Half Pearcey laser beams

Abstract

We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional form-invariant half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Ring et al (2012) Opt. Express 20 18955, since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectra of plane waves, which are non-zero at a half parabola. For functions of HP-beam complex amplitudes, the orthogonality properties have been revealed. Using a spatial phase modulator, we generated superposition of HP-beams. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively.

Paraxial Propagation Properties of Symmetric Dual Pearcey Gaussian Beams in Free Space

“…where x ′ and y ′ are the transverse scaling factors of beams, w 0 denotes the Gaussian beam waist width. For the vth-order half-Pearcey beams, [15] when v=1, they can be defined as follows:…”

“…The electric field of the symmetric dual Pearcey beams (SDPBs) in the initial plane is defined as: $$\begin{equation} \begin{aligned} E{\left(x_0,y_0,0 \right)} &= \mathrm{HPe}^+{\left(\frac{x_0}{x^{\prime }},\frac{y_0}{y^{\prime }} \right)} +\mathrm{HPe}^-{\left(-\frac{x_0}{x^{\prime }},-\frac{y_0}{y^{\prime }} \right)} \end{aligned} \end{equation}$$where $$x^{\prime }$$ and $$y^{\prime }$$ are the transverse scaling factors of beams, w 0 denotes the Gaussian beam waist width. For the v th‐order half‐Pearcey beams, [ 15 ] when v =1, they can be defined as follows: $$\begin{equation} \begin{aligned} \mathrm{HPe}^+{\left(X,Y \right)} =\int _0^{+\infty }{\exp {\left[ \mathrm{i}{\left(s^4+s^2Y+sX \right)} \right]} \mathrm{d}s} \end{aligned} \end{equation}$$ $$\begin{equation} \begin{aligned} \mathrm{HPe}^-{\left(X,Y \right)} =...$$…”

“…Due to these properties, the Pearcey beams have potential application in many fields such as optical tweezers [ 11 ] and imaging systems, [ 12 ] thus having caused extensive research. [ 13,14 ] Before long, the form‐invariant half‐Pearcey beams (HP‐beams) were proposed and experimentally demonstrated, [ 15 ] which greatly expanded the family of the form‐invariant auto‐focusing beams. Correspondingly, it has been reported that the form‐invariant dual Pearcey beams (DPBs) are successfully generated by the interference of two half‐Pearcey beams.…”

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.…”

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey–Gaussian beam

“…[14] In Ref. [15] Pearcey beams were generalized into half Pearcey beams and it is shown that such beams, which are form-invariant, [12,15,16] propagate with acceleration and autofocusing.…”