Related papers: Sub-luminal wave bullets: Exact Localized sublumin…
We show that localized (non-evanescent) solutions to Maxwell equations exist, which propagate without distortion along normal waveguides with Superluminal speed.
In recent experiments, localized and stationary pulses have been generated in second-order nonlinear processes with femtosecond pulses, whose asymptotic features relate with those of nondiffracting and nondispersing polychromatic Bessel…
In this paper, we develop a theoretical analysis to efficiently handle superpositions of waves with concentrated wavevector and frequency spectra, allowing an easy analytical description of fields with interesting transverse profiles.…
Recognized for their non-diffracting properties, Bessel beams can be conveniently combined to generate the so-called Frozen Waves, which are monochromatic beams endowed with topological charge and whose longitudinal intensity pattern can be…
This is a summary directed to PhD students of the research work conducted on the problem of the production of "light bullets", or multidimensional wave packets that propagate without distortion in unbounded, homogeneous, nonlinear media,…
The existence of resonant enhanced transmission and collimation of light waves by subwavelength slits in metal films [for example, see T.W. Ebbesen et al., Nature (London) 391, 667 (1998) and H.J. Lezec et al., Science, 297, 820 (2002)]…
The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general…
In recent years the topic of localized wave solutions of the homogeneous scalar wave equation, i.e., the wave fields that propagate without any appreciable spread or drop in intensity, has been discussed in many aspects in numerous…
Shaping electron beams with the cycles of light provides femtosecond and attosecond time resolution in electron microscopy and enables fundamental quantum-coherent measurements. However, efficient light-electron control requires a prolonged…
In this paper we analyze the physical meaning of sub- and superluminal soliton-like solutions (as the X-waves) of the relativistic wave equations and of some non-trivial solutions of the free Schr\"odinger equation for which the concepts of…
In this work we construct Gaussian beam approximations to solutions of the high frequency Helmholtz equation with a localized source. Under the assumption of non-trapping rays we show error estimates between the exact outgoing solution and…
This paper is concerned with the asymptotic description of high-frequency waves in locally periodic media. A key issue is that the Bloch-dispersion curves vary with the local microstructure, giving rise to hidden singularities associated…
Ultrasonic superresolution images can be generated by means of (super) focusing acoustic beams to subwavelength dimensions or using algorithm-based methods. Here, we demonstrate that ultrasonic pulses which are superfocused by a ball-shaped…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
The existence of resonant enhanced transmission and collimation of light waves by subwavelength slits in metal films [for example, see T.W. Ebbesen et al., Nature (London) 391, 667 (1998) and H.J. Lezec et al., Science, 297, 820 (2002)]…
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…
Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell-Bloch equations. The nonlocal symmetries of the reduced Maxwell-Bloch equations are obtained by the truncated…
We present a mathematical approach that simplifies the theoretical treatment of electromagnetic localization in random media and leads to closed form analytical solutions. Starting with the assumption that the dielectric permittivity of the…
Overcoming the diffraction limit, meaning focusing waves on a sub-wavelength scale, has received considerable attention for applications involving light and acoustics. Indeed, the intense focusing achieved enhances the interactions between…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…