Related papers: Gauss Optics and Gauss Sum on an Optical Phenomena
This paper gives new explicit formulas for sums of powers of integers and their reciprocals.
After a brief introduction to gravitational lensing theory, a rough overview of the types of gravitational lensing statistics that have been performed so far will be given. I shall then concentrate on recent results of galaxy-galaxy…
The effect of the existence of tails on the propagation of scalar waves in curved space-time is considered via an analysis of flux integrals of the energy-stress-momentum tensor of the waves. The geometric optics approximation is formulated…
The distribution of the performed work for spin glasses with gauge symmetry is considered. With the aid of the gauge symmetry, which leads to the exact/rigorous results in spin glasses, we find a fascinating relation of the performed work…
Wave optics may need to be considered when studying the lensed waveforms of gravitational waves (GWs). However, the computation of the diffraction integral (amplification factor) in wave optics is challenging and time-consuming. It is vital…
It is often convenient to use Gaussian blur in studying image quality or in data augmentation pipelines for training convoluional neural networks. Because of their convenience, Guassians are sometimes used as first order approximations of…
Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves.…
Explicit and compact expressions describing the reflection and the transmission of a Gaussian beam by anisotropic parallel plates are given. Multiple reflections inside the plate are taken into account as well as arbitrary optical axis…
The optical memory effect is a well-known type of wave correlation that is observed in coherent fields that scatter through thin and diffusive materials, like biological tissue. It is a fundamental physical property of scattering media that…
An exact analogy between wave mechanics in quantum theory and the scalar wave treatment of optics emerges from the marriage of Newtonian formulation of geometrical optics [1] and the ``formal quantum theory of light rays'' [2]. Here the…
Recently, an intriguing relationship (the "double copy") has been discovered between theories like electromagnetism, and gravity. This potentially gives us a new way to think about gravity, and there are also practical applications…
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We consider $q$-analytic derivations of the $q$-Gauss summation formula for a $\, _2\phi _1$ that respect the symmetry in its upper parameters.
Uncertainty relations for light pulses found in [Phys. Rev. A {\bf 86}, 022118 (2012)] were derived in the three-dimensional case which emphasized the localization in a volume. Here we derive the uncertainty relation for light beams in the…
Gaussian periods are certain sums of roots of unity whose study dates back to Gauss's seminal work in algebra and number theory. Recently, large scale plots of Gaussian periods have been revealed to exhibit striking visual patterns, some of…
Advances in micro-technology of the last years have made it possible to carry optics textbooks experiments over to atomic and molecular beams, such as diffraction by a double slit or transmission grating. The usual wave-optical approach…
If an extended source, such as a galaxy, is gravitationally lensed by a massive object in the foreground, the lensing distorts the observed image. It is straightforward to simulate what the observed image would be for a particular lens and…
We have previously discussed the characteristics of the gravitational waves (GW) and have, theoretically, shown that, like the corresponding electromagnetic (EM) waves, they also demonstrate, under certain conditions, holographic…
4-dimensional optics is here introduced axiomatically as the space that supports a Universal wave equation which is applied to the postulated Higgs field. Self-guiding of this field is shown to produce all the modes necessary to provide…