Related papers: Gauss Optics and Gauss Sum on an Optical Phenomena
We consider the optical Hall conductivity of a general electronic medium and prove that the optical Hall angle obeys a new sum rule. This sum rule governs the response of an electronic fluid to a Lorentz electric field and can thought of as…
We review Gordon's optical metric and the transport equations for the amplitude and polarization of a geometrical optics wave traveling in a gravity field. We apply the theory to the FLRW cosmologies by associating a refraction index with…
We prove a general independent equidistribution result for Gauss sums associated to $n$ monomials in $r$ variable multiplicative characters over a finite field, which generalizes several previous equidistribution results for Gauss and…
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for…
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and…
The traditional optical concept for the object does not provide an experimental feasibility to speak for itself, due to the fact that no measuring instrument catches up with the fluctuation of light fields. Using the theory of coherence, we…
A review of probability representation of quantum states in given for optical and photon number tomography approaches. Explicit connection of photon number tomogram with measurable by homodyne detector optical tomogram is obtained. New…
We investigate the finite source size effect in the context of the wave optics in the gravitational lensing. The magnification of an extended source is presented in an analytic manner for the singular isothermal sphere lens model as well as…
We connect Dedekind sums and some formulas for numerical semigroups.
Optical beams are solutions to the paraxial wave equation (PWE). In this work we report a new, to our knowledge, optical beam. We solve the PWE by using the angular spectrum of plane waves theory in circular cylindrical coordinates. This…
In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.
Like light, gravitational waves can be gravitationally lensed by massive objects along their travel path. Strong lensing produces several images from the same binary coalescence and is forecasted to have a promising rate in ground-based…
In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
Gravitational lensing by gravitational wave is considered. We notice that although final and initial direction of photons coincide, displacement between final and initial trajectories occurs. This displacement is calculated analytically for…
The total magnification due to a point lens has been of particular interest as the theorem that gravitational lensing results in light amplification for all observers appears to contradict the conservation of photon number. This has been…
The gravitational lensing of gravitational waves should be treated in the wave optics instead of the geometrical optics when the wave length $\lambda$ of the gravitational waves is larger than the Schwarzschild radius of the lens mass $M$.…
This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic…
The coherent superposition of orthogonal modes can result in transverse offsets, variations of the Rayleigh length and a reduction of the beam quality factor of the coherent sum of modes in comparison to the incoherent sum. Relations for…
It is shown that the amplification of a light beam by gravitational waves in scalar-tensor theories of gravity is a first order effect in the wave amplitudes. In general relativity, instead, the effect is only of second order.
The theoretically expected amplitude of the associations of background quasars with foreground galaxies as a result of gravitational lensing has been updated in this paper. Since the galactic matter alone yields an amplitude of quasar…