We show both experimentally and numerically, control over the acceleration of two-dimensional Airy beam propagating in optically induced photonic lattice. Varying the lattice strength and including various defects we can reach a state, where the acceleration is completely stopped. We find an additional class of discrete lattice beams, localized and defect modes observed with Airy beams propagat...

We demonstrate experimentally the manipulation of Airy surface plasmon beams in a linear potential. For this purpose, we fabricate dielectric-loaded plasmonic structures with a graded refractive index by negative-tone gray-scale electron beam lithography. Using such carefully engineered potentials, we show that the bending of an Airy surface plasmon beam can be fully reversed by the potential.

We investigate the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations. We show that this class of finite energy waves can retain their intensity features over several diffraction lengths. The possibility of other physical realizations involving spatiotemporal Airy wave packets is also considered.

In this paper, we consider the discrete Laguerre polynomials [Formula: see text] orthogonal with respect to weight function supported on infinite nodes text]. We focus “band-saturated region” situation when parameter As text], uniform expansions for are achieved in different regions complex plane. Typically, Airy-function and Gamma-function derived near endpoints of band origin, respectively. T...

The small crater Airy-0 was selected from Mariner 9 images to be the reference for the Mars prime meridian. Initial analyses in the year 2000 tied Viking Orbiter and Mars Orbiter Camera images of Airy-0 to the evolving Mars Orbiter Laser Altimeter global digital terrain model to update the location of Airy-0. Based upon this tie and radiometric tracking of landers/rovers from Earth, new express...

We present a class of solutions to the discrete Painlevé-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati determinants whose entries are discrete Airy functions. The analogy between the τ function for the discrete PII and the that of the discrete Toda molecule equation is pointed out.

Our study is initiated by a multi-component particle system underlying the tiling of a half hexagon by three species of rhombi. In this particle system species j consists of ⌊j/2⌋ particles which are interlaced with neigbouring species. The joint probability density function (PDF) for this particle system is obtained, and is shown in a suitable scaling limit to coincide with the joint eigenvalu...

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...

Airy beams maintain their intensity profiles over a large propagation distance without substantial diffraction and exhibit lateral bending during propagation1-5. This unique property has been exploited for micromanipulation of particles6, generation of plasma channels7 and guidance of plasmonic waves8, but has not been explored for high-resolution optical microscopy. Here, we introduce a self-b...

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