Journal ArticleDOI
Parabolic nondiffracting optical wave fields
TLDR
The existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and their associated angular spectrum is demonstrated and their eigenvalue spectrum is continuous.Abstract:
We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.read more
Citations
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Accelerating finite energy Airy beams
TL;DR: This work investigates the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations and shows that this class of finite energy waves can retain their intensity features over several diffraction lengths.
Journal ArticleDOI
Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities
TL;DR: The authors survey the steady refinement of techniques used to create optical vortices, and explore their applications, which include sophisticated optical computing processes, novel microscopy and imaging techniques, the creation of ‘optical tweezers’ to trap particles of matter, and optical machining using light to pattern structures on the nanoscale.
Journal ArticleDOI
Advanced optical trapping by complex beam shaping
TL;DR: In this paper, two promising adjacent approaches tackle fundamental limita- tions by utilizing non-optical forces which are, however, induced by optical light fields, namely, dielectrophoretic and photophoretic forces.
Journal ArticleDOI
Helmholtz–Gauss waves
TL;DR: In this article, a detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z = 0 is modulated by a Gaussian envelope is presented.
Journal ArticleDOI
Diffraction-free space–time light sheets
TL;DR: In this paper, the temporal degree of freedom can be exploited to efficiently synthesize one-dimensional pulsed light sheets that propagate self-similarly in free space, with no need for nonlinearity or dispersion.
References
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Journal ArticleDOI
Nondiffracting bulk-acoustic x waves in crystals
TL;DR: In this paper, the concept of nondiffracting waves is generalized to encompass bulk-acoustic waves within crystalline media, and acoustic Bessel beams and generalized X waves for anisotropic elastic materials are introduced.
Journal ArticleDOI
Lie theory and the wave equation in space-time. 3. Semisubgroup coordinates
Ernie G. Kalnins,Willard Miller +1 more
TL;DR: In this article, the authors classify and study coordinate systems which permit R separation of variables for the wave equation in four-dimensional space-time and such that at least one of the variables corresponds to a one-parameter symmetry group.
Journal ArticleDOI
Diffraction and Weber functions
TL;DR: The diffraction of harmonic plane waves at a perfectly conducting half-plane leads to a Dirichlet or Neumann problem for the two-dimensional (2D) Helmholtz equation as proved by Bateman; the solution may be expressed in terms of Weber functions.