Related papers: Diffraction of wave packets in space and time in t…
Starting from the wave equation for a medium with material properties that vary periodically, we study a system of recurrence relations that describe propagation of wave packets that oscillate on the microscale (i.e. on lengths of the order…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with…
We study the diffusion of monochromatic classical waves in a disordered acoustic medium by scattering theory. In order to avoid artifacts associated with mathematical point scatterers, we model the randomness by small but finite insertions.…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…
We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…
We depict and analyze a new effect for wavepackets falling freely under a barrier or well. The effect appears for wavepackets whose initial spread is smaller than the combination $\ds \sqrt{\frac{l_g^3}{|z_0|}}$, between the gravitational…
Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by…
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…
The dielectric function for electron gas with parabolic energy bands is derived in a fractional dimensional space. The static response function shows a good dimensional dependance. The plasma frequencies are obtained from the roots of the…
We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation…
We consider the scattering of linear waves in two dimensions by a rectangular region at the junction of four waveguides. A solution to the frequency domain problem is obtained by exploiting reflective symmetry to reduce the full problem to…
We describe a simple experimental apparatus which allows one to observe the wave properties of light in a new way. This apparatus also makes possible to introduce and illustrate, in a very suggestive way, some fundamental principles of…
Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics, such as propagation invariance and tunable group velocity. We study in…
A theory of light transmission through a quantum well (QW) in a magnetic field perpendicular to the QW plane is developed. The light wave length is supposed comparable with the QW width. The formulas for reflection, absorption and…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are…