Optimal Light Beams and Mirror Shapes for Future LIGO Interferometers

TL;DR

This paper identifies optimal mirror shapes and light beams for LIGO that significantly reduce thermal noise, potentially tripling the gravitational wave detection rate compared to current designs.

Contribution

It introduces a new beam and mirror shape design that lowers thermal noise in LIGO by over two times, enhancing detector sensitivity.

Findings

Thermal noise reduced by a factor of 2.32 with new beam shape.

Mirror shapes are roughly conical with mild Fresnel-scale corrections.

Potential threefold increase in gravitational wave event detection rate.

Abstract

We report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the shape of mirrors, while fixing the mirror radius and maintaining a low diffractional loss. The result of this minimization is a beam with thermal noise a factor of 2.32 (in power) lower than previously considered Mesa Beams and a factor of 5.45 (in power) lower than the Gaussian beams employed in the current baseline design. Mirrors that confine these beams have been found to be roughly conical in shape, with an average slope approximately equal to the mirror radius divided by arm length, and with mild corrections varying at the Fresnel scale. Such a mirror system, if built, would impact the sensitivity of LIGO, increasing the event rate of observing gravitational waves in the frequency range of maximum sensitivity roughly by a factor of three compared to an Advanced LIGO using Mesa beams (assuming all other noises remain unchanged). We discuss the resulting beam and mirror properties and study requirements on mirror tilt, displacement and figure error, in order for this beam to be used in LIGO detectors.