Thermoelastic Noise and Homogeneous Thermal Noise in Finite Sized Gravitational-Wave Test Masses

An analysis is given of thermoelastic noise (thermal noise due to thermoelastic dissipation) in finite sized test masses of laser interferometer gravitational-wave detectors. Finite-size effects increase the thermoelastic noise by a modest amount; for example, for the sapphire test masses tentatively planned for LIGO-II and plausible beam-spot radii, the increase is less than or of order 10 per cent. As a side issue, errors are pointed out in the currently used formulas for conventional, homogeneous thermal noise (noise associated with dissipation which is homogeneous and described by an imaginary part of the Young's modulus) in finite sized test masses. Correction of these errors increases the homogeneous thermal noise by less than or of order 5 per cent for LIGO-II-type configurations.Comment: 10 pages and 3 figures; RevTeX; submitted to Physical Review

Second-Order Nonlinear Optical Properties of Multiaddressable Indolinooxazolidine Derivatives: Joint Computational and Hyper-Rayleigh Scattering Investigations

The linear and nonlinear optical (NLO) properties of two indolinooxazolidine derivatives acting as multiaddressable switches are reported. The second-order hyperpolarizability contrasts upon commutation between their closed and open forms are characterized using hyper-Rayleigh scattering (HRS) measurements, and rationalized by means of density functional theory and post Hartree–Fock ab initio calculations. It is evidenced that the addition of a withdrawing substituent on the indolinic subunit leads to a more effective photoinduced charge transfer while decreasing the transition energy of the S0 → S1 transition, which induces a significant enhancement of the HRS response of the open form. This substitution is however detrimental to the NLO contrast, due to the concomitant increase of the HRS response of the closed form

Thermal and back-action noises in dual-sphere gravitational-waves detectors

We study the sensitivity limits of a broadband gravitational-waves detector based on dual resonators such as nested spheres. We determine both the thermal and back-action noises when the resonators displacements are read-out with an optomechanical sensor. We analyze the contributions of all mechanical modes, using a new method to deal with the force-displacement transfer functions in the intermediate frequency domain between the two gravitational-waves sensitive modes associated with each resonator. This method gives an accurate estimate of the mechanical response, together with an evaluation of the estimate error. We show that very high sensitivities can be reached on a wide frequency band for realistic parameters in the case of a dual-sphere detector.Comment: 10 pages, 7 figure

Internal thermal noise in the LIGO test masses : a direct approach

The internal thermal noise in LIGO's test masses is analyzed by a new technique, a direct application of the Fluctuation-Dissipation Theorem to LIGO's readout observable, $x(t)=$(longitudinal position of test-mass face, weighted by laser beam's Gaussian profile). Previous analyses, which relied on a normal-mode decomposition of the test-mass motion, were valid only if the dissipation is uniformally distributed over the test-mass interior, and they converged reliably to a final answer only when the beam size was a non-negligible fraction of the test-mass cross section. This paper's direct analysis, by contrast, can handle inhomogeneous dissipation and arbitrary beam sizes. In the domain of validity of the previous analysis, the two methods give the same answer for $S_x(f)$, the spectral density of thermal noise, to within expected accuracy. The new analysis predicts that thermal noise due to dissipation concentrated in the test mass's front face (e.g. due to mirror coating) scales as $1/r_0^2$, by contrast with homogeneous dissipation, which scales as $1/r_0$ ($r_0$ is the beam radius); so surface dissipation could become significant for small beam sizes.Comment: 6 pages, RevTex, 1 figur

Optomechanical characterization of acoustic modes in a mirror

We present an experimental study of the internal mechanical vibration modes of a mirror. We determine the frequency repartition of acoustic resonances via a spectral analysis of the Brownian motion of the mirror, and the spatial profile of the acoustic modes by monitoring their mechanical response to a resonant radiation pressure force swept across the mirror surface. We have applied this technique to mirrors with cylindrical and plano-convex geometries, and compared the experimental results to theoretical predictions. We have in particular observed the gaussian modes predicted for plano-convex mirrors.Comment: 8 pages, 8 figures, RevTe

Noise spectroscopy of optical microcavity

The intensity noise spectrum of the light passed through an optical microcavity is calculated with allowance for thermal fluctuations of its thickness. The spectrum thus obtained reveals a peak at the frequency of acoustic mode localized inside the microcavity and depends on the size of the illuminated area. The estimates of the noise magnitude show that it can be detected using the up-to-date noise spectroscopy technique.Comment: 10 pages, 1 figur

Cooling of a mirror by radiation pressure

We describe an experiment in which a mirror is cooled by the radiation pressure of light. A high-finesse optical cavity with a mirror coated on a mechanical resonator is used as an optomechanical sensor of the Brownian motion of the mirror. A feedback mechanism controls this motion via the radiation pressure of a laser beam reflected on the mirror. We have observed either a cooling or a heating of the mirror, depending on the gain of the feedback loop.Comment: 4 pages, 6 figures, RevTe

Huge Electro-/photo-/acidoinduced Second-order Nonlinear Contrasts from Multiaddressable Indolinooxazolodine

In this work, linear and nonlinear optical properties of electro-/acido-/photoswitchable indolino[2,1-b]oxazolidine derivatives were investigated. The linear optical properties of the closed and open forms have been characterized by UV–visible and IR spectroscopies associated with DFT calculations. Nonlinear optical properties of the compounds have been obtained by ex situ and in situ hyper-Rayleigh experiments in solution. We show that protonated, oxidized, and irradiated open forms exhibit the same visible absorption and NLO features. In particular, the closed and open forms exhibit a huge contrast of the first hyperpolarizability with an enhancement factor of 40–45. Additionally, we have designed an original electrochemical cell that allows to monitor in situ the hyper-Rayleigh response upon electrical stimulus. We report notably a partial but good and reversible NLO contrast in situ during oxidation/reduction cycles. Thereby, indolinooxazolidine moieties are versatile trimodal switchable units which are very promising for applications in devices

The variable finesse locking technique

Virgo is a power recycled Michelson interferometer, with 3 km long Fabry-Perot cavities in the arms. The locking of the interferometer has been obtained with an original lock acquisition technique. The main idea is to lock the instrument away from its working point. Lock is obtained by misaligning the power recycling mirror and detuning the Michelson from the dark fringe. In this way, a good fraction of light escapes through the antisymmetric port and the power build-up inside the recycling cavity is extremely low. The benefit is that all the degrees of freedom are controlled when they are almost decoupled, and the linewidth of the recycling cavity is large. The interferometer is then adiabatically brought on to the dark fringe. This technique is referred to as variable finesse, since the recycling cavity is considered as a variable finesse Fabry-Perot. This technique has been widely tested and allows us to reach the dark fringe in few minutes, in an essentially deterministic way