Unveiling the propagation dynamics of self-accelerating vector beams.

We study theoretically and experimentally the varying polarization states and intensity patterns of self-accelerating vector beams. It is shown that as these beams propagate, the main intensity lobe and the polarization singularity gradually drift apart. Furthermore, the propagation dynamics can be manipulated by controlling the beams' acceleration coefficients.

Dislocation parity effects in crystals with quadratic nonlinear response.

The effect of edge topological dislocations on the phase matching spectrum of quadratic nonlinear photonic crystals was studied theoretically and experimentally. We have found that the parity of the dislocation's topological charge governs the transfer of energy between an input wave and its second harmonic. A dislocation with an odd topological charge nulls the efficiency of the otherwise optimal phase matched wavelength, whereas high conversion is now achieved at new wavelengths that exhibited low efficiency without the dislocation.

Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.

We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump's radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new "virtual beam" having multiple values of OAM that are determined by the nonlinear process.

Generation of electron Airy beams.

Within the framework of quantum mechanics, a unique particle wave packet exists in the form of the Airy function. Its counterintuitive properties are revealed as it propagates in time or space: the quantum probability wave packet preserves its shape despite dispersion or diffraction and propagates along a parabolic caustic trajectory, even though no force is applied. This does not contradict Newton's laws of motion, because the wave packet centroid propagates along a straight line.

Twisting light by nonlinear photonic crystals.

We report the observation of nonlinear interactions in quadratic nonlinear crystals having a geometrically twisted susceptibility pattern. The quasi-angular-momentum of these crystals is imprinted on the interacting photons during the nonlinear process so that the total angular momentum is conserved. These crystals affect three basic physical quantities of the output photons: energy, translational momentum, and angular momentum.

Omnidirectional phase matching of arbitrary processes by radial quasi-periodic nonlinear photonic crystal.

We investigate second-harmonic generation in a nonlinear photonic crystal having radial quasi-periodic order and continuous rotational symmetry. This device enables us to simultaneously phase match different nonlinear interactions in any arbitrary direction of propagation. We have fabricated such a crystal by electric field poling of a magnesium-doped stoichiometric LiTaO(3) and demonstrated frequency doubling of two different pump wavelengths at three different angles.

Nonlinear diffraction from a virtual beam.

We observe experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic grating. We demonstrate that when the nonlinear grating is illuminated simultaneously by two noncollinear beams, a second-harmonic diffraction pattern is generated by a virtual beam propagating along the bisector of the two pump beams. The observed diffraction phenomena is a purely nonlinear effect that has no analogue in linear diffraction.