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Stefano De Leo

Publications and source records attributed to Stefano De Leo.

At least 37 records · Page 2Linked to original sources
arXiv2016

Closed form expression for the Goos-Haenchen lateral displacement

The Artmann formula provides an accurate determination of the Goos-Haenchen lateral displacement in terms of the light wavelength, refractive index and incidence angle. In the total reflection region, this formula is widely used in the literature and confirmed by experiments. Nevertheless, for incidence at critical angle, it tends to infinity and numerical calculations are needed to reproduce the experimental data. In this paper, we overcome the divergence problem at critical angle and find, for Gaussian beams, a closed formula in terms of modified Bessel functions of the first kind. The formula is in excellent agreement with numerical calculations and reproduces, for incidence angles greater than critical ones, the Artmann formula. The closed form also allows one to understand how the breaking of symmetry in the angular distribution is responsible for the difference between measurements done by considering the maximum and the mean value of the beam intensity. The results obtained in this study clearly show the Goos-Haenchen lateral displacement dependence on the angular distribution shape of the incoming beam. Finally, we also present a brief comparison with experimental data and other analytical formulas found in the literature.

physics.optics↗
arXiv2016

Hartree-Fock and Random Phase Approximation theories in a many-fermion solvable model

We present an ideal system of interacting fermions where the solutions of the many-body Schroedinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree-Fock and the Random Phase Approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.

nucl-th↗
arXiv2015

Quaternioninc Dirac Scattering

The scattering of a Dirac particle has been studied for a quaternionic potential step. In the potential region an additional diffusion solution is obtained. The quaternionic solution which generalizes the complex one presents an amplification of the reflection and transmission rates. A detailed analysis of the quaternionic spinorial velocities sheed new light on the additional solution. For pure quaternionic potentials, the interesting and surprising result of total transmission is found. This suggests that the presence of pure quaternionic potentials cannot be seen by analyzing the reflection or transmission rates. It has be observed by measuring the mean value of some operator.

math-ph↗
arXiv2015

Axial dependence of optical weak measurements in the critical region

The interference between optical beams of different polarizations plays a fundamental role in reproducing the optical analog of the electron spin weak measurement. The extraordinary point in optical weak measurements is represented by the possibility to estimate with great accuracy the Goos-Haenchen (GH) shift by measuring the distance between the peak of the outgoing beams for two opposite rotation angles of the polarizers located before and after the dielectric block. Starting from the numerical calculation of the GH shift, which clearly shows a frequency crossover for incidence near to the critical angle, we present a detailed study of the interference between s and p polarized waves in the critical region. This allows to determine in which conditions it is possible to avoid axial deformations and reproduce the GH curves. In view of a possible experimental implementation, we give the expected weak measurement curves for Gaussian lasers of different beam waist sizes propagating through borosilicate (BK7) and fused silica dielectric blocks.

physics.optics↗
arXiv2014

Maximal breaking of symmetry at critical angle and closed form expression for angular deviations of the Snell law

A detailed analysis of the propagation of laser gaussian beams at critical angles shows in which conditions it is possible to maximize the breaking of symmetry in the angular distribution and for which values of the laser wavelength and beam waist is possible to find an analytic formula for angular deviations of the Snell law. For propagation throughout $N$ dielectric blocks and for a full breaking of symmetry, overcoming the well known problem of the infinity at critical angle, a closed expression for the Goos-Haenchen shift is obtained. The multiple peaks phenomenon clearly represents an additional evidence of the breaking of symmetry in the angular distribution of optical beams. Finally, laser wavelength and beam waist conditions to produce focal effects in the outgoing beam are also briefly discussed.

physics.optics↗
arXiv2014

The frequency crossover for the Goos-Hanchen shift

For total reflection, the Goos-Hanchen (GH) shift is proportional to the wavelength of the laser beam. At critical angles, such a shift is instead proportional to the square root of the product of the beam waist and wavelength. By using the stationary phase method (SPM) and, when necessary, numerical calculations, we present a detailed analysis of the frequency crossover for the GH shift. The study, done in different incidence regions, sheds new light on the validity of the analytic formulas found in literature.

physics.optics↗
arXiv2014

Dirac solutions for quaternionic potentials

In this paper, the quaternionic Dirac equation is solved for quaternionic potentials, iV0+jW0. The study shows two different solutions. The first solution contains particles and anti-particles and leads to the diffusion, tunneling and Klein energy zones. The complex limit is recovered from this solution. The second solution, which does not have a complex counterpart, can be seen as a V0-antiparticle or |W0|-particle.

math-ph↗
arXiv2014

The Snell law for quaternionic potentials

By using the analogy between optics and quantum mechanics, we obtain the Snell law for the planar motion of quantum particles in the presence of quaternionic potentials.

quant-ph↗
arXiv2013

The asymmetric Goos-Hänchen effect

We show in which conditions optical gaussian beams, propagating throughout an homogeneous dielectric right angle prism, present an asymmetric Goos-Hänchen (GH) effect. This asymmetric behavior is seen for incidence at critical angles and happens in the propagation direction of the outgoing beam. The asymmetric GH effect can be also seen as an amplification of the standard GH shift. Due to the fact that it only depends on the ratio between the wavelength and the minimal waist size of the incoming gaussian beam, it can be also used to determine one of these parameters. Multiple peaks interference is an additional phenomenon seen in the presence of such asymmetric effects.

physics.optics↗
arXiv2013

Antiparticle creation in tunneling

We study particle interaction with a Dirac step potential. In the standard Klein energy zone, the hypothesis of Klein pair production predicts the existence of free/oscillatory antiparticles. In this paper, we discuss the tunneling energy zone characterized by evanescent wave functions in the classically forbidden region. We ask the question of the nature, particle or antiparticle, of the densities within the classically forbidden region. The answer to this question is relevant to the correct form of the reflection coefficient.

quant-ph↗
arXiv2013

Resonance, multiple diffusion and critical tunneling for Gaussian lasers

We present a detailed study of the gaussian laser propagation through a dielectric system composed by two right angle prisms. We investigate the transition between the spatial coherence limit, which exhibits wave-like properties and for which the resonance phenomenon can be seen, and the decoherence limit, which exhibits particle-like properties and for which the multiple diffusion occurs. We also analyze the tunneling at critical angles. In our numerical analysis, we shall use BK7 and Fused Silica prisms and a gaussian He-Ne laser with a wavelength of 632.8 nm and beam waists of 2 mm and 200 micron.

physics.optics↗
arXiv2013

Light transmission through a triangular air gap

Due to the recent interest in studying propagation of light through triangular air gaps, we calculate, by using the analogy between optics and quantum mechanics and the multiple step technique, the transmissivity through a triangular air gap surrounded by an homogeneous dielectric medium. The new formula is then compared with the formula used in literature. Starting from the qualitative and quantitative differences between these formulas, we propose optical experiments to test our theoretical results.

physics.optics↗
arXiv2013

A study of transit times in Dirac tunneling

Based on the Dirac equation, the behavior of relativistic electrons which tunnel a potential barrier of height V0 for incoming energies between V0 and V0+m is studied by using the wave packet formalism. The choice of this incoming energy zone guarantees that only electrons participate to the tunneling process. In the opaque limit, as shown in a previous analysis, the transit velocity is proportional to the barrier width and for relativistic potential tends to a constant value greater than $c$. In this paper, a new numerical study shows a very surprising result: superluminal transmissions are also evident for thin barriers.

quant-ph↗
arXiv2012

Relative helicity phases in planar Dirac scattering

We study planar Dirac scattering for an electrostatic stratified barrier potential. The general expressions for transmitted and reflected waves are derived. Of particular interest is the information upon relative helicity phases. We also briefly discuss some possible applications.

quant-ph↗
arXiv2012

The octonionic eigenvalue problem

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.

math-ph↗
arXiv2012

Delay Time in Quaternionic Quantum Mechanics

In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.

math-ph↗
arXiv2012

Graphene tests of Klein phenomena

Graphene is characterized by chiral electronic excitations. As such it provides a perfect testing ground for the production of Klein pairs (electron/holes). If confirmed, the standard results for barrier phenomena must be reconsidered with, as a byproduct, the accumulation within the barrier of holes.

quant-ph↗