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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Journal ArticleDOI
Conversion of any finite bandwidth optical field into a shape invariant beam
TL;DR: In this article, a method to transform any optical field, with finite frequency bandwidth, into a shape invariant beam with transverse scaling, dependent on the propagation distance, is discussed.
Journal ArticleDOI
Propagation characteristics of non-diffracting Lommel beams in a gradient-index medium
Yuanfei Hui,Zhiwei Cui,Pan Song +2 more
TL;DR: In this paper, the propagation of the Lommel beams in a gradient-index medium was investigated based on the ABCD transfer matrix and Collins diffraction integral formula, and the analytical expressions of the complex expressions were derived.
Journal ArticleDOI
Bohmian Trajectories of Airy Packets
TL;DR: In this paper, the authors presented new features of Airy wave packet solutions to the Schrodinger equation with time-dependent quadratic potentials, and provided some insights to the problem by calculating the corresponding Bohmian trajectories.
Journal ArticleDOI
Pendulum beams: optical modes that simulate the quantum pendulum
TL;DR: In this paper, it was shown that the optical Fourier transform of a simple pendulum has a spatial intensity distribution that is proportional to the quantum mechanical probability for the pendulum.
Journal ArticleDOI
Demonstrating Arago–Fresnel laws with Bessel beams from vectorial axicons
TL;DR: This work uses a digital micro-mirror device to interfere orthogonal conical waves from a holographic axicon, and studies the boundary of scalar and vectorial states in the context of structured light using the Arago-Fresnel laws.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Journal ArticleDOI
Methods of Theoretical Physics. By P.M. Morse and H. Feschbach. 2vols., Pp.xxii, 1978. 120s. each vol. 1953.(McGraw-Hill)
Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Journal ArticleDOI
Exact solutions for nondiffracting beams. I. The scalar theory
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.