Related papers: Circles in diffraction
This paper establishes connections between the group-Fourier transform and the geometry of measures in the Heisenberg group. Firstly, it is shown that if the Fourier transform of a compactly supported, finite, Radon measure is square…
We show theoretically that a directional dipole wave can be perfectly reflected by a single point-like oscillating dipole. Furthermore, we find that in the case of a strongly focused plane wave up to 85 % of the incident light can be…
We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three…
For typical perturbations of convex integrable Hamiltonian system with three degrees of freedom, a path of diffusion is established to cross strong double resonant point. Together with the uniform hyperbolicity of invariant cylinders got in…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
X-ray diffractometers primarily designed for surface x-ray diffraction are often used to measure the diffraction from powders, textured materials, and fiber-texture samples in so-called $2\theta$ scans. Unlike high-energy powder diffraction…
The formula for the frequency shift of a plane-polarized light wave reflected from a uniformly moving mirror is derived directly from the constant light speed postulate and the basic principles of wave optics. Unlike the original derivation…
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension.…
Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…
Optical cavities provide high sensitivity to dispersion since their resonance frequencies depend on the index of refraction. We present a direct, broadband, and accurate measurement of the modes of a high finesse cavity using an optical…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
A simple method for presenting a dynamic transition between Fresnel and Fraunhofer diffraction zones is considered. Experiments are conducted on different apertures and diffraction patterns are photographed at various distances between the…
We derive analytical expressions to describe how light is frequency-shifted when interacting with ultrasound within scattering media, due to the modulation of the refractive index induced by the ultrasound pressure waves. The model is…
The distributions of the angular transmission coefficient and of the total transmission are calculated for multiple scattered waves. The calculation is based on a mapping to the distribution of eigenvalues of the transmission matrix. The…
Interfering liquid surface waves are generated by electrically driven vertical oscillations of two or more equispaced pins immersed in a liquid (water). The corresponding intensity distribution, resulting from diffraction of monochromatic…
In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…
We study transmission and reflection properties of a perfectly amplifying as well as absorbing medium analytically by using the tight binding equation. Different expressions for transmittance and reflectance are obtained for even and odd…
We follow the trajectories of phase singularities at nulls of intensity in the speckle pattern of waves transmitted through random media as the frequency of the incident radiation is scanned in microwave experiments and numerical…