Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns

We generate both accelerated Airy and accelerated parabolic beams using phase-only patterns encoded onto a liquid crystal display (LCD). The usual system length is 2f, where f is the focal length of the Fourier transform lens. We develop a compact optical system having a total system length of f. However, the mask must now incorporate the Fresnel diffraction that is not provided by the reduced optical system length. Finally we incorporate the Fourier transform lens onto the mask. We obtain excellent experimental results with a phase-only pattern and a shorter optical system. This approach makes these beams much easier to implement.