Erika D'Ambrosio

Considerations on parametric instability in Fabry-Perot interferometer

We evaluate the parametric phenomenon for the main optical mode coupled to other resonant waves excited by acoustic interaction with the mirrors of a Fabry–Perot. We apply this to the arm cavity of a gravitational wave antenna. Under certain assumptions we find that the amplitude of these parasitic modes is expressed by analytic solutions that are always damped. We analyze both the zero detuning and the detuned case and solve the equations. The form of the solution shows that for equally spaced and excited cavity modes the instability is expressed by a threshold condition, which is well approximated for LIGO arm resonator parameters.

Advanced LIGO: Non-Gaussian beams

By using non-Gaussian, flat-topped beams in the advanced gravitational wave interferometers currently being designed, one can reduce the impact on the interferometer sensitivity of a variety of fundamental disturbances (thermoelastic noise, noise in mirror coatings, thermal lensing, etc). This may make beating the standard quantum limit an achievable goal.

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 located in Livingston, Louisiana. In the interferometers normal mode of operation, the recycling cavity is stabilized by inducing a thermal lens in the cavity mirrors with an external CO2 laser. During our study, 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.

Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO

This paper is concerned with a study of the analytic structure of a family of hyperboloidal beams introduced by Bondarescu and Thorne which generalizes the nearly-flat and nearly-concentric mesa beam configurations of interest for advanced LIGO. 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. 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 is obtained. Possible implications for the advanced-LIGO optical cavity design are discussed.

Duality relation between nonspherical mirror optical cavities and its application to gravitational-wave detectors

In this paper, we analytically prove a unique duality relation between the eigenspectra of paraxial optical cavities with nonspherical mirrors: a one-to-one mapping between eigenmodes and eigenvalues of cavities deviating from flat mirrors by h(r) and cavities deviating from concentric mirrors by -h(r), where h need not be a small perturbation. We then illustrate its application to optical cavities, proposed for advanced interferometric gravitational-wave detectors, where the mirrors are designed to support beams with rather flat intensity profiles over the mirror surfaces. This unique mapping might be very useful in future studies of alternative optical designs for advanced gravitational wave interferometers or experiments employing optical cavities with nonstandard mirrors.

Design and construction of a prototype of a flat top beam interferometer and initial tests

A non-Gaussian, flat-top laser beam profile, also called Mesa Beam Profile, supported by non spherical mirrors known as Mexican Hat (MH) mirrors, has been proposed as a way to depress the mirror thermal noise and thus improve the sensitivity of future interferometric Gravitational Wave detectors, including Advanced LIGO [1]. Non-Gaussian beam configurations have never been tested before [2] hence the main motivation of this project is to demonstrate the feasibility of this new concept. A 7m rigid suspended Fabry-Perot (FP) cavity which can support a scaled version of a Mesa beam applicable to the LIGO interferometers has been developed. The FP cavity prototype is being designed to prove the feasibility of actual MH mirror profiles, determine whether a MH mirror cavity is capable of transforming an incoming Gaussian beam into a flat top beam profile, study the effects of unavoidable mirror imperfections on the resulting beam profile and gauge the difficulties associated with locking and maintaining the alignment of such an optical cavity. We present the design of the experimental apparatus and simulations comparing Gaussian and Mesa beams performed both with ideal and current (measured) mirror profiles. An overview of the technique used to manufacture this kind of mirror and initial results showing Mesa beam properties are presented.

Study of the different responsive behaviour of the sidebands in LIGO I

Gravitational waves may be measured by detecting the length change induced by them in a Fabry–Perot cavity. In order to amplify the effect on the laser beam driving the cavity, the end mirrors are almost totally reflective so that when the resonant conditions are achieved, the electromagnetic field reflected from the cavity only changes in phase when the resonator changes in length. Several techniques may be used for the signal extraction; for example sidebands can be generated by phase modulation of the laser beam, which are minimally sensitive to any length change in the Fabry–Perot cavity when the carrier is resonating in there. Therefore, they can be used as a reference for the measurement of the variation induced by the gravitational wave upon the carrier. In an ideal case they are symmetric around the carrier for an unperturbed configuration. If the symmetry is broken, the combination of electromagnetic fields, which is supposed to be proportional to the gravitational strain, is a non-zero quantity because of a variety of imperfections in the real interferometers. We will discuss the fundamental mechanism beneath this phenomenon that is observed experimentally.

Asymmetry between the sidebands used for detecting gravitational waves in laser interferometric antennas

We develop an analytical approach in order to understand the causes of sidebands imbalance. The results have been tested by two different and more sophisticated numerical tools. The main static perturbations that can generate sidebands imbalance are described and fully analyzed, with a special attention to the design of the Laser Interferometer Gravitational Wave Observatory I, whose typical parameters have been used for numerical estimations of this phenomenon.

Characterization of a low frequency power spectral density f−γ in a threshold model

This 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.