Computational inverse design for ultra-compact single-piece metalenses free of chromatic and angular aberration

Zin Lin,Marin Soljačić,Charles Roques-Carmes,Steven G Johnson,Rasmus E Christiansen

doi:10.1063/5.0035419

Zin Lin, Marin Soljačić + Show 3 more

Open Access

https://doi.org/10.1063/5.0035419

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Abstract

We present full-Maxwell topology-optimization design of a single-piece multilayer metalens, about 10 wavelengths λ in thickness, which simultaneously focuses over a 60° angular range and a 23% spectral bandwidth without suffering chromatic or angular aberration, a “plan-achromat.” At all angles and frequencies, it achieves diffraction-limited focusing (Strehl ratio &gt;0.8) and an absolute focusing efficiency of &gt;50%. Both 2D and 3D axisymmetric designs are presented, optimized over ∼105 degrees of freedom. We also demonstrate shortening the lens-to-sensor distance while producing the same image as for a longer “virtual” focal length and maintaining plan-achromaticity. These proof-of-concept designs demonstrate the ultra-compact multifunctionality that can be achieved by exploiting the full wave physics of subwavelength designs and motivate future work on design and fabrication of multilayer metaoptics.

Highlights

Modern AR/VR applications demand increasingly sophisticated optical components with ultra-compact form-factors that can deliver the same level of performance as their conventional bulky counterparts
We propose new nanophotonic solutions for miniaturization of optics, which reduce the role of ray mechanics and free-space propagation, by exploiting the much richer wave interactions occurring in nanostructured photonic media
Topology optimization (TO) discovers a design with a fairly uniform Strehl ratio (SR) ≈ 0.89, achieving aberration-free diffraction-limited focusing for all the design frequencies and angles; the uniformity is a typical by-product of the epigraph formulation [35]. (In between the frequencies and angles targeted in the design process, SR averages to above 0.7) In addition to SR, it is instructive to compute the absolute focusing effciency (AE), defined as the fraction of transmitted power within three full-widths at half-maximum (FWHM) around the focal peak divided by the total incident power

Summary

Introduction

Modern AR/VR applications demand increasingly sophisticated optical components with ultra-compact form-factors that can deliver the same level of performance as their conventional bulky counterparts. We present single-piece nanophotonic plan-achromats (Fig. 1b) for achromatic, aplanatic and curvature-free focusing, that is, realizing diffraction-limited focal spots (Strehl ratio > 0.8 and absolute focusing efficiency of up to 65%) at precisely prescribed positions on a flat sensor over finite spectral and angular bandwidths (Sections 2 and 3). These results motivate future work to combine advances in 3D fabrication [13,14,15,16] with computational methods for imposing fabrication constraints [17,18,19] in order to tailor these capabilities and explore manufacturing tradeoffs for specific applications. Achieving single-piece plan-achromaticity (i.e. aberration-free focusing over simultaneous spectral and angular bandwidths) remains an open problem. Our computational results indicate that it is possible to design single-piece uni-body plan-achromats, enabled by utilizing 3D nanophotonics, circumventing the necessity of multiplet ray-optics designs

Inverse design of a single-piece plan-achromat

Axisymmetric inverse design for off-axis incidence

Plan-achromat with a virtual focal length

Findings

Summary and outlook