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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Proceedings ArticleDOI
Rotary solitons in elliptical photonic lattices
TL;DR: In this paper, the problem of shaping the transverse propagation invariant intensity pattern of an optical beam to create a photonic lattice for trapping and propagating spatial optical solitons in a stable elliptic motion with a varying rotation rate was studied.
Proceedings ArticleDOI
Peculiarities of the generalized and fractional parabolic diffraction-free beams
TL;DR: In this article, the rotational symmetry of the intensity distribution of the order depending on the index value is investigated and two approaches to perform a correction of the angular spectrum in the input plane are proposed.
Posted Content
Free-space non-separability decay of clasicaly-entangled modes.
Xiao-Bo Hu,Benjamin Perez-Garcia,Valeria Rodríguez-Fajardo,Raul I. Hernandez-Aranda,Andrew Forbes,Carmelo Rosales-Guzmán +5 more
TL;DR: In this article, a novel type of classically-entangled modes that experience an entanglement decay upon free-space propagation was demonstrated, and the decay was verified by numerical simulations and corroborate experimentally.
Journal ArticleDOI
Modeling the formation of non-diffraction parabolic beams
TL;DR: In this paper, a numerical study of the generalization of parabolic non-diffraction beams of two orders formed from an analytically given distribution of the ring spatial spectrum is performed.
Proceedings ArticleDOI
(2D+1) pendulum beams: non-diffracting optical spatial wavepackets that simulate quantum pendulum dynamics
TL;DR: In this article , a three-dimensional pendulum wavepacket made of a superposition of Helical Mathieu-Gaussian modes was constructed in such a way that the components of the wave-vectors along the propagation direction are proportional to the pendulum energies.
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.