arXiv subjects

Stefano De Leo

Publications and source records attributed to Stefano De Leo.

At least 19 recordsLinked to original sources

arXiv2022

Goos-Haenchen lateral displacements and angular deviations: When these optical effects offset each other

For optical beams, transmitted by a right angle prism, the Goos-Haenchen shift can never be seen as a pure effect. Indeed, the lateral displacement, caused by the total internal reflection, will always be accompanied by angular deviations generated by the transmission through the incoming and outgoing interfaces. This combined effect can be analysed by using the Taylor expansion of the Fresnel coefficients. The analytic expression found for the transmitted beam allows to determine the beam parameters, the incidence angles, and the axial distance for which lateral displacements are compensated by angular deviations. Proposals to optimize experimental implementations are also briefly discussed.

physics.optics↗

arXiv2022

From the delay time in Quantum Mechanics to the Goos-Hänchen shift in Optics

Delay times in quantum mechanics always represented an intriguing challenge for physicists. Due to the fact that quantum mechanical experiments are, often, hard to be implemented, the possibility to connect delay times with laser lateral displacements gives us the opportunity to prepare, in optical laboratories, experiments which are equivalent to the quantum mechanical ones in detecting delay times. In this article, we will show in detail not only the relationship between delay times and Goos-Haenchen shifts, but also the close connection between the impulse change in quantum mechanics and angular deviations in optics. Lateral shifts are caused by the phase of Fresnel coefficients whereas angular deviations by the breaking of symmetry of the wave number distributions. The classical formula for the delay time is based on the use of the stationary phase method and contains a divergence for incidence at a critical potential energy. For Gaussian beams, the mean value calculation removes such a divergence. The closed expression for the delay time for incidence at critical energy show an excellent agreement with the numerical calculation. The three-dimensional analysis of delay times allow to find the final and definitive connection between wave packets reflected by a potential in quantum mechanics and optical beams reflected by a dielectric/air interface.

quant-ph↗

arXiv2021

Angular deviations: From a cubic equation to a universal closed formula to determine the peak position of reflected and (upper) transmitted beams

Angular deviations and lateral displacements are optical effects widely investigated in literature. In this paper, by using the Taylor expansion of the Fresnel coefficients, we obtain an analytic expression for the beam reflected by and (upper) transmitted through a dielectric prism. These analytical approximations lead to a cubic equation which allows to determine the angular deviations of the optical beams. Near the Brewster angles, under specific conditions, we obtain a universal formulation for the cubic equation. Its explicit solution determines the peak position of the reflected and (upper) transmitted beams. The universal solution could be of great utility in future experimental implementations. The analytic results show an excellent agreement with the numerical calculation and the analytic expressions given for the reflected and (upper) transmitted beams should play an important role in the weak measurements analysis.

physics.optics↗

arXiv2021

A modelling study across the Italian regions: Lockdown, testing strategy, colored zones, and skew-normal distributions. How a numerical index of pandemic criticality could be useful in tackling the CoViD-19

As Europe is facing the second wave of the CoViD-19 pandemic, each country should carefully review how it dealt with the first wave of outbreak. Lessons from the first experience should be useful to avoid indiscriminate closures and, above all, to determine universal (understandable) parameters to guide the introduction of containment measures to reduce the spreading of the virus. The use of few (effective) parameters is indeed of extreme importance to create a link between authorities and population, allowing the latter to understand the reason for some restrictions and, consequently, to allow an active participation in the fight against the pandemic. Testing strategies, fitting skew parameters (as mean, mode, standard deviation, and skewness), mortality rates, and weekly CoViD-19 spreading data, as more people are getting infected, were used to compare the first wave of the outbreak in the Italian regions and to determine which parameters have to be checked before introducing restrictive containment measures. We propose few \textit{universal} parameters that, once appropriately weighed, could be useful to correctly differentiate the pandemic situation in the national territory and to rapidly assign the properly pandemic risk to each region.

q-bio.PE↗

arXiv2020

Laser planar trapping

We investigate the phenomenon of the transverse breaking of symmetry of Gaussian lasers transmitted through dielectrics, showing for which incidence conditions and beam parameters it can be observed in optical experiments. The numerical analysis, done by using the integral form of the transmitted beam at the lower interface of a dielectric prism, shows, for incidence approaching the critical region, a laser planar trapping. By using an analytic approximation for the intensity of lower transmitted beam, we model the wave front curvature by a closed expression which depends on the refractive index, on the geometrical properties of the dielectric block, and, finally, on the incidence angle of the incoming beam. The analytic formula shows an excellent agreement with the numerical analysis and it could be useful in future experimental implementations.

physics.optics↗

arXiv2020

The quaternionic Goos-Haenchen shift

We investigate the lateral displacement of electronic waves when partially and totally reflected by a quaternionic potential. Following the analogy between Quantum Mechanics and Optics we introduce a refractive index for the complex and the pure quaternionic case. For incidence greater than the critical one (total reflection) the quaternionic potentials amplify the lateral displacement found in the complex case. For incidence below the critical angle, we find, in the quaternionic case, an additional shift. The analytical formula found for the quaternionic lateral displacement gives the possibility to observe quantitative and qualitative differences between the complex and quaternionic Goos-Haenchen shift.

quant-ph↗

arXiv2019

Power oscillations induced by the relative Goos-Haenchen phase

By using an optical interferometer composed of a dielectric laser ellipsometer, to change the optical response of transverse electric and magnetic incident radiation, and two polarisers, to trigger the interference pattern induced by the relative Goos-Haenchen phase, we show under which conditions it is possible to optimize the laser power oscillations induced by the relative phase difference between orthogonal polarised states. The Goos-Haenchen interference can then be used to sense rotation, to test optical components, and to simulate quarter and half wave plates.

physics.optics↗

arXiv2019

Quaternionic perturbation theory

In this paper we present a perturbation theory for constant quaternionic potentials. The effects of quaternionic perturbations are explicitly treated for bound states of hydrogen atom, infinite potential well and harmonic oscillator. Comparison with relativistic corrections is also briefly discussed.

quant-ph↗

arXiv2019

The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Haenchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted beam, it is possible to determine in which transversal and parallel dielectric blocks configuration the transversal symmetry breaking is maximized or when the symmetry is recovered. We also discuss the axial spreading delay.

physics.optics↗

arXiv2018

Incidence angles maximizing the Goos-Haenchen shift in seismic data analysis

In the solid/liquid and liquid/solid scenarios, for the cases in which the P and S reflected waves are represented by complex amplitudes, we give the closed formulas for the Goos-Haenchen phase from which we can then determine the lateral displacements. We compare the results of the analysis done by using the Zoeppritz equations with the calculations which appear in Optics. We also discuss under which circumstances the plane wave analysis is valid and what happens for critical incidence where divergences appear. For the liquid/solid interface, the incidence angles maximizing the lateral displacement are given as solutions of a polynomial equation.

physics.geo-ph↗

arXiv2018

Analytical and numerical analysis of the complete Lipkin-Meshkov-Glick Hamiltonian

The Lipkin-Meshkov-Glick is a simple, but not trivial, model of a quantum many-body system which allows us to solve the many-body Schrödinger equation without making any approximation. The model, which in its unperturbed case is composed only by two energy levels, includes two interacting terms. A first one, the $V$ interaction, which promotes or degrade pairs of particles, and a second one, the $W$ interaction, which scatters one particle in the upper and another in the lower energy level. In comparing this model with other approximation methods, the $W$ term interaction is often set to zero. In this paper, we show how the presence of this interaction changes the global structure of the system, generates degeneracies between the various eigenstates and modifies the energy eigenvalues structure. We present analytical solutions for systems of two and three particles and, for some specific cases, also for four, six and eight particles. The solutions for systems with more than eight particles are only numerical but their behaviour can be well understood by considering the extrapolations of the analytical results. Of particular interest it is the study of how the $W$ interaction affects the energy gap between the ground state and the first-excited state.

nucl-th↗

arXiv2018

Optimizing power oscillations in an ellipsometric system

Ellipsometry is a powerful and well-established optical technique used in the characterisation of materials. It works by combining the components of elliptically polarized light in order to draw information about the optical system. We propose an ellipsometric experimental set up to study polarization interference in the total internal reflection regime for Gaussian laser beams. The relative phase between orthogonal states can be measured as a power oscillation of the optical beam transmitted through a dielectric block and whose orthogonal components are then mixed by a polarizer. We show under which conditions the plane wave analysis is valid and when the power oscillation can be optimized to reproduce a full pattern of oscillation and to simulate quarter and half wave plates.

physics.optics↗

arXiv2018

Optical weak measurements without removing the Goos-Haenchen phase

Optical weak measurements are a powerful tool for measuring small shifts of optical paths. When applied to the measurement of the Goos-Haenchen shift, in particular, a special step must be added to its protocol: the removal of the relative Goos-Haenchen phase, since its presence generates a destructive influence on the measurement. There is, however, a lack of description in the literature of the precise effect of the Goos-Haenchen phase on weak measurements. In this paper we address this issue, developing an analytic study for a Gaussian beam transmitted through a dielectric structure. We obtain analytic expressions for weak measurements as a function of the relative Goos-Haenchen phase and show how to remove it without the aid of waveplates.

physics.optics↗

arXiv2017

Optimizing weak measurements to detect angular deviations

We analyze and compare the angular deviations for an optical beam reflected by and transmitted through a dielectric triangular prism. The analytic expressions derived for the angular deviations hold for arbitrary incidence angles. For incidence approaching the internal and external Brewster angles, the angular deviations transverse magnetic waves present the same behavior leading to the well-known giant Goos-Haenchen angular shift. For incidence near the critical angle a new region of large shift is seen both for transverse magnetic and transverse electric waves. While a direct measuring procedure is better in the vicinity of the Brewster region, a weak measurement breaks off the giant Goos-Haenchen effect, preserving the amplification in the critical region. We discuss under which conditions it is possible to optimize the amplification and we also determine when a weak measurement is preferred to a direct measuring procedure.

physics.optics↗

arXiv2017

The oscillatory behavior of light in the composite Goos-Haenchen shift

For incidence in the critical region, the propagation of gaussian lasers through triangular dielectric blocks is characterized by the joint action of angular deviations and lateral displacements. This mixed effect, known as composite Goos-Haenchen shift, produces a lateral displacement dependent on the axial coordinate, recently confirmed by a weak measurement experiment. We discuss under which conditions this axial lateral displacement, which only exists for the composite Goos-Haenchen shift, presents an oscillatory behavior. This oscillation phenomenon shows a peculiar behavior of light for critical incidence and, if experimentally tested, could stimulate further theoretical studies and lead to interesting optical applications.

physics.optics↗

arXiv2016

Experimental confirmation of the transversal symmetry breaking in laser profiles

The Snell phase effects on the propagation of optical beams through dielectric blocks have been matter of recent theoretical studies. The effects of this phase on the laser profiles have been tested in our experiment. The data show an excellent agreement with the theoretical predictions confirming the axial spreading modification and the transversal symmetry breaking. The possibility to set, by rotating the dielectric blocks, different configurations allows to recover the transversal symmetry. Based on this experimental evidence, dielectric blocks can be used as alternative optical tools to control the beam profile.

physics.optics↗

arXiv2016

Weak measurement og the composite Goo-Haenchen shift in the critical region

By using a weak measurement technique, we investigated the interplay between the angular and lateral Goos-Haenchen shift of a focused He-Ne laser beam for incidence near the critical angle. We verified that this interplay dramatically affects the composite Goos-Haenchen shift of the propagated beam. The experimental results confirm theoretical predictions that recently appeared in the literature.

physics.optics↗

arXiv2016

Transversal symmetry breaking and axial spreading modification for Gaussian optical beams

For a long time it was believed there was no reason to include the geometrical phase in studying the propagation of gaussian optical beams through dielectric blocks. This can be justified by the fact that the first order term in the Taylor expansion of this phase is responsible for the lateral shift of the optical beam which is also predicted by ray optics. From this point of view, the geometrical phase can be seen as a purely auxiliary concept. In this paper, we show how the second order term in the Taylor expansion accounts for the symmetry breaking of the transversal spatial distribution and acts as an axial spreading modifier. These new effects clearly shows the importance of the geometrical phase in describing the correct behavior of light. To test our theoretical predictions, we briefly discuss a possible experimental implementation.

physics.optics↗