LISA as a dark energy probe

Recently, it has been shown that the inclusion of higher signal harmonics in the inspiral signals of binary supermassive black holes (SMBH) leads to dramatic improvements in the parameter estimation with Laser Interferometer Space Antenna (LISA). In particular, the angular resolution becomes good enough to identify the host galaxy or galaxy cluster, in which case the redshift can be determined by electromagnetic means. The gravitational wave signal also provides the luminosity distance with high accuracy, and the relationship between this and the redshift depends sensitively on the cosmological parameters, such as the equation-of-state parameter w = p(DE)/rho(DE) of dark energy. Using binary SMBH events at z < 1 with appropriate masses and orientations, one would be able to constrain w to within a few per cent. We show that, if the measured sky location is folded into the error analysis, the uncertainty on w goes down by an additional factor of 2-3, leaving weak lensing as the only limiting factor in using LISA as a dark energy probe.

Towards a gravitational wave observatory designer: sensitivity limits of spaceborne detectors

The most promising concept for low frequency (millihertz to hertz) gravitational wave observatories are laser interferometric detectors in space. It is usually assumed that the noise floor for such a detector is dominated by optical shot noise in the signal readout. For this to be true, a careful balance of mission parameters is crucial to keep all other parasitic disturbances below shot noise. We developed a web application that uses over 30 input parameters and considers many important technical noise sources and noise suppression techniques to derive a realistic position noise budget. It optimizes free parameters automatically and generates a detailed report on all individual noise contributions. Thus one can easily explore the entire parameter space and design a realistic gravitational wave observatory. In this document we describe the different parameters, present all underlying calculations, and compare the final observatory's sensitivity with astrophysical sources of gravitational waves. We use as an example parameters currently assumed to be likely applied to a space mission proposed to be launched in 2034 by the European Space Agency. The web application itself is publicly available on the Internet at http://spacegravity.org/designer. Future versions of the web application will incorporate the frequency dependence of different noise sources and include a more detailed model of the observatory's residual acceleration noise.

Transportable setup for amplifier phase fidelity measurements

One possible laser source for the Laser Interferometer Space Antenna (LISA) consists of an Ytterbium-doped fiber amplifier originally developed for inter-satellite communication, seeded by the laser used for the technology demonstrator mission LISA Pathfinder. LISA needs to transmit clock information between its three spacecraft to correct for phase noise between the clocks on the individual spacecraft. For this purpose phase modulation sidebands at GHz frequencies will be imprinted on the laser beams between spacecraft. Differential phase noise between the carrier and a sideband introduced within the optical chain must be very low. We report on a transportable setup to measure the phase fidelity of optical amplifiers.

An Optically recombined laser interferometer for gravitational wave detection

Kilometer scale interferometers for the detection of gravitational waves are currently under construction by the LIGO (Laser Interferometer Gravitational-wave Observatory) and VIRGO projects. These interferometers will consist of two Fabry-Perot cavities illuminated by a laser beam which is split in half by a beam splitter. A recycling mirror between the laser and the beam splitter will reflect the light returning from the beam splitter towards the laser back into the interferometer. The positions of the optical components in these interferometers must be controlled to a small fraction of a wavelength of the laser light. Schemes to extract signals necessary to control these optical components have been developed and demonstrated on the tabletop. In the large scale gravitational wave detectors the optical components must be suspended from vibration isolation platforms to achieve the necessary isolation from seismic motion. These suspended components present a new class of problems in controlling the interferometer, but also provide more exacting test of interferometer signal and noise models.

This thesis discusses the first operation of a suspended-mass Fabry-Perot-Michelson interferometer, in which signals carried by the optically recombined beams are used to detect and control all important mirror displacements. This interferometer uses an optical configuration and signal extraction scheme that is planned for the full scale LIGO interferometers with the simplification of the removal of the recycling mirror. A theoretical analysis of the performance that is expected from such an interferometer is presented and the experimental results are shown to be in generally good agreement.

In situ surface topography measurement method of granite base in scanning wafer stage with laser interferometer

Topography of a granite surface has an effect on the vertical positioning of a wafer stage in a lithographic tool, when the wafer stage moves on the granite. The inaccurate measurement of the topography results in a bad leveling and focusing performance. In this paper, an in situ method to measure the topography of a granite surface with high accuracy is present. In this method, a high-order polynomial is set up to express the topography of the granite surface. Two double-frequency laser interferometers are used to measure the tilts of the wafer stage in the X- and Y-directions. From the sampling tilts information, the coefficients of the high-order polynomial can be obtained by a special algorithm. Experiment results shows that the measurement reproducibility of the method is better than 10 nm. (c) 2006 Elsevier GmbH. All rights reserved.

Study on eight-pass dual-frequency laser interferometer with nanometer precision

A new dual-frequency laser displacement measurement interferometer with nanometer precision has been developed. An eight-pass optical subdivision technology is proposed to improve resolution based on commercial interferometers. A static positioning error measuring method has been used to examine the precision and repeatability of the laser interferometer. An optical resolution of 1.24 nm and an accuracy of nanometer scale have been achieved.

Real-time far distance micro-vibration measurement using an external cavity semiconductor laser interferometer with a feedback control system

An external cavity semiconductor laser interferometer used to measure far distance micro-vibration in real time is proposed. In the interferometer, a single longitudinal mode and excellent coherent characteristic grating external cavity semiconductor laser is constructed and acted as a light source and a phase compensator. Its coherent length exceeds 200 meters. The angle between normal and incidence beam of the far object is allowed to change in definite range during the measurement with this interferometer, and this makes the far distance interference measurement easier and more convenient. Also, it is not required to keep the amplitudes of the first and second harmonic components equal, and then the dynamic range is increased. A feedback control system is used to compensate the phase disturbance between the two interference beams introduced by environmental vibration.

Self-similar motion of laser half-space plasmas. I. Deflagration regime

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density 0,produced by the (anomalous) absorption of a laser pulse of irradiation = (j>0f/T(0< (< T) at the critical density nc(«c/«0=eoKe)213, where k, m, are Boltzmann's constant and the ion mass, and Ke X (electron temperature)5'2 = heat conductivity. If a >e- 4 ' 3 , a deflagration wave separates an isentropic compression with a shock bounding the undisturbed plasma, and an isentropic expansion flow to the vacuum. The structures of these three regions are completely determined; in particular, the Chapman-Jouguet condition is proved and the density behind the deflagration is found. The deflagration-compression thickness ratio is large (small) for a^e- 5 ' 3(a>e- 5 ' 3 ) . The compression to expansion ratio for both energy and thickness is 0(e"2). For Z,- large, a deflagration exists even if a~e~413. Condition a>e~4'3 may be applied to pulses that are not linear.

Self-similar motion of laser half-space plasmas. II. Thermal waves and intermediate regimes

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density n,produced by the (anomalous) absorption of a laser pulse of irradiation

€~4'3, a qualitative discussion of how plasma behavior changes with a, is given.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Space-selective co-precipitation of silver and gold nanoparticles in femtosecond laser pulses irradiated Ag+, Au3+ co-doped silicate glass

We report on space-selective co-precipitation of silver and gold nanoparticles in Ag+, Au3+ co-doped silicate glasses by irradiation of femtosecond laser pulses and subsequent annealing at high temperatures. The color of the irradiated area in the glass sample changed from yellow to red with the increase of the annealing temperature. The effects of average laser power and annealing temperature on precipitation of the nanoparticles were investigated. A reasonable mechanism was proposed to explain the observed phenomena. (c) 2006 Elsevier Ltd. All rights reserved.