Virtual source of a Pearcey beam

Abstract

A virtual source that yields a family of a Pearcey wave is demonstrated. A closed-form expression is derived for the Pearcey wave that simplifies to the paraxial Pearcey beam (PB) in the appropriate limit. From the perturbative series representation of a complex-source-point spherical wave, an infinite series nonparaxial correction expression for a PB is obtained. The infinite series expression of a PB can give accuracy up to any order of the diffraction angle. By applying the integral representation of the Pearcey wave, the first three terms in the nonparaxial correction series to the paraxial PB are provided.

Electron Symmetric Pearcey Gaussian Vortex Beams

“…[12]. Let us apply an inverse Fourier transform to it, then we add a Gaussian term $$\begin{align} \text{G}(x,y)=\exp \left(-\frac{x^2+y^2}{w_0^2}\right) \end{align}$$and a vortex term $$\begin{align} \text{V}(x,y)={\left[\frac{(x-x_v)+\text{i}(y-y_v)}{w_0}\right]}^l \end{align}$$where w 0 is the initial beam width, l is the topological charge, $$(x_v,y_v)$$ are the coordinates of the vortex, to obtain ESPGVBs, [ 11,13 ] which can be expressed as $$\begin{align} \nonumber \operatorname{ESPGVB}(x,y)=&\operatorname{Pe}{\left(\frac{x}{b...$$…”

“…where w 0 is the initial beam width, l is the topological charge, (x v , y v ) are the coordinates of the vortex, to obtain ESPGVBs, [11,13] which can be expressed as ESPGVB(x, y) = Pe ] l (3) where Pe( ⋅ ) is the Pearcey function, b 1 , p 1 and b 2 , p 2 are the distribution factors along x and y axes, respectively.…”

Controllable Dispersive Wave Radiation from Pearcey Gaussian Pulses

“…[1] Since it was first proposed DOI: 10.1002/andp.202100479 in 1946, its generation, control and application have been intensively investigated. [2][3][4][5][6] With the unique properties of inversion, auto-focusing and self-healing, the theoretical introduction and experimental realization in optics, [7] Pearcey beams have attracted widespread attention in recent years, leading to different types of Pearcey beams generation such as dual Pearcey beams, [8] ring and symmetric Pearcey Gaussian (PG) beams [9,10] and partially coherent PG beams. [11] Especially, by imposing Gaussian truncation on ideal Pearcey beams, the physical realization of PG beams with finite energy becomes possible because ideal Pearcey beams have infinite energy.…”

Paraxial Propagation Properties of Radially Polarized Odd‐Pearcey Gaussian Beams in Free Space

“…In 2012, Ring et al theoretically confirmed that the Pearcey function is a particular solution of wave equation under paraxial approximation and successfully generated the Pearcey beams experimentally. [25] In 2014, a virtual source to generate Pearcey beams was demonstrated by Deng et al [26] In 2015, Kovalev et al [27] generated and introduced a family of form-invariant half-Pearcey beams (HP-beams). In 2016, it was reported that, based on the Fresnel diffraction catastrophes, dual Pearcey beams (DP beams) were successfully obtained by interfering a pair of half DP beams, [28] and the form-invariant Bessel beams were experimentally confirmed as particular forms of DP beams.…”