This document records the results of a comparison of the interferometer simulation Finesse against an analytic (MATLAB based) calculation of the alignment sensing signals of a Fabry Perot cavity. This task was started during the commissioning worksho
p at the LIGO Livingston site between the 28.1. and 1.02 2013 with the aim of creating a reference example for validating numerical simulation tools. The FFT based simulation OSCAR joined the battle later.
Finesse is a fast interferometer simulation program. For a given optical setup, it computes the light field amplitudes at every point in the interferometer assuming a steady state. To do so, the interferometer description is translated into a set of
linear equations that are solved numerically. For convenience, a number of standard analyses can be performed automatically by the program, namely computing modulation-demodulation error signals, transfer functions, shot-noise-limited sensitivities, and beam shapes. Finesse can perform the analysis using the plane-wave approximation or Hermite-Gauss modes. The latter allows computation of the properties of optical systems like telescopes and the effects of mode matching and mirror angular positions.
Several km-scale gravitational-wave detectors have been constructed world wide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind;
developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques; however, the complex optical layouts provide a new challenge. In this review we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.
The third generation of gravitational wave observatories, aiming to provide 100 times better sensitivity than currently operating interferometers, is expected to establish the evolving field of gravitational wave astronomy. A key element for achievin
g the ambitious sensitivity goal is the exploration of new interferometer geometries, topologies and configurations. In this article we review the current status of the ongoing design work for third-generation gravitational wave observatories. The main focus is set on the evaluation of the detector geometry and detector topology. In addition we discuss some promising detector configurations and potential noise reduction schemes.
The upcoming European design study `Einstein gravitational-wave Telescope represents the first step towards a substantial, international effort for the design of a third-generation interferometric gravitational wave detector. It is generally believed
that third-generation instruments might not be installed into existing infrastructures but will provoke a new search for optimal detector sites. Consequently, the detector design could be subject to fewer constraints than the on-going design of the second generation instruments. In particular, it will be prudent to investigate alternatives to the traditional L-shaped Michelson interferometer. In this article, we review an old proposal to use three Michelson interferometers in a triangular configuration. We use this example of a triple Michelson interferometer to clarify the terminology and will put this idea into the context of more recent research on interferometer technologies. Furthermore the benefits of a triangular detector will be used to motivate this design as a good starting point for a more detailed research effort towards a third-generation gravitational wave detector.
Diffraction gratings have been proposed as core optical elements in future laser-interferometric gravitational-wave detectors. In this paper we derive equations for the coupling between alignment noise and phase noise at diffraction gratings. In comp
arison to a standard reflective component (mirror or beam splitter) the diffractive nature of the gratings causes an additional coupling of geometry changes into alignment and phase noise. Expressions for the change in angle and optical path length of each outgoing beam are provided as functions of a translation or rotation of the incoming beam with respect to the grating. The analysis is based entirely on the grating equation and the geometry of the setup. We further analyse exemplary optical setups which have been proposed for the use in future gravitational wave detectors. We find that the use of diffraction gratings yields a strong coupling of alignment noise into phase noise. By comparing the results with the specifications of current detectors we show that this additional noise coupling results in new, challenging requirements for the suspension and isolation systems for the optical components.
We introduce a concept that uses detuned arm cavities to increase the shot noise limited sensitivity of LIGO without increasing the light power inside the arm cavities. Numerical simulations show an increased sensitivity between 125 and 400 Hz, with
a maximal improvement of about 80% around 225 Hz, while the sensitivity above 400Hz is decreased. Furthermore our concept is found to give a sensitivity similar to that of a conventional RSE configuration with a Signal-Recycling mirror of moderate reflectivity. In the near future detuned arm cavities might be a beneficial alternative to RSE, due the potentially less hardware intensive implementation of the proposed concept.
