Written by: Ido Dolev

Nonlinear photonic crystals are crystals in which the second order susceptibility is spatially modulated with micron or even sub-micron resolution. These structures are often used in nonlinear optics applications for compensating the phase mismatch between interacting waves, usually using the quasi phase matching technique. Whereas usually both the input beams, as well as the generated beams are assumed to be Gaussian (and hence diffracting) beams, we consider nonlinear interactions with so-called non-diffracting beams. These beams can be sub-divided into beams that propagate, in free space, in a straight line – Bessel and Mathieu beams; and in a parabolic trajectory (accelerating beams) – Airy beam and parabolic beams. Our work explores methods of generation, manipulation and nonlinear mixing of special non-diffracting and accelerating laser beams, in one and two-dimensionally modulated nonlinear photonic crystals.

We demonstrate experimentally nonlinear generation and mixing of non-diffracting and accelerating beams: Using a specially designed asymmetric nonlinear photonic crystal, a fundamental Gaussian beam can be converted into an accelerating 1-D Airy beam at a new frequency by either second harmonic generation (SHG) or by difference frequency generation (DFG) processes [1-3]. Efficient three-wave-mixing of non-diffracting beams can be achieved in standard one-dimensional nonlinear crystals [4], provided that the process is performed with the Fourier transform of the input beams.

References:

1. T. Ellenbogen, N. Voloch, A.Ganany-Padowicz, and A. Arie, "Nonlinear generation and manipulation of Airy beams", Nat. Photonics, 3, 395-398 (2009) pdf.
2. I. Dolev, T. Ellenbogen, N. Voloch, and A. Arie, "Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals", Applied Physics Letters 95, 201112 (2009) pdf.
3. I. Dolev, T. Ellenbogen, and A. Arie, "Switching the acceleration direction of Airy beams by a nonlinear optical process", Optics Letters, 35, 1581-1583 (2010) pdf.
4. I. Dolev, and A. Arie, “Three Wave Mixing of Airy Beams in a Quadratic Nonlinear Photonic Crystal”, Applied Physics Letters, 97, 171102 (2010) pdf.