Review of the Laguerre-Gauss mode technology research program at Birmingham
Paul Fulda, Charlotte Bond, Daniel Brown, Frank Br\"uckner, Ludovico, Carbone, Simon Chelkowski, Stefan Hild, Keiko Kokeyama, Mengyao Wang, Andreas, Freise

TL;DR
This paper reviews Birmingham's research on using higher-order Laguerre-Gauss modes to reduce thermal noise in advanced gravitational wave detectors, covering simulations, experiments, and prototype implementations.
Contribution
It summarizes Birmingham's comprehensive research program on LG mode technology for improving gravitational wave detector sensitivity.
Findings
LG modes can potentially reduce thermal noise in optics.
Successful implementation of LG modes in prototype cavities.
Progress from simulations to high-power laser bench experiments.
Abstract
Gravitational wave detectors from the advanced generation onwards are expected to be limited in sensitivity by thermal noise of the optics, making the reduction of this noise a key factor in the success of such detectors. A proposed method for reducing the impact of this noise is to use higher-order Laguerre-Gauss (LG) modes for the readout beam, as opposed to the currently used fundamental mode. We present here a synopsis of the research program undertaken by the University of Birmingham into the suitability of LG mode technology for future gravitational wave detectors. This will cover our previous and current work on this topic, from initial simulations and table-top LG mode experiments up to implementation in a prototype scale suspended cavity and high-power laser bench.
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