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
Optical beam shaping and diffraction free waves: A variational approach
TL;DR: In this paper, the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis was investigated, and it was shown that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval.
Journal ArticleDOI
A general conformal framework for regular cusp beams
TL;DR: In this paper , a conformal framework is presented to describe the generation and propagation of regular polygon beams, which can be described as the envelope of hypocycloid caustics generated by a circular sector transformation acting on a standard input beam.
Journal ArticleDOI
Structurally Stable Hyperbolic Beam
Rijuparna Chakraborty,Ajay Ghosh +1 more
TL;DR: In this paper, a technique for generating a structurally stable hyperbolic beam using Fourier transform holography is reported, and the resulting beam keeps its shape unchanged up to ~45 cm.
Proceedings ArticleDOI
Experimental realization of nondiffracting Parabolic beams
TL;DR: In this article, the experimental realization of zero-order Parabolic Non-Defracting Beams (PNDB) has been reported and the observed transverse patterns have an inherent parabolic structure and exhibit the common features of general nondiffracting beams.
Proceedings ArticleDOI
Self-healing of beams with angular momentum
Job Mendoza Hernandez,Maximino L. Arroyo Carrasco,Marcela M. Méndez Otero,Marcelo David Iturbe Castillo,Sabino Chávez-Cerda +4 more
TL;DR: In this article, the self-healing of beams with rotating wave front is demonstrated experimentally and explained theoretically, and it is shown that partially obstructed high-order Bessel beams present the same dynamics as partially-obstructed parabolic beams.
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.