Related papers: Half-integer order Bessel beams
We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…
Bessel beams are known for their property of maintaining propagation-invariant transverse intensity distribution. The true Bessel beams has unlimited energy, however the experimental realization of limited energy Bessel-like beams provides…
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of…
The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the…
Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce…
The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P(x). For polynomial solutions, this nonlinear…
We present a mathematical formalism describing the propagation of a completely general electromagnetic wave in a birefringent medium. Analytic formulas for the refraction and reflection from a plane interface are obtained. As a particular…
This paper investigates higher order wave-type equations of the form $\partial_{tt}u+P(D_{x})u=0$, where the symbol $P(\xi)$ is a real, non-degenerate elliptic polynomial of the order $m\ge4$ on ${\bf R}^n$. Using methods from harmonic…
Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a single curve through the physical domain. They can also be extended to some dispersive wave equations, such as…
The electromagnetic field of optical vortices is in most cases derived from vector and scalar potentials using either a procedure based on the Lorenz or the Coulomb gauge. The former procedure has been typically used to derive paraxial…
In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and…
We show that new families of accelerating and almost nondiffracting beams (solutions) for Maxwell's equations can be constructed. These are complex geometrical optics (CGO) solutions to Maxwell's equations with nonlinear limiting Carleman…
In this paper, we propose Plane Wave Elastography (PWE), a novel ultrasound shear wave elastography (SWE) approach. Currently, commercial methods for SWE rely on directional filtering based on the prior knowledge of the wave propagation…
In this work, we optically trapping microparticles with higher order Frozen Wave using holographic optical tweezers. Frozen Waves are diffraction resistant optical beams, obtained by superposing copropagating Bessel beams with the same…
An ill-posed problem of synthesis of the Pierce electrodes for a cylindrical beam with a polygonal cross-section is considered. It is assumed that a beam of charged particles is extracted from a space-charge-limited planar diode and the…
Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because of their property of limited diffraction and their capacity to carry orbital angular momentum. Here we report the creation of a…
We recently introduced a new class of optical beams with a Bessel-like transverse profile and increasing beam width during propagation, akin to an "inverted pin". Owing to their specially engineered distribution, these beams have shown…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
We investigate the dynamics of spatiotemporal optical waves with one transverse dimension that are obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different…
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…