Toward High‐Efficiency Ultrahigh Numerical Aperture Freeform Metalens: From Vector Diffraction Theory to Topology Optimization

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Abstract
Optical metasurface is a 2D array of subwavelength meta‐atoms that arbitrarily manipulates amplitude, polarization, and wavefront of incident light, offering great advantages in miniaturization and integration. However, the presuppositions hidden in conventional unit‐cell‐based design approach, including discrete phase sampling, local periodicity approximation, and normal response, imply that the responses and interactions of meta‐atoms are almost impossible to be accurately modeled, thus impeding the effective design of high‐efficiency ultrahigh numerical aperture (NA) metalens. Here, based on vector diffraction theory and plane wave expansion method, theoretical limitation of metalens efficiency is comprehensively investigated. It is identified that for high‐NA metalens, theoretical focusing efficiency is limited by diffraction capability of vector field, while evanescent wave attenuation dominates theoretical efficiency decline for ultrahigh‐NA metalens. It is also shown that the efficiency of conventional metalens has a huge gap from theoretical limitation, owing to imperfect diffractive focusing and impedance mismatch reflections. To fill such efficiency gap, the high‐efficiency high‐NA freeform metalens based on topology optimization is further demonstrated. Particularly, topology geometric constraints are utilized to reduce minimum feature size while keeping high efficiency. The results could shed new light on the understanding and design of ultrahigh‐NA metalens and find promising applications in optical imaging, microscopy, and lithography.
Funding Information
  • National Natural Science Foundation of China (U20A20217, 62105338)

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