Recently, multilevel diffractive lenses (MDLs) have attracted considerable attention, mainly due to their superior wave-focusing performance; however, efforts to reduce chromatic aberration are still ongoing. Here, we present a numerical design and experimentally demonstrate a high-numerical aperture ($\sim 0.99$), diffraction-limited achromatic multilevel diffractive lens (AMDL), operating in the microwave range of 10–14 GHz. A multi-objective differential evolution (MO-DE) algorithm was incorporated with the three-dimensional (3D) finite-difference time-domain method to optimize the heights and widths of each concentric ring (zone) of the AMDL structure. To the best of our knowledge for the first time, in this study, the desired focal distance was also treated as an optimization parameter in addition to the structural parameters of the zones. Thus, MO-DE diminishes the necessity of predetermined focal distance and center wavelength by also providing an alternative method for phase profile tailoring. The proposed AMDL can be considered an ultra-compact and flat lens since it has the radius of $3.7{\lambda }_c$ and a thickness of $\sim {\lambda }_c$, where ${\lambda }_c$ is the center wavelength of 24.98 mm (i.e., 12 GHz). The numerically calculated full width at half maximum values are $<0.554\lambda$ and focusing efficiency values are varying between 28% and 45.5%. To experimentally demonstrate the functionality of the optimized lens, the AMDL composed of polylactic acid material polymer is fabricated via 3D-printing technology. The numerical and experimental results are compared, discussed in detail, and observed to be in good agreement. Moreover, the verified AMDL in the microwave regime is scaled down to the visible wavelengths to observe achromatic and diffraction-limited focusing behavior between 380 and 620 nm wavelengths.

中文翻译：

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通过元启发式方法的超紧凑、高数值孔径消色差多级衍射透镜

最近，多级衍射透镜（MDL）引起了相当大的关注，主要是由于其优越的波聚焦性能；然而，减少色差的努力仍在进行中。在这里，我们提出了一个数值设计并通过实验证明了高数值孔径（$～0.99$)，衍射极限消色差多级衍射透镜 (AMDL)，在 10-14 GHz 的微波范围内工作。多目标差分进化 (MO-DE) 算法与三维 (3D) 有限差分时域方法相结合，以优化 AMDL 结构的每个同心环（区域）的高度和宽度。据我们所知，在本研究中，除了区域的结构参数之外，所需的焦距也被视为优化参数。因此，MO-DE 还提供了一种用于相位轮廓剪裁的替代方法，从而减少了预定焦距和中心波长的必要性。所提出的 AMDL 可以被认为是一种超紧凑的平面透镜，因为它的半径为$3.7{\lambda }_C$ 和厚度 $～{\lambda }_C$， 在哪里 ${\lambda }_C$是中心波长 24.98 毫米（即 12 GHz）。数值计算的半高全宽值为$<0.554\lambda$和聚焦效率值在 28% 和 45.5% 之间变化。为了通过实验证明优化镜片的功能，通过 3D 打印技术制造了由聚乳酸材料聚合物组成的 AMDL。数值和实验结果进行了比较，详细讨论，并观察到良好的一致性。此外，在微波领域经过验证的 AMDL 被缩小到可见波长，以观察 380 和 620 nm 波长之间的消色差和衍射限制聚焦行为。