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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Composite multi-vortex diffraction-free beams and van Hove singularities in honeycomb lattices
TL;DR: In this paper, diffraction-free beams for graphene and MoS$_2$-type honeycomb optical lattices are obtained in the Dirac limit, where the effects of the valley degree of freedom and the mass are analyzed.
Journal ArticleDOI
Generation of on-demand quasi-Mathieu beams with a controlled generation of spatial spectrum of angular Mathieu-Gauss functions with a digital laser.
Ly Nguyễn Thị,Shu Chun Chu +1 more
TL;DR: In this paper , an intra-cavity method for the selective generation of all kinds of quasi-Mathieu beams was proposed, which employed L-type digital lasers to selectively generate the Fourier spectrum of the gaussian-modulated angular Mathieu function.
Journal ArticleDOI
Light propagation in aperiodic photonic lattices created by synthesized Mathieu–Gauss beams
Jadranka M. Vasiljević,Alessandro Zannotti,D. V. Timotijević,Cornelia Denz,Dragana M. Jović Savić +4 more
TL;DR: In this paper, the authors investigated light propagation in a two-dimensional aperiodic refractive index lattice realized using the interference of multiple Mathieu-Gauss beams and demonstrated experimentally and numerically that such a lattice effectively hinders linear light expansion and leads to light localization.
Posted Content
Non-diffracting chirped Bessel waves in optical antiguides
TL;DR: The new waves exhibit a remarkable resistance against the defocusing effect of the unstable index potentials, outperforming standard Gaussians with the same full width at half-maximum and is also capable of self-healing like standard diffraction-free beams in free space.
Journal ArticleDOI
Generation and propagation dynamics of Airy beam with the tunable tail
TL;DR: In this paper, a new kind of Airy beam with the tunable tail was introduced, which can be obtained by adjusting the ration of the beam width of elliptical flat-topped Gaussian beam.
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.