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Journal ArticleDOI

A vector wave analysis of a Bessel beam

01 Sep 1991-Optics Communications (North-Holland)-Vol. 85, pp 159-161
TL;DR: In this article, a vector wave analysis of a Bessel beam is presented in which electric and magnetic field vectors satisfy Maxwell's equations, and the results are compared with those obtained in the scalar wave theory.
About: This article is published in Optics Communications.The article was published on 1991-09-01. It has received 188 citations till now. The article focuses on the topics: Plane wave & Vector potential.
Citations
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Journal ArticleDOI
TL;DR: In this article, it is shown that a nondiffracting beam disturbed by an obstacle is able to reconstruct its initial amplitude profile under free propagation, and simple theoretical explanation, numerical simulation and experimental verification of the effect are presented.

459 citations

Journal ArticleDOI
TL;DR: An annular pupil, which can be used to produce a Bessel beam, when combined with radially polarized illumination promises improvements in microscope resolution, increased packing density for optical storage, and finer optical lithography.
Abstract: An annular pupil, which can be used to produce a Bessel beam, when combined with radially polarized illumination promises improvements in microscope resolution, increased packing density for optical storage, and finer optical lithography. When combined with a circular detection pupil in confocal microscopy a point-spread function 112 nm wide results (lambda = 488 nm). Radially polarized annular illumination of a solid-immersion lens can yield a focal spot smaller than 100 nm for lambda = 488 nm. Use of radially polarized illumination with pupil masks is discussed.

323 citations

Journal ArticleDOI
TL;DR: In this article, a common Gaussian beam is transformed into a vector Bessel beam, which is useful for particle trapping, near-field probes, and laser machining, enabling applications such as tractor beams in compact nanoscale devices.
Abstract: Metamaterial surfaces (metasurfaces) can generate tailored electromagnetic wavefronts with spatially varying phase and polarization profiles. In this study a common Gaussian beam is transformed into a vector Bessel beam, which is useful for particle trapping, near-field probes, and laser machining. Going forward, the design and fabrication methodology presented here could be used to create efficient metasurfaces even at optical wavelengths, enabling applications such as tractor beams in compact nanoscale devices.

205 citations


Cites methods from "A vector wave analysis of a Bessel ..."

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  • ...Vector Bessel beams are axially symmetric beam solutions to Maxwell’s equations [18,19]....

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Journal ArticleDOI
TL;DR: In this paper, the physical concept of the nondiffracting propagation is presented and the basic properties of the non-defracting beams are reviewed, and attention is also focused to the experimental realization and to applications of the nonsmooth beams.
Abstract: The controversial term “nondiffracting beam” was introduced into optics by Durnin in 1987. Discussions related to that term revived interest in problems of the light diffraction and resulted in an appearance of the new research direction of the classical optics, dealing with the localized transfer of electromagnetic energy. In this paper, the physical concept of the nondiffracting propagation is presented and the basic properties of the nondiffracting beams are reviewed. Attention is also focused to the experimental realization and to applications of the nondiffracting beams.

189 citations

Book ChapterDOI
TL;DR: In this paper, Turunen and Friberg dealt with a class of fields with propagation-invariant properties such as the optical intensity distribution and applied them to scalar and electromagnetic approaches.
Abstract: The first article by Turunen and Friberg deals with a class of fields with propagation-invariant properties such as the optical intensity distribution. Coherent and partially coherent stationary and pulsed solutions are treated in view of scalar and electromagnetic approaches. Approximations of ideal propagation-invariant fields and methods for their generation are discussed. Finally, some application areas are covered.

149 citations

References
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Journal ArticleDOI
TL;DR: The first experimental investigation of nondiffracting beams, with beam spots as small as a few wavelengths, can exist and propagate in free space, is reported.
Abstract: It was recently predicted that nondiffracting beams, with beam spots as small as a few wavelengths, can exist and propagate in free space. We report the first experimental investigation of these beams.

2,919 citations

Journal ArticleDOI
TL;DR: In this paper, exact nonsingular solutions of the scalar-wave equation for beams that are non-diffracting were presented, which means that the intensity pattern in a transverse plane is unaltered by propagating in free space.
Abstract: We present exact, nonsingular solutions of the scalar-wave equation for beams that are nondiffracting. This means that the intensity pattern in a transverse plane is unaltered by propagating in free space. These beams can have extremely narrow intensity profiles with effective widths as small as several wavelengths and yet possess an infinite depth of field. We further show (by using numerical simulations based on scalar diffraction theory) that physically realizable finite-aperture approximations to the exact solutions can also possess an extremely large depth of field.

2,283 citations

Journal ArticleDOI
TL;DR: In this paper, the paraxial approximation to the exact Maxwell equations is shown to be incompatible with the exact equations of light beam propagation through an inhomogeneous, isotropic medium with a possibly nonlinear index of refraction.
Abstract: In this paper we are concerned with the propagation of a light beam through an inhomogeneous, isotropic medium with a possibly nonlinear index of refraction. The customary paraxial approximations of neglecting grad $\mathrm{div}\mathcal{E}$ and seeking a plane-polarized solution are shown to be incompatible with the exact Maxwell equations. By starting from Maxwell's equations, and scaling transverse and longitudinal distances by the beam waist ${w}_{0}$ and diffraction length $l$, respectively, an expansion procedure in powers of $\frac{{w}_{0}}{l}$ is developed. The exact equations obeyed by the zeroth-order fields are not Maxwell's equations but the customary paraxial approximation to Maxwell's equations. Equations for the first-, second-, and third-order fields are developed. The first-order field is found to be a longitudinal field. It is solved for explicitly in terms of the zeroth-order field which is transverse. Thus a precise knowledge of the meaning and accuracy of paraxial wave optics is obtained.

773 citations

Journal ArticleDOI
L. W. Davis1
TL;DR: In this paper, a relatively simple method for calculating the properties of a paraxial beam of electromagnetic radiation propagating in vacuum is presented, where the vector potential field is assumed to be plane-polarized.
Abstract: A relatively simple method for calculating the properties of a paraxial beam of electromagnetic radiation propagating in vacuum is presented. The central idea of the paper is that the vector potential field is assumed to be plane-polarized. The nonvanishing component of the vector potential obeys a scalar wave equation. A formal solution employing an expansion in powers of $\frac{{w}_{0}}{l}$ is obtained, where ${w}_{0}$ is the beam waist and $l$ the diffraction length. This gives the same result for the lowest-order components of the transverse and longitudinal electric field of a Gaussian beam that was derived by Lax, Louisell, and McKnight using a more complicated approach. We derive explicit expressions for the second-order transverse electric field and the third-order longitudinal field corrections.

559 citations