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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Book ChapterDOI
Some Selected Applications of Bohmian Mechanics
TL;DR: In this article, the authors show that Bohmian mechanics is a powerful route to bring about new solutions to problems discussed by conventional quantum mechanical approaches, apart from allowing some striking correspondence between both frameworks.
Journal ArticleDOI
Thermally-affected Cosine-Gauss and Parabolic-Gauss beams and comparisons of Helmholtz–Gauss beam families
Hamid Nadgaran,Reza Fallah +1 more
TL;DR: In this article, the authors investigated the thermal effects on the generation of Bessel-Gauss and Mathieu-Gauuss beams and showed that thermal effects have severe impact on the laser output, so that true distinguishing of thermally-affected and non-thermal intensity profiles is unlikely feasible.
Journal ArticleDOI
Compensation of Beer-Lambert attenuation using non-diffracting Bessel beams
Quentin Fontaine,Huiqin Hu,Simon Pigeon,Tom Bienaimé,Eliza Wu,Elisabeth Giacobino,Alberto Bramati,Quentin Glorieux +7 more
TL;DR: In this article, the authors exploit diffraction-limited Bessel beams and tailored on-axis intensity profiles which are generated using a phase-only spatial light modulator to compensate the linear attenuation in a medium.
Spectral generation and control of linear and nonlinear self-accelerating beams and pulses.
TL;DR: In this paper, an analytical approach was proposed to predict the trajectory of self-accelerating wave packets in the one-dimensional (1+1)D, two-or (2+1D)D and three-dimensional(i.e., spatio-temporal or (3+1)-D) cases.
Journal ArticleDOI
Diffraction theory of general nondiffracting beams generated with finite-aperture systems
TL;DR: In this article, the authors solved the Fresnel diffraction integral corresponding to the propagation of a general nonsmooth beam generated from an arbitrary finite-aperture system, and they showed that the performance of a J 0 beam diffracted by a circular aperture may be intuitively understood from the characteristics of the diffraction pattern of the circular aperture.
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.