Coating-Free Mirrors for Ultra-Sensitive Interferometry

Abstract

Thermodynamical fluctuations impose random noise on the position of optical components. It is predicted that this thermal noise will limit the sensitivity of interferometric gravitational-wave detectors in their most sensitive frequency band. Thermal noise originating from optical coatings was first considered in the context of interferometric gravitational wave detectors. Its true significance was, however, only revealed after Y. Levin introduced a new method in 1998 to calculate the resulting phase noise of a laser beam reading out the position of a coated mirror. A result of this analysis is that the reflective optical coatings introduce a particularly large portion of thermal noise. ¶ As a consequence, coating thermal noise is expected to prevent the detection of the standard quantum limit; a limitation to the sensitivity of an interferometric measurement caused by quantum fluctuations in the optical field. Elimination of the coating thermal noise will increase the likelihood of the successful observation of the standard quantum limit, thus enabling the investigation of quantum noise in the regime of optical squeezing. This project investigated a means to eliminate the effects of coating thermal noise, with the design and characterisation of a highly reflective coating-free mirror. This mirror utilised the phenomenon of total internal reflection and the Brewster angle to reflect light without the use of coatings. The dimensions of the mirror were governed by its expected implementation in an experiment to measure the standard quantum limit. ¶ The design of the coating-free mirror undertaken as the initial part of this project is presented in detail. Once a CFM had been created according to this design, its spatial dimensions were measured. The weight of the mirror is 0.43 ± 0.01 g, well within the design goal of 0.5 g. ¶ In order to analyse the reflectivity of the coating-free mirror it was incorporated, together with a high quality conventional mirror, into a triangular ring cavity. This cavity was stabilised to the laser frequency by the Pound-Drever-Hall technique. This enabled the interrogation of the stable cavity properties by an AM-sideband transfer scheme. The reflectivity of the mirror was analysed for optimum rotational alignment and as a function of its rotational alignment angle. The maximum reflectivity deviated from the expected value calculated from the mirror design. Most of the excess loss was attributed to scattering due to surface roughness at the points of total internal reflection and a necessary deviation from the Brewster angle due to the geometry of the cavity combined with the flat front face of the coating free mirror. ¶ For optimum alignment a cavity finesse of about 4000 was measured, corresponding to a reflectivity of the coating free mirror of 99.89%. Thus, the objective of creating a highly reflective lightweight coating-free optic was achieved. The obtained reflectivity can be further increased by using a substrate that is super polished at the faces of total internal reflection.