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
Self-healing of structured light: a review
TL;DR: In this paper , a comprehensive review of the history and development of self-healing effects, especially highlighting its importance in vector vortex beams carrying spin and orbital angular momenta, is presented.
Journal ArticleDOI
Parabolic non-diffracting beams: geometrical approach
Citlalli Teresa Sosa-Sánchez,Gilberto Silva-Ortigoza,Salvador Alejandro Juárez-Reyes,Omar de Jesús Cabrera-Rosas,Ernesto Espíndola-Ramos,Israel Julián-Macías,Paula Ortega-Vidals +6 more
TL;DR: In this article, the authors presented a geometrical characterization of parabolic non-diffracting beams and derived the one-parameter family of solutions of the eikonal equation associated with this type of beam.
Journal ArticleDOI
Propagation of an Airy-Gaussian beam passing through the ABCD optical system with a rectangular aperture
TL;DR: By expanding the hard rectangular aperture function into a finite sum of complex Gaussian functions, the analytical formula for the propagation of an AiG beam passing through a paraxial ABCD optical system was derived in this paper.
Journal ArticleDOI
Structured light beams constituted of incoming and outgoing waves
Job Mendoza-Hernández,Maximino Luis Arroyo-Carrasco,M. D. Iturbe-Castillo,Sabino Chávez-Cerda +3 more
TL;DR: In this article, the authors demonstrate that structured light beams are constituted by two traveling waves which transverse components are in opposite directions, that is, incoming and outgoing from the axis of propagation.
Spin-momentum law for structured guided modes: the generalized quantum spin-Hall effect for light
TL;DR: In this article, a generalized spin-momentum relationship that governs vectorial properties of a two-dimensional vector field of structured guided wave has been demonstrated with four kinds of surface structured waves and proven both theoretically and experimentally.
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.
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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.