Related papers: Gauss Optics and Gauss Sum on an Optical Phenomena
We revisit the gravitational lensing phenomenon using a new visualization technique. It consists in projecting the observers sky into the source plane, what gives rise to a folded and stretched surface. This provides a clear graphical tool…
The cyclic sieving phenomenon provides a link between a polynomial analogue of Gauss congruence known as $q$-Gauss congruence, and a combinatorial analogue of Gauss congruence based on sequences of cyclic group actions. We strengthen this…
It is standard practice to study the lensing of gravitational waves (GW) using the geometric optics regime. However, in many astrophysical configurations this regime breaks down as the wavelength becomes comparable to the Schwarzschild…
In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables.…
An optical approach begins by interpreting the gravitational redshift resulting to a change in the relative velocity of light due to the medium of propagation in the gravitational field. The discussion continues by pointing out an agreement…
In this text we describe the role of optical chirality in the context of plasmonics. We clearly distinguish between 2D an 3D optical chirality and connect the problem with reciprocity and time symmetry. We compare our analysis with recent…
Wave effects in lensing form a rich phenomenon at the intersection of classical caustic singularities and quantum interference, yet are notoriously difficult to model. A large number of recently observed pulsars and fast radio bursts in…
We found strong similarities between the gravitational lensing and the conventional optical lensing. The similarities imply a graded refractive index description of the light deflection in gravitational field. We got a general approach to…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
The theory of the thin vapor layers linear optical properties is presented for the case of specular reflection of atoms colliding with the walls. The effects of light absorption and the shift in the resonance frequency are taken into…
Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on…
Gravitational waves from the distant sources are gravitationally lensed during their propagation through the intervening matter inhomogeneities before arriving at detectors. It has been proposed in the literature that the variance of the…
We study in an explicit manner the partial sums of the multiplicative inverse of the Riemann zeta function and its derivative.
Using a one-to-one correspondence between observables and their spectral resolutions, we introduce the sum of any two bounded observables of a $\sigma$-MV-effect algebra. This sum is commutative, associative and with neutral element. Under…
Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536-540) found a paraxial…
It is proposed that to the usual probability theory, three definitions and a new theorem are added, the resulting theory allows one to displace the central role usually given to the notion of conditional probability. When a mapping $\phi$…
We initiate the study of gravitational-wave lensing in the wave-optics regime within modified gravity. We consider a phenomenological setup in which the gravitational-wave amplitude obeys a curvature-coupled propagation equation. This…
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation.…
We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series approach. We then extend these results to generalized…