We combine metasurface optics and refractive optics to form hybrid lenses, where the refractive elements provide the optical power but metasurfaces are used to correct aberrations. We introduce an algorithm to optimize layout of metasurfaces (MSs) in hybrid lens designs where the MSs can be located anywhere in the optical train. This algorithm uses a ray-based, scalar field method to propagate through refractive optics with speed comparable to Fourier methods, which are limited to propagation between planar surfaces. This method supports propagation of real optical fields and derived adjoint fields, both forward and backward, which enables inverse design with adjoint gradient methods to optimize the MS nanostructured layout. In contrast to previous image-space optimizations which neatly partition the problem into separate ray-optics and wave-optics domains, this algorithm provides the freedom to arbitrarily interleave metasurface optics with refractive optics during hybrid lens design. A hybrid lens design example in mid-wave infrared is presented to demonstrate this framework.
We present the design of a “hole” meta-atom basis, the inverse of nanorods, in the silicon-on-insulator (SOI) platform with a zinc sulfide (ZnS) anti-reflection (AR) layer that gives an average transmittance of 92% across half of the midwave infrared (MWIR) band from 3.5 to 4.5 μm. We numerically show this hole meta-atom exhibits reduced phase dispersion across the MWIR compared to the archetypal rod geometry. Effective index modelling is shown to accurately describe propagation phase delay through hole meta-atom periodic array. Bloch eigenmode analysis further reveals the small phase dispersion originates from its small modal index dispersion. A simple, analytical effective index model that only involves geometric and material parameters such as array filling factor and material refractive index is demonstrated. We further use this hole meta-atom to design a pair of metasurfaces to correct optical aberrations from a conventional lens and show that the performance is superior to its rod counterpart due to the reduced phase dispersion.
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