Design methods for diffractive waveplate geometric phase elements

Geometric phase diffractive optics technology is rapidly advancing including patterned liquid crystal and polymer liquid crystal elements and devices. The need exists for a set of design methods and tools to engineer optical components and systems. Numerical and analytical design methods are discussed with an emphasis on optical systems. Multilevel simulation methods are used incorporating full numerical electromagnetic solutions, diffraction theory, and ray tracing. Additionally, iterative algorithms are used to design the local anisotropic axis orientation of various regions in order to produce the desired diffraction effects. Elements are optimized for both amplitude and phase. Examples are presented including an optical system based on geometric phase elements that sorts the orbital and spin angular momentum states of an optical beam. Designs are demonstrated in polymer liquid crystal diffractive waveplate thin film elements fabricated through photo-alignment with a spatial light polarization modulator. The array of numerical design technique presented allow the rapid design of optical phase patterns, integration with real optical systems, and evaluation of physical materials and device properties.