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. Here we study the case of second-order harmonic vortex beams, generated from a gaussian pump beam. These crystals can be used to produce multidimensional entanglement of photons by angular momentum states or for shaping the vortex's structure and polarization.

We present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadratic media, which are also the first nonlinear self-accelerating beams in any symmetric nonlinearity. Notably, we show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another, but the coupled harmonics exhibit joint acceleration within the nonlinear medium. Finally, we demonstrate the impact of self-healing effects on the jointly accelerating first and second harmonics.

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.

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We report analytical solutions for spatial solitons supported by layers of a quadratically nonlinear (χ (2) ) material embedded into a linear planar waveguide. A full set of symmetric, asymmetric, and antisymmetric modes pinned to a symmetric pair of the nonlinear layers is obtained. The solutions describe a bifurcation of the subcritical type, which accounts for the transition from the symmetric to asymmetric modes. The antisymmetric states (which do not undergo the bifurcation) are completely stable (the stability of the solitons pinned to the embedded layers is tested by means of numerical simulations). Exact solutions are also found for nonlinear layers embedded into a nonlinear waveguide, including the case when the uniform and localized χ (2) nonlinearities have opposite signs (competing nonlinearities). For the layers embedded into the nonlinear medium, stability properties are explained by comparison to the respective cascading limit.+∞ −∞ |u(x)| 2 dx ≡ 1. In particular, the formal application of the Vakhitov-Kolokolov (VK) criterion, dP/dµ < 0, which is a necessary stability condition for solitons in self-focusing nonlinear media [8], predicts neutral stability of solutions (3). In fact, all these degenerate solitons are unstable, collapsing into a singularity or decaying, as illustrated by another analytical solution to Eq. (1), which explicitly describes the onset of the collapse at z → −0 [9]:Here x 0 > 0 is an arbitrary real constant, and z is negative. The same solution (4) with x 0 < 0 describes decaying solitons at z > 0 [9]. The power of this solution is also P = 1, irrespective of the value of x 0 . The solitons may be stabilized if a linear periodic potential is added to Eq. (1) [9]. The stability is also achieved if the single δ-function in Eq. (1) is replaced by a symmetric pair, which corresponds to the equation introduced in Ref.[10], iu z + (1/2)ψ xx + [δ(x − L/2) + δ(x + L/2)] |ψ| 2 ψ = 0.(5)

A method is proposed for nonlinear beam shaping, employing a non‐collinear quasi phase‐matched interaction in a crystal whose nonlinear coefficient is encoded by a computer generated hologram pattern. In this method the same axis is used for both satisfying the phase‐matching requirements and encoding the holographic information, the result is a single shaped beam in the generated frequency. This allows to shape beams in one‐dimension using a very simple method to fabricate patterned nonlinear crystals and to shape beams in two‐dimensions with high conversion efficiency. The one‐dimensional case is experimentally demonstrated by converting a fundamental Gaussian beam into Hermite‐Gaussian beams at the second harmonic in a KTiOPO4 crystal. The two‐dimensional case is demonstrated by generating Hermite‐Gaussian and Laguerre‐Gaussian beams in a stoichiometric lithium tantalate crystal. The suggested scheme enables broad wavelength tuning by simply tilting the crystal.