Asymmetric Transmissive Optical Surface Design

The patent applies asymmetry by removing symmetry assumptions from the optical beam-shaping system design. The invention enables design of asymmetric optical surfaces that can transform both symmetric and asymmetric input beam profiles into desired output profiles. This is achieved through a variational formulation that does not require symmetry constraints, allowing the optical surfaces to be optimized for general asymmetric cases while maintaining mathematical solvability through the use of transport equations and variational principles.

The patent applies local quality by designing optical surfaces with spatially varying properties that locally correct the non-uniform power distribution. The variational formulation allows optimization of the optical surface at each point to transform the local intensity and phase, enabling uniform power distribution across the entire expanded beam while maintaining the desired cross-sectional area expansion.

The patent applies merging by combining the functions of multiple optical elements into a single transmissive optical element. Instead of using separate reflectors that require precise alignment, the invention integrates the beam-shaping functionality into one element with optimized surfaces, eliminating alignment issues between multiple components while maintaining the ability to transform asymmetric profiles.

The patent applies asymmetry by formulating the optical design problem without symmetry assumptions, enabling direct design of asymmetric optical surfaces. The variational approach provides mathematical solvability for the general asymmetric case, and the resulting single-element design reduces manufacturing complexity by eliminating alignment requirements between multiple components.