Finite Gaussian wavelet superposition and Fresnel diffraction integral for calculating the propagation of truncated, non-diffracting and accelerating beams

Cywiak, Moisés; Cywiak, David; Yáñez, Etna

doi:10.1016/j.optcom.2017.08.015

Cited by 7 publications

(5 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As mentioned previously, the Fresnel diffraction integral is usually used to characterize the propagation of paraxial light beams in a homogeneous medium. In Cartesian coordinates, the Fresnel diffraction integral is expressed as [14][15][16][17]…”

Section: Fresnel Diffraction Integralmentioning

confidence: 99%

“…There have been extensive studies on the propagation effects of structured light beams using various scalar diffraction theories, which can be divided into four categories: the Fresnel diffraction integral [14][15][16][17], the Collins formula [18][19][20][21][22][23][24], the angular spectrum representation [25][26][27][28][29][30], and the Rayleigh-Sommerfeld diffraction integral [31][32][33][34][35][36][37][38][39][40]. The Fresnel diffraction integral, which is an approximation of the Kirchhoff diffraction formula, is usually used to study the propagation of paraxial light beams in a homogeneous medium.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

Wu,

Luo,

Cui

2023

Photonics

View full text Add to dashboard Cite

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams.

show abstract

Section: Fresnel Diffraction Integralmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

Wu,

Luo,

Cui

2023

Photonics

View full text Add to dashboard Cite

show abstract

“…A straightforward technique to achieve a Bessel beam with shorter DOF is to truncate the incident Gaussian beam with a circular aperture [28]. However, in view of keeping away the undesired effects from the imperfect apex of the axicon, that induce intensity modulations along the propagation axis, we additionally block the central area of the beam.…”

Section: Generation and Characterization Of A Short-dof Beam By Truncmentioning

confidence: 99%

Truncated Gaussian-Bessel beams for short-pulse processing of small-aspect-ratio micro-channels in dielectrics

Liu¹,

Li²,

Sikora³

et al. 2019

Opt. Express

View full text Add to dashboard Cite

In order to control the length of micro-channels ablated at the surface of dielectrics, we use annular filtering apertures for tailoring the depth of focus of micrometric Gaussian-Bessel beams. We identify experimentally and numerically the appropriate beam truncation that promotes a smooth axial distribution of intensity with a small elongation, suitable for processing micro-channels of small aspect ratio. Single-shot channel fabrication is demonstrated on the front surface of a fused silica sample, with sub-micron diameter, highquality opening, and depth of few micrometers, using 1 ps low-energy (< 0.45 µJ) pulse. Finally, we realize 10 × 10 matrices of densely packed channels with aspect ratio ~5 and a spatial period down to 1.5 μm, as a prospective demonstration of direct laser fabrication of 2D photonic-crystal structures.

show abstract

“…Limited by the small face of the GRIN-MMFs, the incident of a large Gaussian spot will bring the result of partial Gaussian light injection, which makes the dynamic propagation complex. The partial Gaussian beam can be represented properly by the finite superposition of the Gaussian wavelet, and the propagation of the partial Gaussian beam was calculated [32]. The analytical expression for the kurtosis parameter of partially simplified general-type beams was derived based on the second-and fourth-order moment formalism [33].…”

Section: Introductionmentioning

confidence: 99%

Oscillating propagation and parametric instability of the partial Gaussian beam in graded-index multimode fibers

et al. 2022

View full text Add to dashboard Cite

We investigate the input and propagation characteristics and geometric parametric instability of the partial Gaussian beam limited by the fiber face area in a graded-index multimode fiber. The theoretical simulation shows that the energy of the partial Gaussian beam and the coupling efficiency of the fiber face are restricted by the fiber face area for the different powers and spot sizes of the input Gaussian beam. The spot intensity pattern of the partial Gaussian beam exhibits a standard oscillating distribution in space as the beam undergoes periodic oscillations with propagation. Also, the dynamic evolution process from parametric sidebands to a supercontinuum is affected by the peak power, the spot size of the partial Gaussian beam, and the fiber length. Finally, the experimental output spectra with different powers of the partial Gaussian beam and fiber lengths in a graded-index multimode fiber confirm the prediction of theoretical simulations. This work provides practical guidance for optimizing supercontinuum source expansion and spectral power density.

show abstract

Finite Gaussian wavelet superposition and Fresnel diffraction integral for calculating the propagation of truncated, non-diffracting and accelerating beams

Cited by 7 publications

References 13 publications

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

Truncated Gaussian-Bessel beams for short-pulse processing of small-aspect-ratio micro-channels in dielectrics

Oscillating propagation and parametric instability of the partial Gaussian beam in graded-index multimode fibers

Contact Info

Product

Resources

About