Related papers: A bound on group velocity for Bloch wave packets
The universal theory of weakly nonlinear wave packets given by the nonlinear Schr\"odinger equation is revisited. In the limit where the group and phase velocities are very close together, a multiple scale analysis carried out beyond all…
By using a recently derived upper bound on the allowed equilibrium current in a ring, it is proved that the magnitude of the group velocity of a Bloch electron in a one-dimensional periodic potential is always less than or equal to the…
The motion of a quantum particle in a one-dimensional periodic potential can be described in terms of Bloch wave packets. Like free-particle wave packets, they can propagate without attenuation. Here, we examine this similarity more closely…
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct…
We investigate the behavior of waves in a periodic medium containing small soft inclusions or cavities of arbitrary shape, such that the homogeneous Dirichlet conditions are satisfied at the boundary. The leading terms of Bloch waves, their…
The group velocity of 'space-time' wave packets $-$ propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations $-$ can take on arbitrary values in free space. Here we investigate theoretically and…
All known realizations of optical wave packets that accelerate along their propagation axis, such as Airy wave packets in dispersive media or wave-front-modulated X-waves, exhibit a constant acceleration; that is, the group velocity varies…
We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\R^n$, $n \in \{1, 2, 3\}$. Standard homogenization theory provides, for the limit of a small periodicity length…
We consider Bloch oscillations of Bose-Einstein condensates in presence of a time-modulated s-wave scattering length. Generically, interaction leads to dephasing and decay of the wave packet. Based on a cyclic-time argument, we…
We consider acoustic wave propagation through a periodic array of the inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength is fixed. We derive and rigorously justify the dispersion…
Mugnai et al. have reported an experiment in which microwave packets appear to travel in air with a speed substantially greater than c. They calculate the group velocity of their packets and find that it agrees with their experimental…
The semiclassical equations of motion for a Bloch electron include an anomalous velocity term analogous to a $k$-space "Lorentz force", with the Berry connection playing the role of a vector potential. By examining the adiabatic evolution…
We developed a novel universal eigenvalue analysis for 2D arbitrary nanostructures comprising dispersive and lossy materials. The complex dispersion relation (or complex Bloch band structure) of a metallic grating is rigorously calculated…
We consider wave propagation and scattering governed by one dimensional Schrodinger operators with truncated periodic potentials. The propagation of wave packets with narrow frequency supports is studied. The goal is to describe potentials…
We consider the propagation of acoustic, electromagnetic and elastic waves in a one-dimensional periodic two-component material. Accurate asymptotic formulas are provided for the group velocity as a function of the material parameters when…
We consider pulse propagation in a linear anomalously dispersive medium where the group velocity exceeds the speed of light in vacuum (c) or even becomes negative. A signal velocity is defined operationally based on the optical…
Bloch oscillations of spatio-temporal light wave packets in arrays of nonlinear fibers with high-order dispersion are studied. The light wave experiences discrete spatial diffraction along the waveguide array coordinate together with…
Although a plethora of techniques are now available for controlling the group velocity of an optical wave packet, there are very few options for creating accelerating or decelerating wave packets whose group velocity varies controllably…
Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…
A universal relation has been established between the local energy transport velocity along the direction of propagation and the group velocity of scalar and vector-valued propagation-invariant spatiotemporally localized superluminal and…