Longitudinal optical field modulation is of critical importance in a wide range of applications, including optical imaging, spectroscopy, and optical manipulation. However, it remains a considerable challenge to realize a uniformly distributed light field with extended depth-of-focus. Here, a high-efficiency extended depth-of-focus metalens is proposed by adjoint-based topology-shape optimization approach, wherein the theoretical electric field intensity corresponding to a variable focal-length phase is utilized as the figure of merit. Using a dozen of metalens with random structure parameters as initial structures, the average focal depth of topology-shape optimized metalens is greatly improved up to 18.80 μm (about 29.7λ), which is 1.54 times higher than the diffraction-limited focal depth. Moreover, all the topology-shape optimized metalens exhibit high diffraction efficiency exceeding 0.7 over the whole focal depth range, which is approximately three times greater than that of the forward design. Our results offer a new insight into the design of extended depth-of-focus metalens and may find potential applications in imaging, holography, and optical fabrication.

中文翻译：

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通过拓扑形状优化设计高效扩展焦深元透镜

纵向光场调制在广泛的应用中至关重要，包括光学成像、光谱学和光学操作。然而，实现具有扩展焦深的均匀分布的光场仍然是一个相当大的挑战。在这里，通过基于伴随的拓扑形状优化方法提出了一种高效的扩展焦深元透镜，其中将对应于可变焦距相位的理论电场强度用作品质因数。使用十几个具有随机结构参数的元透镜作为初始结构，拓扑形状优化的元透镜的平均焦深大大提高至18.80 μm（约29.7λ)，比衍射极限焦深高 1.54 倍。此外，所有拓扑形状优化的元透镜在整个焦深范围内都表现出超过 0.7 的高衍射效率，大约是正向设计的三倍。我们的研究结果为扩展焦深超透镜的设计提供了新的见解，并可能在成像、全息术和光学制造中找到潜在的应用。