Optimization of the geometrical stability in square ring laser gyroscopes

TL;DR

This paper explores how to optimize and stabilize the geometry of square ring laser cavities to meet the high precision requirements of detecting relativistic effects like frame-dragging, focusing on measurement and control strategies.

Contribution

It introduces a control strategy for maintaining the geometrical stability of square ring laser cavities using diagonal and perimeter measurements.

Findings

Stability increases with a system measuring mirror distances.

Geometry stabilization achieved by monitoring diagonals and perimeter.

A set of mirror adjustments can maintain a square cavity shape.

Abstract

Ultra sensitive ring laser gyroscopes are regarded as potential detectors of the general relativistic frame-dragging effect due to the rotation of the Earth: the project name is GINGER (Gyroscopes IN GEneral Relativity), a ground-based triaxial array of ring lasers aiming at measuring the Earth rotation rate with an accuracy of 10^-14 rad/s. Such ambitious goal is now within reach as large area ring lasers are very close to the necessary sensitivity and stability. However, demanding constraints on the geometrical stability of the laser optical path inside the ring cavity are required. Thus we have started a detailed study of the geometry of an optical cavity, in order to find a control strategy for its geometry which could meet the specifications of the GINGER project. As the cavity perimeter has a stationary point for the square configuration, we identify a set of transformations on the mirror positions which allows us to adjust the laser beam steering to the shape of a square. We show that the geometrical stability of a square cavity strongly increases by implementing a suitable system to measure the mirror distances, and that the geometry stabilization can be achieved by measuring the absolute lengths of the two diagonals and the perimeter of the ring.