arXiv subjects
Publications and source records attributed to Andrea Aiello.
In this work we review and further develop the controversial concept of "classical entanglement" in optical beams. We present a unified theory for different kinds of light beams exhibiting classical entanglement and we indicate several possible extensions of the concept. Our results shed new light upon the physics at the debated border between the classical and the quantum representations of the world.
We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange equations reproduces either Helmholtz and paraxial wave equations with the $z$-coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energy-momentum tensor and determine the continuity equations relating "energy" and "momentum" of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.
We generate tightly focused optical vector beams whose electric fields spin around an axis transverse to the beams' propagation direction. We experimentally investigate these fields by exploiting the directional near-field interference of a dipole-like plasmonic field probe, placed adjacent to a dielectric interface, which depends on the transverse electric spin density of the excitation field. Near- to far-field conversion mediated by the dielectric interface enables us to detect the directionality of the emitted light in the far-field and, therefore, to measure the transverse electric spin density with nanoscopic resolution. Finally, we determine the longitudinal electric component of Belinfante's elusive spin momentum density, a solenoidal field quantity often referred to as 'virtual'.
Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.
We present a study of radially and azimuthally polarized Bessel-Gauss beams in both the paraxial and nonparaxial regimes. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for Bessel-Gauss beams. We show that, independently from the ratio between the Bessel aperture cone angle $\vartheta_0$ and the Gauss beam divergence $θ_0$, the nonparaxial corrections are always very small and therefore negligible. Explicit expressions for the nonparaxial vector electric field components are also reported.
We discuss how to implement the Legendre transform using the Faddeev-Popov method of Quantum Field Theory. By doing this, we provide an alternate way to understand the essence of the Faddeev-Popov method, using only concepts that are very familiar to the students (such as the Legendre transform), and without needing any reference to Quantum Field Theory. Two examples of Legendre transform calculated with the Faddeev-Popov method are given to better clarify the point.
Numerical evolutions of whispering gallery modes of both isotropic and anisotropic spheroidal resonators are presented and used to build analytical approximations of these modes. Such approximations are carried out mainly to have the possibility to have a manageable analytic formulas for the eigenmodes and eigenfrequencies of anisotropic resonators. A qualitative analysis of ellipsoidal anisotropic modes in term of superposition of spherical modes is also presented.
Quantum approaches relying on entangled photons have been recently proposed to increase the efficiency of optical measurements. We demonstrate here that, surprisingly, the use of classical light with entangled degrees of freedom can also bring outstanding advantages over conventional measurements in polarization metrology. Specifically, we show that radially polarized beams of light allow to perform real-time single-shot Mueller matrix polarimetry. Our results also indicate that quantum optical procedures requiring entanglement without nonlocality can be actually achieved in classical optics regime.
Traditionally, the angular momentum of light is calculated for "bullet-like" electromagnetic wave packets, although in actual optical experiments "pencil-like" beams of light are more commonly used. The fact that a wave packet is bounded transversely and longitudinally while a beam has, in principle, an infinite extent along the direction of propagation, renders incomplete the textbook calculation of the spin/orbital separation of the angular momentum of a light beam. In this work we demonstrate that a novel, extra surface part must be added in order to preserve the gauge invariance of the optical angular momentum per unit length. The impact of this extra term is quantified by means of two examples: a Laguerre-Gaussian and a Bessel beam, both circularly polarized.
In a comment, Wang, Zhu and Zubairy repeat their previous claim that the spatial Goos-Hänchen (GH) shift happening at total internal reflection at a dielectric-air interface depends on the spatial coherence of the incident beam. This contradicts our theoretical and experimental findings. Here, we show that the apparent disagreement between their numerical simulations and our results occurs only in a parameter range where the concept of a spatial beam shift is invalid, and that therefore their claim is inapplicable. We clarify this by discussing two key issues.
We report on a new class of exact solutions of the scalar Helmholtz equation obtained by carefully engineering the form of the angular spectrum of a Bessel beam. We consider in particular the case in which the angular spectrum of such generalized beams has, in the paraxial zone, the same radial structure as Laguerre-Gaussian beams. We investigate the form of these new beams as well as their peculiar propagation properties.
We study the classical optics effects known as Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-vs-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transverse components of the wave vector. Moreover, we extent our treatment to the enhancement of beam shifts via weak measurements and relate our results to recent experiments.
The spin Hall effect of light (SHEL) is the photonic analogue of spin Hall effects occurring for charge carriers in solid-state systems. Typical examples of this intriguing phenomenon occur when a light beam refracts at an air-glass interface, or when it is projected onto an oblique plane, the latter effect being known as geometric SHEL. It amounts to a polarization-dependent displacement perpendicular to the plane of incidence. Here, we experimentally demonstrate the geometric SHEL for a light beam transmitted across an oblique polarizer. We find that the spatial intensity distribution of the transmitted beam depends on the incident state of polarization and its centroid undergoes a positional displacement exceeding one wavelength. This novel phenomenon is virtually independent from the material properties of the polarizer and, thus, reveals universal features of spin-orbit coupling.
Polarizers are key components in optical science and technology. Thus, understanding the action of a polarizer beyond oversimplifying approximations is crucial. In this work, we study the interaction of a polarizing interface with an obliquely incident wave experimentally. To this end, a set of Mueller matrices is acquired employing a novel procedure robust against experimental imperfections. We connect our observation to a geometric model, useful to predict the effect of polarizers on complex light fields.
In the recent and very enjoyable paper (Paul Strange, "Semiclassical and Quantum Analysis of a Focussing Free Particle Hermite Wavefunction", arXiv:1309.6753[quant-ph]), Professor Strange has studied a particular solution of the free particle Schroedinger equation in which the time and space dependence are not separable. After recognizing the fact that "The Schroedinger equation has an identical mathematical form to the paraxial wave equation [...]", he claims to "describe and try to gain insight into an exotic, apparently accelerating solution of the free particle Schroedinger equation that is square integrable and which also displays some unusual characteristics." It is the main aim of this short note to show that the wavefunction described by Prof. Strange is simply one particular Hermite-Gauss solution of the paraxial wave equation and even more "exotic" examples can be found by considering, e.g., Laguerre-Gauss solutions.
Recently, it was shown that a non-zero transverse angular momentum manifests itself in a polarization dependent intensity shift of the barycenter of a paraxial light beam [A. Aiello et al., Phys. Rev. Lett. 103, 100401 (2009)]. The underlying effect is phenomenologically similar to the spin Hall effect of light, but does not depend on the specific light-matter interaction and can be interpreted as a purely geometric effect. Thus, it was named the geometric spin Hall effect of light. Here, we experimentally investigate the appearance of this effect in tightly focused vector-beams. We use an experimental nano-probing technique in combination with a reconstruction algorithm to verify the relative shifts of the components of the electric energy density in the focal plane, which are linked to the intensity shift. By that, we experimentally demonstrate the geometric spin Hall effect of light in a focused light beam.
We study the problem of particle indistinguishability for the three cases known in nature: identical classical particles, identical bosons and identical fermions. By exploiting the fact that different types of particles are associated with Hilbert space vectors with different symmetries, we establish some relations between the expectation value of several different operators, as the particle number one and the interparticle correlation one, evaluated for states of a pair of identical (a) classical particles, (b) bosons and (c) fermions. We find that the quantum behavior of a pair of identical classical particles has exactly half fermionic and half bosonic characteristics.
We address the question of whether there exists a hidden relationship between the near-field distribution generated by an oscillating electric dipole and the so-called cross polarization of a collimated beam of light. We find that the answer is affirmative by showing that the complex field distributions occurring in both cases have a common physical origin: the requirement that the electromagnetic fields must be transverse.