Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories

Penciu, Raluca-Sorina; Paltoglou, Vassilis; Efremidis, Nikolaos K.

doi:10.1364/ol.40.001444

Cited by 20 publications

(25 citation statements)

References 30 publications

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“…Theoretical analysis of Airy beams (and more generally of accelerating beams) can be carried out by utilizing fundamental principles of ray optics and catastrophe theory [11,12]. The starting point in the case of one transverse dimension, is selected to be the Rayleigh-Sommerfeld diffraction formula [13] ψ…”

Section: Airy Wavesmentioning

confidence: 99%

Airy beams and accelerating waves: an overview of recent advances

Efremidis¹,

Chen²,

Segev³

et al. 2019

Optica

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406

149

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Over the last dozen of years, the area of accelerating waves has made considerable advances not only in terms of fundamentals and experimental demonstrations but also in connection to a wide range of applications. Starting from the prototypical Airy beam that was proposed and observed in 2007, new families of accelerating waves have been identified in the paraxial and nonparaxial domains in space and/or time, with different methods developed to control at will their trajectory, amplitude, and beam width. Accelerating optical waves exhibit a number of highly desirable attributes. They move along a curved or accelerating trajectory while being resilient to perturbations (self-healing), and, are diffraction-free. It is because of these particular features that accelerating waves have been utilized in a variety of applications in the areas of filamentation, beam focusing, particle manipulation, biomedical imaging, plasmons, and material processing among others.

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Section: Airy Wavesmentioning

confidence: 99%

Airy beams and accelerating waves: an overview of recent advances

Efremidis¹,

Chen²,

Segev³

et al. 2019

Optica

Self Cite

406

149

View full text Add to dashboard Cite

show abstract

“…(2) and (4). For the particular examples presented in this paper we are going to utilize classes of trajectories that lead to closed-form expressions [27]. In Figs.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The above equation can be analytically integrated for different classes of convex trajectories such as circular, elliptic, power-law, and exponential [27]. We are going to utilize these closed-form expressions below.…”

Section: Amplitude and Trajectory/beam-width Engineeringmentioning

confidence: 99%

Independent amplitude and trajectory/beam-width control of nonparaxial beams

2018

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We show that it is possible to generate non-paraxial optical beams with pre-engineered trajectories and designed maximum amplitude along these trajectories. The independent control of these two degrees of freedom is made possible by engineering both the amplitude and the phase of the optical wave on the input plane. Furthermore, we come to the elegant conclusion that the beam width depends solely on the local curvature of the trajectory. Thus, we can generate beams with pre-defined amplitude and beam-width by appropriately selecting the local curvature. Our theoretical results are in excellent agreement with numerical simulations. We discuss about methods that can be utilized to experimentally generate such beam. Our work might be useful in applications where precise beam control is important such as particle manipulation, filamentation, and micromachining.

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“…We follow a similar approach as in Section II by using the expansion r = r c +δr, ρ = ρ c +δρ, z = z c close to the caustic and large argument asymtptics for the Bessel function [Eq. (14)]. We keep all the terms in the phase of the integrand in Eq.…”

Section: Amplitude-trajectory Engineering Of Abruptly Autofocusimentioning

confidence: 99%

“…Using a different approach it is possible to generate Bessel-like beams that can even bend along non-convex type of trajectories [6,7]. Accelerating waves in the non-paraxial regime have a main advantage that the trajectory of the beam can bend at large angles [5,[8][9][10][11][12][13][14]. The curved trajectory and self-healing characteristics of such optical waves have been proven very useful in a variety of applications ranging from filamentation [15,16] and electric discharge generation [17] to particle manipulation [18][19][20][21][22], microscopy and imaging [23,24], and micromachining [23,24].…”

Section: Introductionmentioning

confidence: 99%

Precise amplitude, trajectory, and beam-width control of accelerating and abruptly autofocusing beams

Goutsoulas

Efremidis

2018

Phys. Rev. A

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We show that it is possible to independently control both the trajectory and the maximum amplitude along the trajectory of a paraxial accelerating beam. This is accomplished by carefully engineering both the amplitude and the phase of the beam on the input plane. Furthermore, we show that the width of an accelerating beam is related only on the curvature of the trajectory. Therefore, we are able to produce beams with predefined beam widths and amplitudes. These results are useful in applications where precise beam control is important. In addition we consider radially symmetric abruptly autofocusing beams. We identify the important parameters that affect the focal characteristics. Consequently, we can design autofocusing beams with optimized parameters (such as sharper focus and higher intensity contrast). In all our calculations the resulting formulas are presented in an elegant and practical form in direct connection with the geometric properties of the trajectory. Finally we discuss methods that can be utilized to experimentally realize such optical waves. arXiv:1806.05723v1 [physics.optics]

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Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories

Cited by 20 publications

References 30 publications

Airy beams and accelerating waves: an overview of recent advances

Airy beams and accelerating waves: an overview of recent advances

Independent amplitude and trajectory/beam-width control of nonparaxial beams

Precise amplitude, trajectory, and beam-width control of accelerating and abruptly autofocusing beams

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