Bayesian probability theory is applied to the problem of the resolution of closely-spaced objects. The conditions assumed are: point sources, observed through a known smearing function (i.e., point-spread function). For this demonstration we use a Gaussian smearing function so that we can obtain analytic results; however, we present graphical results for both the Gaussian and the Airy smearing ...

Airy beams are non-diffracting optical beams first predicted by Berry and Balazs in 1979 and first demonstrated experimentally by Siviloglou, Broky, Dogariu, and Christodoulides in 2007. What makes an Airy beam unique is that it can be created in one dimension and that its lobe of highest intensity propagates along a parabolic path. Airy beams can be used for a variety of purposes including par...

We consider a discrete polynuclear growth (PNG) process and prove a functional limit theorem for its convergence to the Airy process. This generalizes previous results by Prähofer and Spohn. The result enables us to express the F1 GOE Tracy-Widom distribution in terms of the Airy process. We also show some results, and give a conjecture, about the transversal fluctuations in a point to line las...

The packing of hard-core particles in contact with their neighbors is a statically determinate problem. probability functional method allows deriving the full system equations for stress tensor components analytically. For an isotropic and homogeneous two-dimensional packing, we derive classical Euler–Cauchy Navier equations; latter expressing terms Airy function.

We report the first observation of Airy optical beams. This intriguing class of wave packets, initially predicted by Berry and Balazs in 1979, has been realized in both one- and two-dimensional configurations. As demonstrated in our experiments, these Airy beams can exhibit unusual features such as the ability to remain diffraction-free over long distances while they tend to freely accelerate d...

We report the experimental generation and dynamic trajectory control of plasmonic Airy beams (PABs). The PABs are created by directly coupling free-space Airy beams to surface plasmon polaritons through a grating coupler on a metal surface. We show that the ballistic motion of the PABs can be reconfigured in real time by either a computer addressed spatial light modulator or mechanical means.

In this paper, we establish the linear profile decomposition for the Airy equation with complex or real initial data in L, respectively. As an application, we obtain a dichotomy result on the existence of maximizers for the symmetric Airy-Strichartz inequality.

We report experiments and numerical simulations on the self-focusing and filamentation of ultraintense femtosecond Airy waveforms in water. The accelerating property of Airy waveforms results in the generation of distinct features in the angularly resolved spectra of forward-propagating supercontinuum emission. Fitting these features with appropriate phase-matching conditions allows for the qua...