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Gravitational-wave astronomy will soon become a new tool for observing the Universe. Detecting and interpreting gravitational waves will require deep theoretical insights into astronomical sources. The past three decades have seen…
The propagation of electromagnetic waves in isotropic dielectric media with local dispersion is studied under the assumption of small but nonvanishing $\lambda/l$, where $\lambda$ is the wavelength, and $l$ is the characteristic…
These lectures discuss how the direct detection of gravitational waves can be used to probe the very early Universe. We review the main cosmological mechanisms which could have produced relic gravitational waves, and compare theoretical…
The concept of walking wave is introduced from classical relativistic positions. One- and three-dimensional walking waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and…
In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green…
In this note I introduce a mysterious approximation called the rotating wave approximation (RWA) to undergraduates or non-experts who are interested in both Mathematics and Quantum Optics. In Quantum Optics it plays a very important role in…
We represent and discuss a theory of gravitational holography in which all the involved waves; subject, reference and illuminator are gravitational waves (GW). Although these waves are so weak that no terrestrial experimental set-ups, even…
The propagation of a Bessel beam (or Bessel-X wave) is analyzed on the basis of a vectorial treatment. The electric and magnetic fields are obtained by considering a realistic situation able to generate that kind of scalar field.…
This article presents a comprehensive analysis of the physics of gravitational waves, exploring both the theoretical foundations and the most recent experimental advances. After a general introduction to the theory of general relativity and…
In a simple picture, a Bessel beam is viewed as a transverse standing wave formed in the interference region between incoming and outgoing conical waves. Based on this interpretation we propose an optical resonator that supports modes that…
The first direct observation of gravitational waves' action upon matter has recently been reported by the BICEP2 experiment. Advanced ground-based gravitational-wave detectors are being installed. They will soon be commissioned, and then…
We report on the experimental observation of waves at a liquid foam surface propagating faster than the bulk shear waves. The existence of such waves has long been debated, but the recent observation of supershear events in a geophysical…
We consider the localization of elastic waves in thin elastic structures with spatially varying curvature profiles, using a curved rod and a singly curved shell as concrete examples. Previous studies on related problems have broadly focused…
Like light, gravitational waves are gravitationally lensed by intervening massive astrophysical objects, such as galaxies, clusters, black holes, and stars, resulting in a variety of potentially observable gravitational-wave lensing…
We analyse the temporal properties of the optical pulse wave that is obtained by applying a set of spectral $\pi/2$ phase shifts to continuous-wave light that is phase-modulated by a temporal sinusoidal wave. We develop an analytical model…
We expand on a previous study, offering a generalized wave function associated with the parabolic cylinder function and a connection with a two-particle position-space wave function. We also provide an explicit formula for a wave function…
The local polarization of electromagnetic (EMW) and gravitational waves (GW) is discussed from an operational point of view, in which all the relevant mathematical framework is constructed in terms of measurements of the power absorbed by a…
In this article, which will appear as a chapter in the Handbook of Gravitational Wave Astronomy, we will describe the detection of gravitational waves with space-based interferometric gravitational wave observatories. We will provide an…
Gravitational waves, like light, can be gravitationally lensed by massive astrophysical objects such as galaxies and galaxy clusters. Strong gravitational-wave lensing, forecasted at a reasonable rate in ground-based gravitational-wave…
A gravitational wave passing through a pulsar will lead to a variation in the moment of inertia of the pulsar affecting its rotation. This will affect the extremely accurately measured spin rate of the pulsar as well as its pulse profile…