Related papers: Fourier Transform of Annular Beams
Decades of work on beam deformation on reflection, and especially on lateral shifts, have spread the idea that a reflected beam is larger than the incident beam. However, when the right conditions are met, a beam reflected by a multilayered…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
Predicting the effects of physical perturbations on optical channels is critical for advanced photonic devices, but existing modelling techniques are often computationally intensive or require exhaustive characterisation. We present a novel…
A two-dimensional Fourier transform of hadron form factors allows to determine their charge density in transverse space. We show that this method can be applied to any virtual photon induced transition, such as \gamma *(q)+N -> \pi N. Only…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…
Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for…
The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical…
To describe longitudinal fine structure like microbunching within a particle beam, a classical approach is to define a bunching factor which is the Fourier transform of the particle longitudinal density distribution. Such a 1D definition of…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
The transition from the near to the far field of the fundamental mode radiating out of a photonic crystal fiber is investigated experimentally and theoretically. It is observed that the hexagonal shape of the near field rotates two times by…
We report experimental results of parallel measurement of spectral components of the light. The temporal fluctuations of an optical field mixed with a separate reference are recorded with a high throughput complementary metal oxide…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
Spectral properties of fluorescent radiation from a two-level quantum system with broken inversion spatial symmetry, which can be described by a model of an one-electron two-level atom whose electric dipole moment operator has permanent…
We improve on Fourier transforms (FT) between imaginary time $\tau$ and imaginary frequency $\omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be…
In planar metamaterial lenses, the focal point moves with the frequency. Here it is shown numerically that this movement can be controlled by properly engineering the dimensions of the metamaterial-based phase shifters that constitute the…
A solid-state active beamformer based on the annular-ring diffraction pattern is proposed for an integrated photonic platform. Such a circularly symmetric annular-ring aperture achieves radiating element limited FOV. Furthermore, it is…