cavities

The 40km long arms in Cosmic Explorer (CE) necessitate a much larger beam size in the arms compared to LIGO. Therefore, a redesign of the recycling cavities is needed to ensure that the beam shrinks to an appropriate size while also satisfying other conditions, like the beam size at the Beam-Splitter (BS) and the total length of the cavities while accumulating sufficient Gouy phase to ensure geometrical stability of the recycling and extraction cavities. The solution is to have off-axis telescopes between the arm cavities and the BS. However, the off-axis nature of these telescopes makes them liable to produce astigmatism in the beam, which can lead to mismatch between the arm cavity modes and the signal extraction cavity (SEC) mode. This particular mismatch has been identified as a critical parameter which must be minimized in order to reach the target detector sensitivity, due to its strong interaction with squeezed light states which are injected to reduce the effects of quantum noise.

This talk will cover the theory behind the astigmatism caused by individual optical components in the layout. We will show that by carefully balancing three sources of astigmatism, we can produce an astigmatism-free design for the SEC in a specific realization of the so-called “Long Crab” layout. The method adopted can be extended to other layouts and involves modifying various cavity parameters, such as the radius of curvature of the mirrors and the beam angle of incidence on the optics.