Although diffractive spreading is an unavoidable feature of all wave phenomena, certain waveforms can attain propagation-invariance. A lesser-explored strategy for achieving optical selfsimilar propagation exploits the modification of the spatio-temporal field structure when observed in reference frames moving at relativistic speeds. For such an observer, it is predicted that the associated Lor...

We report the propagation dynamics of Airy light beams under non-paraxial conditions. It is studied using the general approach which deals with Fourier expansion of the beam. We show the transformation of the beam from the Airy form as the paraxiality parameter decreases. The role of evanescent waves in non-paraxial regime is discussed. c © 2009 Optical Society of America OCIS codes: 260.0260, ...

We predict and demonstrate the generation of a plasmonic hot spot on the surface of a metal film by the interference of two Airy surface plasmons. We show that the position of the hot spot can be controlled by the distance between the excitation gratings as well as by the phase front of the initial excitation. The observed effect constitutes a planar analogy to Airy beam autofocusing and offers...

We theoretically and experimentally study the phenomena related to self-phase modulation of Airy pulses in fibers. During nonlinear evolution, most spectral components of the Airy pulses concentrate into one or two peaks for normal and anomalous dispersion, respectively. The resulting peaks self-shift along the propagation, effectively mapping the longitudinal coordinate into the frequency doma...

We demonstrate the existence of accelerating parabolic beams that constitute, together with the Airy beams, the only orthogonal and complete families of solutions of the two-dimensional paraxial wave equation that exhibit the unusual ability to remain diffraction-free and freely accelerate during propagation. Since the accelerating parabolic beams, like the Airy beams, carry infinite energy, we...

We demonstrate both experimentally and theoretically controlled acceleration of one- and two-dimensional Airy beams in optically induced refractive-index potentials. Enhancement as well as reduction of beam acceleration are realized by changing the index gradient, while the beam shape is maintained during propagation through the linear optical potential. Our results of active acceleration manip...

We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge...