Bessel ve Airy Denklemleri

Airy–Bessel wave packets as versatile linear light bullets

The generation of spatiotemporal optical wave packets that are impervious to both dispersion and diffraction has been a fascinating challenge1. Despite intense research activity, such localized waves, referred to as light bullets, have remained elusive. In nonlinear propagation, three-dimensional light bullets tend to disintegrate as a result of inherent instabilities2,3. Threedimensional wave ...

Nonparaxial shape-preserving Airy beams with Bessel signature.

Spatially accelerating beams that are solutions to Maxwell equations may propagate along incomplete circular trajectories. Taking these truncated Bessel fields to the paraxial limit, some authors have sustained that it has recovered the known Airy beams (AiBs). Based on the angular spectrum representation of optical fields, we demonstrated that the paraxial approximation rigorously leads to off...

Exploring Bessel beams, Airy beams, and Hydrogen-like linear bullets

Calogero-moser Pairs and the Airy and Bessel Bispectral Involutions

This paper follows upon the study of the Airy bispectral involution made in [KR]. There we gave an analogue, for arbitrary rank, of the rank-one bispectral involution developed by Wilson [W1]. Recently, [W2], Wilson has established a relationship between the rank-one bispectral involution and the complex analogue of the CalogeroMoser phase space. This relationship leads to explicit formulae for...

Rigidity of Determinantal Point Processes with the Airy, the Bessel and the Gamma Kernel

A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main result of this paper is that determinantal point processes with the Airy, the Bessel and the Gamma kernels are rigid. The proof follows the scheme of Ghosh [6]...