arXiv subjects

S. Hacyan

Publications and source records attributed to S. Hacyan.

9 recordsLinked to original sources

arXiv2022

Theoretical and numerical investigation of internal conical refraction of structured light beams

We present an ab-initio numerical investigation of the internal conical refraction of structured light beams in a biaxial crystal. Starting from the solutions of the Fresnel equation, a theoretical analysis is developed without assuming any analytical approximation, thus obtaining a set of exact equations that can be solved by standard methods of integration for any impinging light beam. As examples of applications, we consider the particular cases of linearly and circularly polarized Gaussian and Bessel beams inside a KTP crystal. The numerical calculations follow the evolution of the refracted beam inside the crystal. It is seen that for realistic boundary conditions, a refraction cone appears in a certain range of distances within the crystal and its shape is rather sensitive to the initial conditions.

physics.optics↗

arXiv2020

Quantum non-linear effects in colliding light beams and interferometers

Small corrections to the electromagnetic field in colliding light beams are evaluated taking into account the interaction of light with the quantum vacuum, as predicted by quantum electrodynamics. Possible implications for very energetic light beams and the radiation pressure in interferometers (e.g., gravitational waves detector) are considered. It is also shown that a head-on collision produces secondary waves along conical directions at angles $\arccos (1/3)$.

quant-ph↗

arXiv2017

Some remarks on the Bel-Robinson tensor and gravitational radiation

The asymptotic form of the Bel-Robinson tensor in the gravitational radiation-zone is obtained in terms of the mass quadrupole of the source. A comparison is made with the standard formula for the gravitational power emission. The problem of a fully covariant description of gravitational radiation in terms of this tensor is discussed with some detail.

gr-qc↗

arXiv2008

Electromagnetic waves in uniaxial crystals: General formalism with an application to Bessel beams

We present a mathematical formalism describing the propagation of a completely general electromagnetic wave in a birefringent medium. Analytic formulas for the refraction and reflection from a plane interface are obtained. As a particular example, a Bessel beam impinging at an arbitrary angle is analyzed in detail. Some numerical results showing the formation and destruction of optical vortices are presented.

physics.optics↗

arXiv2007

Geometry as an object of experience: Kant and the missed debate between Poincaré and Einstein

Poincaré held the view that geometry is a convention and cannot be tested experimentally. This position was apparently refuted by the general theory of relativity and the successful confirmation of its predictions; unfortunately, Poincaré did not live to defend his thesis. In this paper, I argue that: 1) Contrary to what many authors have claimed, non-euclidean geometries do not rule out Kant's thesis that space is a form of intuition given {\it a priori}; on the contrary, Euclidean geometry is the condition for the possibility of any more general geometry. 2) The conception of space-time as a Riemannian manifold is an extremely ingenious way to describe the gravitational field, but, as shown by Utiyama in 1956, general relativity is actually the gauge theory associated to the Lorentz group. Utiyama's approach does not rely on the assumption that space-time is curved, though the equations of the gauge theory are identical to those of general relativity. Thus, following Poincaré, it can be claimed that it is only a matter of convention to describe the gravitational field as a Riemannian manifold or as a gauge field in Euclidean space.

physics.hist-ph↗

arXiv2006

A relativistic study of Bessel beams

We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form, the wave appearing to rotate in circles. The concepts of polarization and angular momentum for Bessel beams is also reanalyzed.

physics.optics↗

arXiv2005

Thermodynamics of a quantized electromagnetic field in rectangular cavities with perfectly conducting walls

The thermodynamical properties of a quantized electromagnetic field inside a box with perfectly conducting walls are studied using a regularization scheme that permits to obtain finite expressions for the thermodynamic potentials. The source of ultraviolet divergences is directly isolated in the expression for the density of modes, and the logarithmic infrared divergences are regularized imposing the uniqueness of vacuum and, consequently, the vanishing of the entropy in the limit of zero temperature. We thus obtain corrections to the Casimir energy and pressures, and to the specific heat that are due to temperature effects; these results suggest effects that could be tested experimentally.

quant-ph↗

arXiv2005

Coherent states with elliptical polarization

Coherent states of the two dimensional harmonic oscillator are constructed as superpositions of energy and angular momentum eigenstates. It is shown that these states are Gaussian wave-packets moving along a classical trajectory, with a well defined elliptical polarization. They are coherent correlated states with respect to the usual cartesian position and momentum operators. A set of creation and annihilation operators is defined in polar coordinates, and it is shown that these same states are precisely coherent states with respect to such operators.

quant-ph↗

arXiv2004

Quantum Mechanical Properties of Bessel Beams

Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is shown that the operators that are usually associated to linear momentum, orbital angular momentum and spin do not satisfy the algebra of the translation and rotation group. In particular, what seems to be the spin is more similar to the helicity. Some physical consequences of these results are examined.

quant-ph↗