Continuous beam shaping with optical phased arrays using diffractive optics optimization

Optical Phased Arrays (OPAs) are equivalent to kinoform diffractive optical elements or holograms imparting a phase profile onto a laser beam. Unlike static diffractive elements, OPAs are active, dynamical, and re-writeable. These dynamical components can be used for beam propagation control if provided with control solutions. The goal of the control solutions is identical to the optimization of diffractive optical element design. We have developed a diffractive optics design optimization algorithm based on propagation reciprocity symmetry. The algorithm is completely wave-optics based and can be equally applied to the Fraunhofer and Fresnel diffraction regimes. The framework for the optimization is constrained Lagrangian dynamics and does not involve any stochastic integration. This makes it ideal for application to real-time OPA beam control.