Carrier mode selective working point and side band imbalance in LIGO I

In gravitational wave interferometers, the input laser beam is phase modulated to generate radio-frequency side bands that are used to lock the cavities. The mechanism is the following: the frequency of the side bands and the carrier is chosen in such a way that their response to small changes of the longitudinal degrees of freedom is different. This difference is therefore monitored and it serves as an error signal for controlling the optical cavity lengths, as they are linearly related to the set of observed phases between carrier and side bands. Among the others, one longitudinal degree of freedom is optimally sensitive to the space-time distortions propagating through the cosmos, as predicted by the general theory of relativity. The observation of the astrophysical signal relies on the measurement of that specific degree of freedom. The entire problem is more complex when the transverse degrees of freedom are taken into account, because the relative phase between the fields also depends on their overlap. In order to establish an unambiguous relation between length changes and phase measurements, there must be one circulating optical mode and the only difference between carrier and side bands must be their amplitude. We will show that the variability of the transverse degrees of freedom and their different actions on carrier and side band fields puts a severe limit on this assumption. Unless the system is made of perfect and perfectly matched optical cavities, it is never governed by one unique coherent state and any adjustment of the optical lengths results from a compromise between the lengths that are optimal for the carrier field and the side band ones. Such a compromise alters the correspondence between error signals and cavity lengths, calculated in the one-dimensional treatment. We assess the strength of this effect and relate it to the sensitivity of the instrument (which relies on the reconstruction of that correspondence) in realistic circumstances

Simulation of Supersymmetric Models with a Local Nicolai Map

We study the numerical simulation of supersymmetric models having a local Nicolai map. The mapping can be regarded as a stochastic equation and its numerical integration provides an algorithm for the simulation of the original model. In this paper, the method is discussed in details and applied to examples in 0+1 and 1+1 dimensions.Comment: 18 pages, REVTeX + 2 PostScript figure

Effects of mode degeneracy in the LIGO Livingston Observatory recycling cavity

We analyze the electromagnetic fields in a Pound-Drever-Hall locked, marginally unstable, Fabry-Perot cavity as a function of small changes in the cavity length during resonance. More specifically, we compare the results of a detailed numerical model with the behavior of the recycling cavity of the Laser Interferometer Gravitational-wave Observatory (LIGO) detector that is located in Livingston, Louisiana. In the interferometer's normal mode of operation, the recycling cavity is stabilized by inducing a thermal lens in the cavity mirrors with an external CO2 laser. During the study described here, this thermal compensation system was not operating, causing the cavity to be marginally optically unstable and cavity modes to become degenerate. In contrast to stable optical cavities, the modal content of the resonating beam in the uncompensated recycling cavity is significantly altered by very small cavity length changes. This modifies the error signals used to control the cavity length in such a way that the zero crossing point is no longer the point of maximum power in the cavity nor is it the point where the input beam mode in the cavity is maximized.Comment: Eight pages in two-column format. Six color figures. To be published JOSA

The strategic communication. A content analysis of two different leaders’ discourses

Communication and interaction between Ego and Alter are fundamental processes of social action since the speaker (Ego), and the listener (Alter) refer to the same world, sharing a conventional interpretation of reality. In this respect, every communication act is defined by those linguistic interactions in which all participants pursue their actions and strategies with the use of mutual expressions. Moreover, some interactions are characterized by perlocutive purposes or by those verbal interactions that, through communication, aim to produce a change in the audience (in this regard, according to the German philosopher and sociologist Jürgen Habermas, actions are defined as strategic). For this reason, going more into details into this work, the objective of our research is to carry out a comparative analysis concerning the theory of communication actions using, as an example, the texts of two different religious leaders: Pope Benedict XVI and Pope Francis. We examined the Angelus of the two Popes through the content analysis in order to detect the styles of two different modus operandi and to understand two particular communication strategies. In this sense, the analysis of these -ecclesiastical policies. of the two Popes will take into consideration the Angelus recited in the respective first three years of the Pontificate. Therefore, it will be possible to highlight and compare the topics addressed and investigate the type of strategic actions. In this perspective, content analysis reveals its usefulness, combining two elements that are difficult to isolate in the understanding of a communication process (the source and the message transmitted) and it also reveals itself as one valuable tool for the analysis of both cultural and social messages

Perturbative and Numerical Methods for Stochastic Nonlinear Oscillators

Interferometric gravitational wave detectors are devoted to pick up the effect induced on masses by gravitational waves. The variations of the length dividing two mirrors is measured through a laser interferometric technique. The Brownian motion of the masses related to the interferometer room temperature is a limit to the observation of astrophysical signals. It is referred to as thermal noise and it affects the sensitivity of both the projected and the future generation interferometers. In this paper we investigate the relevance of small non-linear effects and point out their impact on the sensitivity curve of interferometric gravitational wave detectors (e.g. VIRGO, LIGO, GEO, ...) through perturbative methods and numerical simulations. We find that in the first order approximation the constants characterizing the power spectrum density (PSD) are renormalized but it retains its typical shape. This is due to the fact that the involved Feynman diagrams are of tadpole type. Higher order approximations are required to give rise to up-conversion effects. This result is predicted by the perturbative approach and is in agreement with the numerical results obtained by studying the system's non-linear response by numerically simulating its dynamics.Comment: 12 pages, REVTeX + 7 PostScript figure

New Seismic Attenuation System (SAS) for the Advanced LIGO Configurations (LIGO2)

A new passive seismic attenuation system is being developed to replace the current passive attenuation stacks in LIGO 2, it is expected to drive the seismic contribution to the interferometer noise below any other noise source. The SAS will be effective completely starting at about 5 Hz, well inside the (uncompensated) gravity gradient noise wall

Characterization of a Low Frequency Power Spectral Density f^(-gamma) in a Threshold Model

his study investigates the modifications of the thermal spectrum, at low frequency, induced by an external damping on a system in heat contact with internal fluctuating impurities. Those impurities can move among locations and their oscillations are associated with a loss function depending on the model. The fluctuation properties of the system are provided by a potential function shaped by wells, in such a way that jumps between the stationary positions are allowed. The power spectral density associated with this dissipation mechanism shows a f^(-gamma)tail. The interest of this problem is that many systems are characterized by a typical f^(-\gamma) spectral tail at low frequency. The model presented in this article is based on a threshold type behaviour and its generality allows applications in several fields. The effects of an external force, introduced to produce damping, are studied by using both analytical techniques and numerical simulations. The results obtained with the present model show that no reduction of the power spectral density is appreciable below the main peak of the spectral density.Comment: 15 pages, 6 figure

On the Analytic Structure of a Family of Hyperboloidal Beams of Potential Interest for Advanced LIGO

For the baseline design of the advanced Laser Interferometer Gravitational-wave Observatory (LIGO), use of optical cavities with non-spherical mirrors supporting flat-top ("mesa") beams, potentially capable of mitigating the thermal noise of the mirrors, has recently drawn a considerable attention. To reduce the severe tilt-instability problems affecting the originally conceived nearly-flat, "Mexican-hat-shaped" mirror configuration, K. S. Thorne proposed a nearly-concentric mirror configuration capable of producing the same mesa beam profile on the mirror surfaces. Subsequently, Bondarescu and Thorne introduced a generalized construction that leads to a one-parameter family of "hyperboloidal" beams which allows continuous spanning from the nearly-flat to the nearly-concentric mesa beam configurations. This paper is concerned with a study of the analytic structure of the above family of hyperboloidal beams. Capitalizing on certain results from the applied optics literature on flat-top beams, a physically-insightful and computationally-effective representation is derived in terms of rapidly-converging Gauss-Laguerre expansions. Moreover, the functional relation between two generic hyperboloidal beams is investigated. This leads to a generalization (involving fractional Fourier transform operators of complex order) of some recently discovered duality relations between the nearly-flat and nearly-concentric mesa configurations. Possible implications and perspectives for the advanced LIGO optical cavity design are discussed.Comment: 9 pages, 6 figures, typos corrected, Eqs. (24) and (26) change

Analytic structure and generalized duality relations for a family of hyperboloidal beams and supporting mirrors of potential interest for future gravitational wave detection interferometers

For the baseline design of future gravitational wave detection interferometers, use of optical cavities with nonsphericalmirrors supporting flat-top ("mesa") beams, potentially capable of mitigating the thermal noise of the mirrors, has recently drawn a considerable attention. To reduce the severe tilt-instability problems affecting the originally conceived nearly-flat, "Mexican-hat-shaped" mirror configuration, K. S. Thorne proposed a nearly-concentric mirror configuration capable of producing the same mesa beam profile on the mirror surfaces. Subsequently, Bondarescu and Thorne introduced a generalized construction that leads to a one-parameter family of "hyperboloidal" beams which allows continuous spanning from the nearly-flat to the nearly-concentric mesa beam configurations. This paper is concerned with a study of the analytic structure of the above family of hyperboloidal beams. Capitalizing on certain results from the applied optics literature on flat-top beams, a physically-insightful and computationally-effective representation is derived in terms of rapidly-converging Gauss-Laguerre expansions. Moreover, the functional relation between two generic hyperboloidal beams is investigated. This leads to a generalization (involving fractional Fourier transform operators of complex order) of some recently discovered duality relations between the nearly-flat and nearly-concentric mesa configurations. Possible implications and perspectives for the advanced Laser Interferometer Gravitational-wave Observatory (LIGO) optical cavity design are discussed