We have developed multifunctional optical beam shapers based on plasmonic metasurfaces. The metasurfaces are composed of subwavelength-spaced polarization- and wavelength-selective optical nanoantennas that allow encoding several beam shapers on a single element. We demonstrate numerically and experimentally beam shapers that can be used to switch between arbitrary beam shapes. We specifically ...

We present experimental control of the acceleration direction of Airy beams generated by nonlinear three-wave mixing processes in an asymmetrically poled nonlinear photonic crystal. Changing the crystal temperature enabled us to switch the phase matching condition between second-harmonic generation and difference-frequency generation in the same nonlinear crystal and thereby to change the accel...

In deriving uniform asymptotic expansions of a certain class of integrals one encounters the problem of expanding a function, that is analytic in some domain Ω of the complex plane, in two points. The first mention of the use of such expansions in asymptotics is given in [1], where Airy-type expansions are derived for integrals having two nearby (or coalescing) saddle points. This reference doe...

We present experimentally the control of free space propagation of an Airy beam. This beam is generated by a nonlinear wave mixing process in an asymmetrically poled nonlinear photonic crystal. Changing the quasi-phase matching conditions, e.g., the crystal temperature or pump wavelength, alters the location of the Airy beam peak intensity along the same curved trajectory. We explain that the v...

We determine the class of entire functions for which the Airy kernel (of random matrix theory) is a reproducing kernel. We deduce an Airy sampling series and quadrature formula. Our results are analogues of well known ones for the Bessel kernel. The need for these arises in investigating universality limits for random matrices at the soft edge of the spectrum. 1. Introduction Universality limit...

In the case of the equidistant discretization of the Airy differential equation (“discrete Airy equation”) the exact solution can be found explicitly. This fact is used to derive a discrete transparent boundary condition (TBC) for a Schrödinger–type equation with linear varying potential, which can be used in “parabolic equation” simulations in (underwater) acoustics and for radar propagation i...