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

Upconversion of optical signals with multi-longitudinal-mode pump lasers

Multi-longitudinal-mode lasers have been believed to be good candidates as pump sources for optical frequency conversion. However, we present a semi-classical model for frequency conversion of optical signals with a multimode pump laser, which shows that fluctuations of the instantaneous pump power limit the conversion efficiency. In an experiment, we upconverted a 1550 nm optical signal in a periodically poled lithium niobate waveguide using with a multi-longitudinal-mode laser, an observed a maximum conversion efficiency of 70%, in good agreement with our theoretical model. Compared to single-mode pumping, multimode pumping is not a suitable technique for attaining stable near-unity-efficiency frequency conversion. However, the results obtained here could find application in characterization of the spectral or temporal structure of multi-longitudinal-mode lasers.Comment: 6 pages, 4 figures, comments are welcome

High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State

Polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed non-zero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time reversal symmetry state in the superconducting state of Sr2RuO4, similar to He3-A

The multiple ionospheric probe Auroral ionospheric report

Multiple impedance and resonance probe payload for ionospheric property observation in Nike- Apache rocke

Mathematical models of magnetospheric convection and its coupling to the ionosphere

Mathematical models of magnetospheric convection and its coupling to ionospher

Nonlinear interaction between two heralded single photons

Harnessing nonlinearities strong enough to allow two single photons to interact with one another is not only a fascinating challenge but is central to numerous advanced applications in quantum information science. Currently, all known approaches are extremely challenging although a few have led to experimental realisations with attenuated classical laser light. This has included cross-phase modulation with weak classical light in atomic ensembles and optical fibres, converting incident laser light into a non-classical stream of photon or Rydberg blockades as well as all-optical switches with attenuated classical light in various atomic systems. Here we report the observation of a nonlinear parametric interaction between two true single photons. Single photons are initially generated by heralding one photon from each of two independent spontaneous parametric downconversion sources. The two heralded single photons are subsequently combined in a nonlinear waveguide where they are converted into a single photon with a higher energy. Our approach highlights the potential for quantum nonlinear optics with integrated devices, and as the photons are at telecom wavelengths, it is well adapted to applications in quantum communication.Comment: 4 pages, 4 figure

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

Titania-doped tantala/silica coatings for gravitational-wave detection

Reducing thermal noise from optical coatings is crucial to reaching the required sensitivity in next generation interferometric gravitational-wave detectors. Here we show that adding TiO2 to Ta2O5 in Ta2O5/SiO2 coatings reduces the internal friction and in addition present data confirming it reduces thermal noise. We also show that TiO2-doped Ta2O5/SiO2 coatings are close to satisfying the optical absorption requirements of second generation gravitational-wave detectors