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 on a laser beam. Unlike static diffractive elements, OPAs are active, dynamical, and rewritable. 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. We have implemented the optimization algorithm in a PC-based design tool for fan-out gratings, radial phase elements, 2D holograms, and refractive correctors. We present many examples of optimized designs for these elements, and show how this design technology can be transitioned to applications that include fiber mode coupling and optical correlators. Innovative physical realizations of these dynamic optical elements can be achieved using spatial light modulators based on liquid crystals or MEMS.