Dynamics of light propagation in spatiotemporal dielectric structures

Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the refractive index are studied by using a two-component, highly symmetric version of Maxwell's equations. The use of any slow varying amplitude approximation is avoided. Transfer matrices of sharp nonstationary interfaces are calculated explicitly, together with the amplitudes of all secondary waves produced in the scattering. Time-varying multilayer structures and spatiotemporal lenses in various configurations are investigated analytically and numerically in a unified approach. Several new effects are reported, such as pulse compression, broadening and spectral manipulation of pulses by a spatiotemporal lens, and the closure of the forbidden frequency gaps with the subsequent opening of wavenumber bandgaps in a generalized Bragg reflector

X and Y waves in the spatiotemporal Kerr dynamics of a self-guided light beam

The nonlinear stage of development of the spatiotemporal instability of the monochromatic Townes beam in a medium with self-focusing nonlinearity and normal dispersion is studied by analytical and numerical means. Small perturbations to the self-guided light beam are found to grow into two giant, splitting Y pulses featuring shock fronts on opposite sides. Each shocking pulse amplifies a co-propagating X wave, or dispersion- and diffraction-free linear wave mode of the medium, with super-broad spectrum.Comment: 9 pages, 9 figure

Criterion for traffic phases in single vehicle data and empirical test of a microscopic three-phase traffic theory

A microscopic criterion for distinguishing synchronized flow and wide moving jam phases in single vehicle data measured at a single freeway location is presented. Empirical local congested traffic states in single vehicle data measured on different days are classified into synchronized flow states and states consisting of synchronized flow and wide moving jam(s). Then empirical microscopic characteristics for these different local congested traffic states are studied. Using these characteristics and empirical spatiotemporal macroscopic traffic phenomena, an empirical test of a microscopic three-phase traffic flow theory is performed. Simulations show that the microscopic criterion and macroscopic spatiotemporal objective criteria lead to the same identification of the synchronized flow and wide moving jam phases in congested traffic. It is found that microscopic three-phase traffic models can explain both microscopic and macroscopic empirical congested pattern features. It is obtained that microscopic distributions for vehicle speed difference as well as fundamental diagrams and speed correlation functions can depend on the spatial co-ordinate considerably. It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic states are qualitatively different. The reason for this is that important spatiotemporal features of congested traffic patterns are it lost in these as well as in many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models, specifically, cellular automata traffic flow models.Comment: 27 pages, 16 figure

On the nature of spatiotemporal light bullets in bulk Kerr media

We present a detailed experimental investigation, which uncovers the nature of light bullets generated from self-focusing in a bulk dielectric medium with Kerr nonlinearity in the anomalous group velocity dispersion regime. By high dynamic range measurements of three-dimensional intensity profiles, we demonstrate that the light bullets consist of a sharply localized high-intensity core, which carries the self-compressed pulse and contains approximately 25% of the total energy, and a ring-shaped spatiotemporal periphery. Sub-diffractive propagation along with dispersive broadening of the light bullets in free space after they exit the nonlinear medium indicate a strong space-time coupling within the bullet. This finding is confirmed by measurements of spatiotemporal energy density flux that exhibits the same features as stationary, polychromatic Bessel beam, thus highlighting the physical nature of the light bullets