Arbitrary accelerating micron-scale caustic beams in two and three dimensions

We generate arbitrary convex accelerating beams by direct application of an appropriate spatial phase profile on an incident Gaussian beam. The spatial phase calculation exploits the geometrical properties of optical caustics and the Legendre transform. Using this technique, accelerating sheet caustic beams with parabolic profiles (i.e. Airy beams), as well as quartic and logarithmic profiles are experimentally synthesized from an incident Gaussian beam, and we show compatibility with material processing applications using an imaging system to reduce the main intensity lobe at the caustic to sub-10 micron transverse dimension. By applying additional and rotational spatial phase, we generate caustic-bounded sheet and volume beams, which both show evidence of the recently predicted effect of abrupt autofocussing. In addition, an engineered accelerating profile with femtosecond pulses is applied to generate a curved zone of refractive index modification in glass. These latter results provide proof of principle demonstration of how this technique may yield new degrees of freedom in both nonlinear optics and femtosecond micromachining.