Related papers: Backflow in vector Gaussian beams
It was recently realized that the polarization bases of the plane-wave modes in the integral representation of a light beam need to be determined by a degree of freedom arising from the divergence-free Maxwell's equation. This is a…
The inverse of an invertible convolution is an important operation that comes up in Normalizing Flows, Image Deblurring, etc. The naive algorithm for backpropagation of this operation using Gaussian elimination has running time $O(n^3)$…
Propagation of electromagnetic plane waves in some directions in gravitationally affected vacuum over limited ranges of spacetime can be such that the phase velocity vector casts a negative projection on the time-averaged Poynting vector.…
We review equilibrium properties for the dynamics of a single particle evolving in a visco--elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the…
Refraction of obliquely incident plane waves due to the interface of a vacuous half-space and a half-space occupied by a simply moving, nondissipative, isotropic dielectric-magnetic medium is considered, when the medium's velocity lies…
The phenomenon of beam focusing of microwaves in a plasma near a turning-point caustic is discussed in the context of the analytical solution to the Gaussian beam-tracing equations in the 2D linear-layer problem. The location of maximum…
For random matrix ensembles with non-gaussian matrix elements that may exhibit some correlations, it is shown that centered traces of polynomials in the matrix converge in distribution to a Gaussian process whose covariance matrix is…
We introduce a new class of optical beams, which feature a spatial profile akin to an ``inverted pin''. In particular, we asymptotically find that close to the axis the transverse amplitude profile of such beams takes the form of a Bessel…
In this paper we investigate the reverse isoperimetric inequality with respect to the Gaussian measure for convex sets in $\mathbb{R}^{2}$. While the isoperimetric problem for the Gaussian measure is well understood, many relevant aspects…
The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…
We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…
Thin vortex tubes, with core sizes within the dissipation range, profuse in a homogeneous and isotropic turbulent flow. Their intersections with an arbitrary plane define, as a mathematical construct, a dilute gas of localized,…
We show that in driven systems the Gaussian nature of the fluctuating force and time-reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the…
We study the evolution of the kinetic energy (or gradient norm) of an incident linearly polarized monochromatic wave propagating in correlated random media. We explore the optical flux transverse to the mean Poynting flux at the…
Negative propagation is an uncommon response produced by the local sign change in Poynting vector components. We present a general Poynting vector expression for all invariant beams with cylindrical symmetry using scalar potentials in order…
Vector vortex beams possess a topological property that derives both from the spatially varying amplitude of the field and also from its varying polarization. This property arises as a consequence of the inherent Skyrmionic nature of such…
A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3 \times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has…
It is shown that the vector-vortex Laguerre-Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized…
We consider the statistical inverse problem of estimating a background fluid flow field $\mathbf{v}$ from the partial, noisy observations of the concentration $\theta$ of a substance passively advected by the fluid, so that $\theta$ is…
Spatially accelerating beams that are solutions to the Maxwell equations may propagate along incomplete circular trajectories, after which diffraction broadening takes over and the beams spread out. Taking these truncated Bessel wave fields…