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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.
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Broadband suppression of quantum noise below the Standard Quantum Limit (SQL) becomes a top-priority problem for the future generation of large-scale terrestrial detectors of gravitational waves, as the interferometers of the Advanced LIGO project, predesigned to be quantum-noise-limited in the almost entire detection band, are phased in. To this end, among various proposed methods of quantum noise suppression or signal amplification, the most elaborate approach implies a so-called *xylophone* configuration of two Michelson interferometers, each optimised for its own frequency band, with a combined broadband sensitivity well below the SQL. Albeit ingenious, it is a rather costly solution. We demonstrate that changing the optical scheme to a Sagnac interferometer with weak detuned signal recycling and frequency dependent input squeezing can do almost as good a job, as the xylophone for significantly lower spend. We also show that the Sagnac interferometer is more robust to optical loss in filter cavity, used for frequency dependent squeezed vacuum injection, than an analogous Michelson interferometer, thereby reducing building cost even more.
The gravitational wave (GW) has opened a new window to the universe beyond the electromagnetic spectrum. Since 2015, dozens of GW events have been caught by the ground-based GW detectors through laser interferometry. However, all the ground-based detectors are L-shaped Michelson interferometers, with very limited directional response to GW. Here we propose a three-dimensional (3-D) laser interferometer detector in the shape of a regular triangular pyramid, which has more spherically symmetric antenna pattern. Moreover, the new configuration corresponds to much stronger constraints on parameters of GW sources, and is capable of constructing null-streams to get rid of the signal-like noise events. A 3-D detector of kilometer scale of such kind would shed new light on the joint search of GW and electromagnetic emission.
We analyze the trajectories of three geostationary satellites forming the GEOstationary GRAvitational Wave Interferometer (GEOGRAWI)~cite{tinto}, a space-based laser interferometer mission aiming to detect and study gravitational radiation in the ($10^{-4} - 10$) Hz band. The combined effects of the gravity fields of the Earth, the Sun and the Moon make the three satellites deviate from their nominally stationary, equatorial and equilateral configuration. Since changes in the satellites relative distances and orientations could negatively affect the precision of the laser heterodyne measurements, we have derived the time-dependence of the inter-satellite distances and velocities, the variations of the polar angles made by the constellations three arms with respect to a chosen reference frame, and the time changes of the triangles enclosed angles. We find that, during the time between two consecutive station-keeping maneuvers (about two weeks), the relative variations of the inter-satellite distances do not exceed a value of $0.05$ percent, while the relative velocities between pairs of satellites remain smaller than about $0.7 {rm m/s}$. In addition, we find the angles made by the arms of the triangle with the equatorial plane to be periodic functions of time whose amplitudes grow linearly with time; the maximum variations experienced by these angles as well as by those within the triangle remain smaller than $3$ arc-minutes, while the East-West angular variations of the three arms remain smaller than about $15$ arc-minutes during the two-weeks period. The relatively small variations of these orbit parameters result into a set of system functional and performance requirements that are less stringent than those characterizing an interplanetary mission.
We present an application of anomaly detection techniques based on deep recurrent autoencoders to the problem of detecting gravitational wave signals in laser interferometers. Trained on noise data, this class of algorithms could detect signals using an unsupervised strategy, i.e., without targeting a specific kind of source. We develop a custom architecture to analyze the data from two interferometers. We compare the obtained performance to that obtained with other autoencoder architectures and with a convolutional classifier. The unsupervised nature of the proposed strategy comes with a cost in terms of accuracy, when compared to more traditional supervised techniques. On the other hand, there is a qualitative gain in generalizing the experimental sensitivity beyond the ensemble of pre-computed signal templates. The recurrent autoencoder outperforms other autoencoders based on different architectures. The class of recurrent autoencoders presented in this paper could complement the search strategy employed for gravitational wave detection and extend the reach of the ongoing detection campaigns.
The future space-based gravitational wave observatory LISA will consist of a constellation of three spacecraft in a triangular constellation, connected by laser interferometers with 2.5 million-kilometer arms. Among other challenges, the success of the mission strongly depends on the quality of the cancellation of laser frequency noise, whose power lies eight orders of magnitude above the gravitational signal. The standard technique to perform noise removal is time-delay interferometry (TDI). TDI constructs linear combinations of delayed phasemeter measurements tailored to cancel laser noise terms. Previous work has demonstrated the relationship between TDI and principal component analysis (PCA). We build on this idea to develop an extension of TDI based on a model likelihood that directly depends on the phasemeter measurements. Assuming stationary Gaussian noise, we decompose the measurement covariance using PCA in the frequency domain. We obtain a comprehensive and compact framework that we call PCI for principal component interferometry, and show that it provides an optimal description of the LISA data analysis problem.
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