相关论文: Invisible obstacles
We propose a universal strategy to realize a broadband control on arbitrary scatterers, through multiple coherent beams. By engineering the phases and amplitudes of incident beams, one can suppress the dominant scattering partial waves,…
A method is given for creating material with a desired refraction coefficient. The method consists of embedding into a material with known refraction coefficient many small particles of size $a$. The number of particles per unit volume…
We consider waves travelling in two different mediums each endowed with a different constant speed of propagation. At the interface between the two mediums, the refraction of the rays of the optic geometry is described by the…
Microscopy and optical imaging are drastically limited by the inhomogeneities encountered by the light while propagating from the object of interest to the detection system. In this context, adaptive optics and wavefront manipulation are…
We consider the propagation of waves in a waveguide with Neumann boundary conditions. We work at low wavenumber with only one propagating mode in the leads, all the other modes being evanescent. We assume that the waveguide is symmetric…
Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied…
The transformation cycle and associated inequality are suggested for the basic demonstration of the wavefunction reduction in a mesoscopic qubit in measurements with quantum-limited detectors. Violation of the inequality would show directly…
We study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects. We derive the…
This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…
Black holes are by definition black, and therefore cannot be directly observed by using electromagnetic radiations. Convincing identification of black holes must necessarily depend on the identification of a very specially behaving matter…
Achieving quantum-limited motional control of optically trapped particles beyond the sub-micrometer scale is an outstanding problem in levitated optomechanics. A key obstacle is solving the light scattering problem and identifying particle…
Wave scattering is considered in a medium in which many small particles are embedded. Equations for the effective field in the medium are derived when the number of particles tends to infinity.
We calculate the ``seeing'' effect on distant sources due to a gravitational wave background. We derive the limit in strain and energy density of the gravitational wave based on the limit of detectability of this effect with the present day…
We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family…
An extended interference pattern close to surface may result in both a transmissive or evanescent surface fields for large area manipulation of trapped particles. The affinity of differing particle sizes to a moving standing wave light…
Obstacles to integrability sometimes hamper the standard Normal Form analysis of perturbed integrable evolution equations. One is then forced to account for them by the Normal Form, which is the dynamical equation obeyed by the zero-order…
Quantum theory implies, and empirical evidence confirms, that while particles $\textit{can}$ exhibit wave-like behavior in interferometric experiments, this behavior is so limited as $\textit{not}$ to allow for third- and higher-order…
Pilot wave theory endows particles with definite positions at all times governed by deterministic dynamics. However, individual particle trajectories are generically undetectable by experiment. This idea might seem to be contested in light…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…