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...

– A unitary operator which relates the system of a particle in a linear potential with time-dependent parameters to that of a free particle, has been given. This operator, closely related to the one which is responsible for the existence of coherent states for a harmonic oscillator, is used to find a general wave packet described by an Airy function. The kernel (propagator) and a complete set o...

We investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence. The Hilbert-Polya operator in this interpretation is the master matrix of the large N matrix model. Using a related function Ξ(z) we develop an analog between this function and the Airy function Ai(z) of the Gaussian matrix model. The analog...

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...

We introduce the generalized Airy-Gauss (AiG) beams and analyze their propagation through optical systems described by ABCD matrices with complex elements in general. The transverse mathematical structure of the AiG beams is form-invariant under paraxial transformations. The conditions for square integrability of the beams are studied in detail. The model of the AiG beam describes in a more rea...

We evaluate the partition functions in the neighbourhood of catastrophes by saddle point integration and express them in terms of generalized Airy functions.