Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns

Davis, Jeffrey A.; Mitry, Mark J.; Bandres, Miguel A.; Ruiz, Isaac; McAuley, Kevin P.; Cottrell, Don M.

doi:10.1364/ao.48.003170

Cited by 48 publications

(15 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We assumed that the laser pulse profile remains undistorted along the propagation; that is, we considered that effects associated with changes in the temporal profile are sufficiently weak (or slow) with respect to the spatial effects induced by self-focusing, plasma defocusing, and multiphoton absorption. This approximation requires justification to guarantee the validity of our model (6) to describe the spatial dynamics of propagating nonlinear pulses. This is the goal of this section, where we evaluate the importance of temporal effects by comparing their characteristic lengths.…”

Section: Validity Of Model Approximationsmentioning

confidence: 99%

“…Airy beams are intrinsically one-dimensional structures [3], but several combinations were demonstrated since 2007 for realizing a two-or three-dimensional nonspreading optical wave packet by linear superposition of subdimensional nonspreading structures [4][5][6]. In 2010, Chong et al generated Bessel-Airy beams consisting of a Bessel beam in the transverse plane and an Airy distribution along the longitudinal dimension [7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear propagation dynamics of finite-energy Airy beams

et al. 2012

View full text Add to dashboard Cite

The nonlinear dynamics of intense truncated Airy beams in Kerr ionizing media are investigated from numerical simulations and experiments. We show numerically that a competition between the linear and nonlinear effects takes place and may be modified by tuning the width of the main lobe of the Airy beam and the size of the truncating diaphragm. Our analysis shows that the acceleration of the Airy peak, an inherent feature of linear Airy beam propagation, is preserved only for powers in the main Airy lobe below a certain threshold. Nonlinear propagation of intense Airy beams with low power in the main lobe is sustained by a continuous energy flux from its neighbors, similarly to the mechanism sustaining nonlinear Bessel beam propagation. Airy beams with higher powers in the main lobe are reshaped into a multifilamentary pattern induced by Kerr and multiphoton nonlinearities. The nucleation of new filaments and their interaction affect the acceleration of the main Airy lobes. We finally show that the size of the truncation constitutes a control parameter for the energy flux that features the Airy beam acceleration. Experiments performed in water corroborate the existence of these two distinct nonlinear propagation regimes.

show abstract

Section: Validity Of Model Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear propagation dynamics of finite-energy Airy beams

et al. 2012

View full text Add to dashboard Cite

show abstract

“…[49,50] Later, alternative methods of production have been proposed, where less expensive optical elements, like cylindrical lenses, replace the rather expensive spatial phase modulators, [52] or Airy patterns are directly produced. [53,54] As to the latter, in fact, on the basis of the approximate expression of the Airy function Ai(ξ ) ξ −1/4 e i 2 3 ξ 3/2 , [40,45,47] Airy beams have been directly generated by neglecting the amplitude dependence and encoding only the 3/2 phase pattern e iCξ 3/2 onto a liquid crystal display. [54] Figure 9 shows the contourplots of the squared amplitude of the wave function ψ (A,ε) (ξ, τ ) evolving from (50) under the Salpeter equation (32).…”

Section: Airy Function-related Solutionmentioning

confidence: 99%

Time‐Dependent Free‐Particle Salpeter Equation: Numerical and Asymptotic Analysis in the Light of the Fundamental Solution

Torre

Lattanzi²,

Levi

2016

Annalen der Physik

View full text Add to dashboard Cite

A detailed study of the spinless (1+1)D free-particle Salpeter equation is presented. It involves several aspects of the topic: from the analysis of the behavior of solutions of the equation, both numerically evaluated and asymptotically approximated for definite initial conditions, to the comparison with the behavior of the corresponding solutions of the Schrödinger equation in order to both highlight the differences and to possibly understand how the latter "flow" in the former. Interesting analogies with other fields of physics, in particular with optics, are suggested. +∞ −∞ e −i p 2 2 m t e i px ψ 0 ( p)dp. (12) As we know, in analogy with (9), the evolution under the Schrödinger equation amounts in the p-domain to an energyrelated phase-factor, and hence to a simple quadratic-phase

show abstract

“…This beam maintains the quoted properties of the quantum wave packet but with the propagation being quasi-nondiffracting due to an exponential apodization in the field profile transforming it in a square-integrable beam. The AiB was experimentally realized by diverse phase mask encoded methods [3][4][5][6] and numerous Airylike beams, variants of that original finite-energy Airy beam, were widely analyzed from theoretical and experimental viewpoint [6][7][8][9][10]. In any case, the AiB and its generalizations have physical meaning only within a paraxial framework since the PEq is a first-order approximation of the full Helmholtz equation (HEq) [11].…”

Section: Introductionmentioning

confidence: 99%

Negative propagation effect in nonparaxial Airy beams

Vaveliuk¹,

Martínez-Matos²

2012

Opt. Express

View full text Add to dashboard Cite

Abstract:Negative propagation is an unusual effect concerning the local sign change in the Poynting vector components of an optical beam under free propagation. We report this effect for finite-energy Airy beams in a subwavelength nonparaxial regime. This effect is due to a coupling process between propagating and evanescent plane waves forming the beam in the spectral domain and it is demonstrated for a single TE or TM mode. This is contrary to what happens for vector Bessel beams and vector X-waves, for which a complex superposition of TE and TM modes is mandatory. We also show that evanescent waves cannot contribute to the energy flux density by themselves such that a pure evanescent Airy beam is not physically realizable. The break of the shape-preserving and diffraction-free properties of Airy beams in a nonparaxial regime is exclusively caused by the propagating waves. The negative propagation effect in subwavelength nonparaxial Airy beams opens new capabilities in optical traps and tweezers, optical detection of invisibility cloacks and selective on-chip manipulation of nanoparticles.

show abstract

Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns

Cited by 48 publications

References 12 publications

Nonlinear propagation dynamics of finite-energy Airy beams

Nonlinear propagation dynamics of finite-energy Airy beams

Time‐Dependent Free‐Particle Salpeter Equation: Numerical and Asymptotic Analysis in the Light of the Fundamental Solution

Negative propagation effect in nonparaxial Airy beams

Contact Info

Product

Resources

About