Publications by authors named "Timor Melamed"

An efficient scheme for the design of aperture fields (distributed sources) that radiate arbitrary trajectory curved (accelerating) beams, with enhanced controllability of various beam features, is presented. The scheme utilizes a frame-based phase-space representation of aperture fields to overcome the main hurdles in the design for large apertures: First, it uses the a-priory localization of caustic beams to significantly reduce the optimization problem's variable space, to that of few Gaussian window coefficients accurately capturing those beams. Then, the optimization problem is solved in the reduced (local) spectral domain.

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We present an algorithm for manipulating and controlling 3-D field patterns, with energy confined to the narrow vicinity of predefined 3-D trajectories in free-space, which are of arbitrary curvature and torsion. This is done by setting the aperture field's phase to form smooth caustic surfaces that include the desired trajectory. The aperture amplitude distribution is constructed to manipulate both the on-axis intensity profile and the off-axis beam-width, and is updated iteratively.

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We present a practical algorithm for designing an aperture field (source) that propagates along a predefined generic beam trajectory that consists of both convex and concave sections. We employ here the mechanism that forms the well-known Airy beam in which the beam trajectory follows a smooth convex caustic of the geometric optics rays and generalize it for a class of beams that are referred to as "caustic beams" (CBs). The implementation is based on "back-tracing" rays from the predefined beam trajectory to the source's aperture to form its phase distribution.

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The present contribution is concerned with applying beam-type expansion to a planar aperture time-dependent (TD) electromagnetic field in which the propagating elements, the electromagnetic pulsed-beams, are a priori decomposed into transverse electric (TE) and transverse magnetic (TM) field polarizations. The propagating field is described as a discrete superposition of tilted, shifted, and delayed TE and TM electromagnetic pulsed-beam propagators over the frame spectral lattice. These waveobjects are evaluated by using TD plane-wave spectral representations.

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The current contribution is concerned with obtaining the relativistic two-dimensional (three-dimensional in relativity jargon) Green's function of a time-harmonic line current that is embedded in a moving dielectric-magnetic medium with a planar discontinuity. By applying a plane-wave (PW) spectral representation for the relativistic electromagnetic Green's function of a dielectric-magnetic medium that is moving in a uniform velocity, the exact reflected and transmitted (refracted) fields are obtained in the form of a spectral integral over PWs in the so-called laboratory and comoving frames. We investigate these spectral representations, as well as their asymptotic evaluations, and discuss the associated relativistic wave phenomena of direct reflected/transmitted rays and relativistic head waves (lateral waves).

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The present contribution is concerned with applying beam-type expansion to planar aperture time-harmonic electromagnetic field distribution in which the propagating elements, the electromagnetic beam-type wave objects, are decomposed into transverse electric (TE) and transverse magnetic (TM) field constituents. This procedure is essential for applying Maxwell's boundary conditions for solving different scattering problems. The propagating field is described as a discrete superposition of tilted and shifted TE and TM electromagnetic beams over the frame-based spatial-directional expansion lattice.

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The present work is concerned with applying a ray-centered non-orthogonal coordinate system which is a priori matched to linearly-phased localized aperture field distributions. The resulting beam-waveobjects serve as the building blocks for beam-type spectral expansions of aperture fields in 2D inhomogeneous media that are characterized by a generic wave-velocity profile. By applying a rigorous paraxial-asymptotic analysis, a novel parabolic wave equation is obtained and termed "Non-orthogonal domain parabolic equation"--NoDope.

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The phase-space beam summation is a general analytical framework for local analysis and modeling of radiation from extended source distributions. In this formulation, the field is expressed as a superposition of beam propagators that emanate from all points in the source domain and in all directions. In this Part I of a two-part investigation, the theory is extended to include propagation in anisotropic medium characterized by a generic wave-number profile for time-harmonic fields; in a companion paper [J.

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