Generation of second-harmonic beams with switchable curved trajectories

Beams which follow curved trajectories are useful in a variety of applications, but up to now have been realized mainly in linear media. We demonstrate theoretically and experimentally the generation of second-harmonic (SH) beams which follow arbitrary convex caustic trajectories. These beams are created in a nonlinear photonic crystal with a second-order susceptibility having a tailored pattern; hence, the SH beam follows the desired trajectory after exiting the crystal. The same crystal can incorporate more than one trajectory, enabling the nonlinear creation of bottle beams as well as beams with switchable caustic trajectories that can be controlled by the phase-matching conditions.