Model of Thermal Wavefront Distortion in Interferometric Gravitational-Wave Detectors I: Thermal Focusing

We develop a steady-state analytical and numerical model of the optical response of power-recycled Fabry-Perot Michelson laser gravitational-wave detectors to thermal focusing in optical substrates. We assume that the thermal distortions are small enough that we can represent the unperturbed intracavity field anywhere in the detector as a linear combination of basis functions related to the eigenmodes of one of the Fabry-Perot arm cavities, and we take great care to preserve numerically the nearly ideal longitudinal phase resonance conditions that would otherwise be provided by an external servo-locking control system. We have included the effects of nonlinear thermal focusing due to power absorption in both the substrates and coatings of the mirrors and beamsplitter, the effects of a finite mismatch between the curvatures of the laser wavefront and the mirror surface, and the diffraction by the mirror aperture at each instance of reflection and transmission. We demonstrate a detailed numerical example of this model using the MATLAB program Melody for the initial LIGO detector in the Hermite-Gauss basis, and compare the resulting computations of intracavity fields in two special cases with those of a fast Fourier transform field propagation model. Additional systematic perturbations (e.g., mirror tilt, thermoelastic surface deformations, and other optical imperfections) can be included easily by incorporating the appropriate operators into the transfer matrices describing reflection and transmission for the mirrors and beamsplitter.Comment: 24 pages, 22 figures. Submitted to JOSA

Thermo-optic noise in coated mirrors for high-precision optical measurements

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 noise in half infinite mirrors with non-uniform loss: a slab of excess loss in a half infinite mirror

We calculate the thermal noise in half-infinite mirrors containing a layer of arbitrary thickness and depth made of excessively lossy material but with the same elastic material properties as the substrate. For the special case of a thin lossy layer on the surface of the mirror, the excess noise scales as the ratio of the coating loss to the substrate loss and as the ratio of the coating thickness to the laser beam spot size. Assuming a silica substrate with a loss function of 3x10-8 the coating loss must be less than 3x10-5 for a 6 cm spot size and a 7 micrometers thick coating to avoid increasing the spectral density of displacement noise by more than 10%. A similar number is obtained for sapphire test masses.Comment: Passed LSC (internal) review. Submitted to Phys. Rev. D. (5/2001) Replacement: Minor typo in Eq. 17 correcte

Effect of heat treatment on mechanical dissipation in Ta2_2O5_5 coatings

Thermal noise arising from mechanical dissipation in dielectric reflective coatings is expected to critically limit the sensitivity of precision measurement systems such as high-resolution optical spectroscopy, optical frequency standards and future generations of interferometric gravitational wave detectors. We present measurements of the effect of post-deposition heat treatment on the temperature dependence of the mechanical dissipation in ion-beam sputtered tantalum pentoxide between 11\,K and 300\,K. We find the temperature dependence of the dissipation is strongly dependent on the temperature at which the heat treatment was carried out, and we have identified three dissipation peaks occurring at different heat treatment temperatures. At temperatures below 200\,K, the magnitude of the loss was found to increase with higher heat treatment temperatures, indicating that heat treatment is a significant factor in determining the level of coating thermal noise.Comment: accepted Classical and Quantum Gravity 201

Investigating the medium range order in amorphous Ta₂O₅ coatings

Ion-beam sputtered amorphous heavy metal oxides, such as Ta2O5, are widely used as the high refractive index layer of highly reflective dielectric coatings. Such coatings are used in the ground based Laser Interferometer Gravitational-wave Observatory (LIGO), in which mechanical loss, directly related to Brownian thermal noise, from the coatings forms an important limit to the sensitivity of the LIGO detector. It has previously been shown that heat-treatment and TiO2 doping of amorphous Ta2O5 coatings causes significant changes to the levels of mechanical loss measured and is thought to result from changes in the atomic structure. This work aims to find ways to reduce the levels of mechanical loss in the coatings by understanding the atomic structure properties that are responsible for it, and thus helping to increase the LIGO detector sensitivity. Using a combination of Reduced Density Functions (RDFs) from electron diffraction and Fluctuation Electron Microscopy (FEM), we probe the medium range order (in the 2-3 nm range) of these amorphous coatings

Quantum Zeno effect in a probed downconversion process

The distorsion of a spontaneous downconvertion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the downconversion in the nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of downconversion. These effects are interpreted as being manifestations of quantum Zeno or anti-Zeno effects, respectively, and they are understood by using the dressed modes picture of the device. The possibility of using the coupling as a nontrivial phase--matching technique is pointed out.Comment: 11 pages, 4 figure

A high-flux source of polarization-entangled photons from a periodically-poled KTP parametric downconverter

We have demonstrated a high-flux source of polarization-entangled photons using a type-II phase-matched periodically-poled KTP parametric downconverter in a collinearly propagating configuration. We have observed quantum interference between the single-beam downconverted photons with a visibility of 99% and a measured coincidence flux of 300/s/mW of pump. The Clauser-Horne-Shimony-Holt version of Bell's inequality was violated with a value of 2.711 +/- 0.017.Comment: 7 pages submitted to Physical Review