Ultra-short beam expander with segmented curvature control: the emergence of a semi-lens.

We introduce direct curvature control in designing a segmented beam expander, and explore novel design possibilities for ultra-compact beam expanders. Assisted by the particle swarm optimization algorithm, we search for an optimal curvature-controlled multi-segment taper that maintains width continuity. Counterintuitively, the optimization yields a structure with abrupt width discontinuity and width compression features. Through spatial phase and parameterized analysis, a semi-lens feature is revealed that helps to flatten the wavefront at the output end for higher coupling efficiency. Such functionality cannot be achieved by normal tapers in a short distance. The structure is fabricated and characterized experimentally. By a figure of merit that accounts for expansion ratio, length, and efficiency, this structure outperforms an adiabatic taper by 9 times.