相关论文: Wide angle near-field diffraction and Wigner distr…
The Wigner time delay of slow particles in the process of their elastic scattering by complex targets formed by several zero-range potentials is investigated. It is shown that at asymptotically large distances from the target, the…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
Diffraction in time of matter waves incident on a shutter which is removed at time $t=0$ is studied in the presence of a linear potential. The solution is also discussed in phase space in terms of the Wigner function. An alternative…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
In this paper, the partial-wave expansion method is applied to describe the difference-frequency pressure generated in a nonlinear scattering of two acoustic waves with an arbitrary wavefront by means of a rigid sphere. Particularly, the…
Wigner distributions play a significant role in formulating the phase space analogue of quantum mechanics. The Schrodinger wave-functional for solitons is needed to derive it for solitons. The Wigner distribution derived can further be used…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
The surface current method known in the theory of electromagnetic waves diffraction is generalized to be applied for the problems of diffraction radiation generated by a charged particle moving nearby an ideally-conducting screen in vacuum.…
By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the time- frequency characteristics of signals which exhibit transient os-…
As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has been increasingly paid attention to in the past decade. Here, in light of Huygens-Fresnel principle, we propose a theoretical frame to study…
We consider the propagation of flexural waves across a nearly flat, thin membrane, whose stress-free state is curved. The stress-free configuration is specified by a quenched height field, whose Fourier components are drawn from a Gaussian…
The far-field pattern of a simple one-dimensional laser array of emitters radiating into free space is considered. In the path of investigating the inverse problem for their near fields leading to a target beam form, surprisingly we found…
Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector…
In this work, near-field imaging by two strongly coupled arrays of split ring resonators is analyzed. A simple theoretical model is developed to obtain the transfer function of the lens. This model shows that magnetoinductive surface waves…
A uniform asymptotic theory of the free-space paraxial propagation of coherent flattened Gaussian beams is proposed in the limit of nonsmall Fresnel numbers. The pivotal role played by the error function in the mathematical description of…
The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
Surface plasmons are usually described as surface waves with either a complex wavevector or a complex frequency. When discussing their merits in terms of field confinment or enhancement of the local density of states, controversies…
Quasicrystals are tempered distributions $\mu$ which satisfy symmetric conditions on $\mu$ and $\widehat \mu$. This suggests that techniques from time-frequency analysis could possibly be useful tools in the study of such structures. In…