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Register a new userEffect of interference on thermal noise and coating optimization in dielectric mirrors
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Optical multilayer coatings of high-reflective mirrors significantly determine the properties of Fabry-Perot resonators. Thermal (Brownian) noise in these coatings produce excess phase noise which can seriously degrade the sensitivity of high-precision measurements with these cavities, in particular in laser gravitational-wave antennas (for example project LIGO), where at the current stage it is one of the main limiting factors. We present a method to calculate this effect accurately and analyze different strategies to diminish it by optimizing the coating. Traditionally this noise is calculated as if the beam is reflected from the surface of the mirror fluctuating due to the sums of the fluctuations of each layer. However the beam in fact penetrates a coating and Brownian expansion of the layers leads to dephasing of interference in the coating and consequently to additional change in reflected phase. Fluctuations in the thickness of a layer change the strain in the medium and hence due to photoelastic effect change the refractive index of this layer. This additional effect should be also considered. It is possible to make the noise smaller preserving the reflectivity by changing the total number of layers and thicknesses of high and low refractive ones. We show how this optimized coating may be constructed analytically rather then numerically as before. We also check the possibility to use internal resonant layers and optimized cap layer to decrease the thermal noise.
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Thermal noise of a mirror is one of the limiting noise sources in the high precision measurement such as gravitational-wave detection, and the modeling of thermal noise has been developed and refined over a decade. In this paper, we present a derivation of coating thermal noise of a finite-size cylindrical mirror based on the fluctuation-dissipation theorem. The result agrees to a previous result with an infinite-size mirror in the limit of large thickness, and also agrees to an independent result based on the mode expansion with a thin-mirror approximation. Our study will play an important role not only to accurately estimate the thermal-noise level of gravitational-wave detectors but also to help analyzing thermal noise in quantum-measurement experiments with lighter mirrors.
Reduction of coating thermal noise is a key issue in precise measurements with an optical interferometer. A good example of such a measurement device is a gravitational-wave detector, where each mirror is coated by a few tens of quarter-wavelength dielectric layers to achieve high reflectivity while the thermal-noise level increases with the number of layers. One way to realize the reduction of coating thermal noise, recently proposed by Khalili, is the mechanical separation of the first few layers from the rest so that a major part of the fluctuations contributes only little to the phase shift of the reflected light. Using an etalon, a Fabry-Perot optical resonator of a monolithic cavity, with a few coating layers on the front and significantly more on the back surface is a way to realize such a system without too much complexity, and in this paper we perform a thermal-noise analysis of an etalon using the Fluctuation-dissipation theorem with probes on both sides of a finite-size cylindrical mirror.
Thermal fluctuations in the coatings used to make high-reflectors are becoming significant noise sources in precision optical measurements and are particularly relevant to advanced gravitational wave detectors. There are two recognized sources of coating thermal noise, mechanical loss and thermal dissipation. Thermal dissipation causes thermal fluctuations in the coating which produce noise via the thermo-elastic and thermo-refractive mechanisms. We treat these mechanisms coherently, give a correction for finite coating thickness, and evaluate the implications for Advanced LIGO.
Thermal fluctuations of different origin in the substrate and in the coating of optical mirrors produce phase noise in the reflected wave. This noise determines the ultimate stabilization capability of high-Q cavities used as a reference system. In particular this noise is significant in interferometric laser gravitational wave antennas. It is shown that simple alteration of a mirror multilayer coating may provide suppression of phase noise produced by thermorefractive, thermoelastic, photothermal and thermoradiation induced fluctuations in the coating.
Grating reflectors have been repeatedly discussed to improve the noise performance of metrological applications due to the reduction or absence of any coating material. So far, however, no quantitative estimate on the thermal noise of these reflective structures exists. In this work we present a theoretical calculation of a grating reflectors noise. We further apply it to a proposed 3rd generation gravitational wave detector. Depending on the grating geometry, the grating material and the temperature we obtain a thermal noise decrease by up to a factor of ten compared to conventional dielectric mirrors. Thus the use of grating reflectors can substantially improve the noise performance in metrological applications.
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