Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.

J Opt Soc Am A Opt Image Sci Vis

Centre d'Optique, Photonique et Laser, Université Laval, Quebec City, Quebec, Canada.

Published: October 2011

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

Download full-text PDF

Source
http://dx.doi.org/10.1364/JOSAA.28.002100DOI Listing

Publication Analysis

Top Keywords

helmholtz equation
8
beam
8
beam waist
8
bessel-gauss beams
4
beams rigorous
4
rigorous solutions
4
solutions helmholtz
4
equation study
4
nonparaxial
4
study nonparaxial
4

Similar Publications

The identification of vibration and reconstruction of sound fields of plate structures are important for understanding the vibroacoustic characteristics of complex structures. This paper presents a data-physics driven (DPD) model integrated with transfer learning (DPDT) for high-precision identification and reconstruction of vibration and noise radiation of plate structures. The model combines the Kirchhoff-Helmholtz integral equation with convolutional neural networks, leveraging physical information to reduce the need for extensive data.

View Article and Find Full Text PDF

To measure the electroacoustic parameters of transducers in the continuous sound field in a limited water area, a reciprocity calibration method of hydrophones using a spatial sampling average method in a non-anechoic tank was developed. The sound propagation in the non-anechoic tank under the impedance boundary condition, with a sound source producing continuous sound, is introduced based on the Helmholtz equation and Green's function. The reciprocity constant is given using the spatial sampling average sound pressure, and the three-transducer reciprocity calibration procedure was established.

View Article and Find Full Text PDF

Sound speed data measured using a dual-path pulse-echo instrument are reported for pure -1,2-dichloroethene (R-1130(E)) and an azeotropic blend of -1,1,1,4,4,4-hexafluorobutene (R-1336mzz(Z)) and R-1130(E) with a composition of 74.8 mass % R-1336mzz(Z) with the balance being R-1130(E). The azeotropic blend of R-1336mzz(Z)/1130(E) is classified as R-514A in ANSI/ASHRAE standard 34.

View Article and Find Full Text PDF

Background: The estimation of glomerular filtration rate (eGFR) is essential in the early detection of diabetic nephropathy. We herein compare the performance of common eGFR formulas against a gold standard measurement of GFR in patients with diabetes mellitus.

Methods: GFR was measured in 93 patients with diabetes mellitus using iohexol clearance as the reference standard.

View Article and Find Full Text PDF

Coherent phase transformations in interstitial solid solutions or intercalation compounds with a miscibility gap are of practical relevance for energy storage materials and specifically for metal hydride or lithium-ion compound nanoparticles. Different conclusions on the size-dependence of the transformation conditions are reached by modeling or theory focusing on the impact of either one (internal, solid-state-) critical-point wetting of the nanoparticle surface or coherency constraints from solute-saturated surface layers. We report a hybrid numerical approach, combining atomistic grand canonical Monte Carlo simulation with a continuum mechanics analysis of coherency stress and modeling simultaneously wetting and mechanical constraints.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!