An exact transverse Helmholtz equation

We derive an exact equation for the transverse component of the electric field propagating along a given longitudinal z direction in the presence of an isotropic refractive-index distribution n(x,y)

The case of the oscillating party balloon: A simple toy experiment requiring a not-so-simple interpretation

The intriguing midair oscillations of a party balloon, which occur once its buoyancy is no longer capable of keeping it against the ceiling, is shown to require a rather sophisticated explanation in terms of variable-mass dynamics. The ubiquity of this phenomenon, the accessibility of its actual observation, and the subtlety of its analytic description provide a good opportunity for an interesting zero-cost classroom demonstration

Vectorial nonparaxial propagation equation in the presence of a tensorial refractive-index perturbation

The standard scalar paraxial parabolic (FockLeontovich) propagation equation is generalized to include all-order nonparaxial corrections in the significant case of a tensorial refractive-index perturbation on a homogeneous isotropic background. In the resultant equation, each higher-order nonparaxial term (associated with diffraction in homogeneous space and scaling as the ratio between beam waist and diffraction length) possesses a counterpart (associated with the refractive-index perturbation) that allows one to preserve the vectorial nature of the problem (∇∇· E ≠ 0). The tensorial character of the refractive-index variation is shown to play a particularly relevant role whenever the tensor elements δnxz and δnyz (z is the propagation direction) are not negligible. For this case, an application to elasto-optically induced optical activity and to nonlinear propagation in the presence of the optical Kerr effect is presented

Perfect Optical Solitons: Spatial Kerr Solitons as Exact Solutions of Maxwell's Equations

We prove that spatial Kerr solitons, usually obtained in the frame of nonlinear Schroedinger equation valid in the paraxial approximation, can be found in a generalized form as exact solutions of Maxwell's equations. In particular, they are shown to exist, both in the bright and dark version, as linearly polarized exactly integrable one-dimensional solitons, and to reduce to the standard paraxial form in the limit of small intensities. In the two-dimensional case, they are shown to exist as azimuthally polarized circularly symmetric dark solitons. Both one and two-dimensional dark solitons exhibit a characteristic signature in that their asymptotic intensity cannot exceed a threshold value in correspondence of which their width reaches a minimum subwavelength value.Comment: 19 pages, 11 figure. Submitted for publication on Josa

Mapping the Americanization of English in Space and Time

As global political preeminence gradually shifted from the United Kingdom to the United States, so did the capacity to culturally influence the rest of the world. In this work, we analyze how the world-wide varieties of written English are evolving. We study both the spatial and temporal variations of vocabulary and spelling of English using a large corpus of geolocated tweets and the Google Books datasets corresponding to books published in the US and the UK. The advantage of our approach is that we can address both standard written language (Google Books) and the more colloquial forms of microblogging messages (Twitter). We find that American English is the dominant form of English outside the UK and that its influence is felt even within the UK borders. Finally, we analyze how this trend has evolved over time and the impact that some cultural events have had in shaping it.Comment: 16 pages, 6 figures, 2 tables. Published versio

Electromagnetic propagation in a turbulent medium: a new approach

A formalism based on coupled-mode theory is presented that allows one to deduce the equations of evolution of the correlation functions of the field propagating in a turbulent medium. As a particular application, the second-order correlation function is evaluated under less stringent conditions than those usually required in the frame of optical propagation theories in random media

Phase conjugation by degenerate four-wave mixing and temporal coherence

The influence of the temporal-coherence properties of the pump and signal waves on the efficiency and the temporal fidelity of the phase-conjugation process associated with degenerate four-wave mixing is examined

Soliton propagation in multimode optical fibers

Soliton propagation in a multimode optical fiber in the presence of an intensity-dependent refractive index is investigated by means of a set of nonlinear coupled equations derived in the frame of coupled-mode theory. In particular, the conditions on modal amplitudes and modal dispersion necessary for soliton existence are derived