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

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.

Multiscale Optical Field Manipulation via Planar Digital Optics

“…55 As shown in Figure 2b, Sang et al comprehensively investigated the efficiency gap between the conventional high numerical aperture (NA) metalens and the theoretical limitation of vector diffraction theory. 64 Moreover, Xu et al first introduced the topology optimization into disordered meta-optics and demonstrated that, with the efficient suppression of the lattice coupling effect, long-range ordered complex electric field could be realized in a disordered freeform metasurface (Figure 2c). 66 Although the computation complexity of topology optimization is relatively low, it is still a great challenge to inversely design a large-scale aperiodic metasurface because full-model rigorous electromagnetic simulation is required.…”

“…By imparting the abrupt phase shift at the interface, LC molecules with spatially variant orientations can be used to generate desired phase profiles based on the PB geometric phase. 84 fabrication resolution has also been developed to precisely control the orientations of LC molecules. The half-wave condition can be realized by controlling the thickness of the LC layer to achieve a high polarization conversion efficiency, up to 100% at the designed wavelength.…”

“…In contrast with the forward design approach, the inverse design could optimize the desired complex functionality by reshaping the regular meta-atoms into arbitrarily irregular topology. − One of the typical inverse design approaches is adjoint-based topology optimization, which is a local gradient descent algorithm requiring only two steps of full-wave electromagnetic simulation for each iteration process . Recently, it has demonstrated great success in realizing complex functionalities of metasurfaces and meta-optics, such as meta-gratings, − metalens, − disordered metasurfaces, , and other freeform metasurfaces. , For example, as shown in Figure a, Sell et al demonstrated a topology-optimized large-angle deflection meta-grating with 75% absolute deflection efficiency at 1050 nm . As shown in Figure b, Sang et al comprehensively investigated the efficiency gap between the conventional high numerical aperture (NA) metalens and the theoretical limitation of vector diffraction theory .…”

Ultra-Broadband Spectrally Selective Absorber for Solar Thermal Absorption Based on TiN Square-Ring Meta-Structure

“…where G is the total incident radiation, which can be expressed as 𝐺 = 𝐶 × 1000𝑊 ∕ 𝑚 2 [31], C is the solar concentrating coefficient, 𝜎 is the Stepan-Boltzmann constant and 𝜎 = 5.67 × 10 −8 𝑊 ∕ (𝑚 2 ⋅ 𝐾 4 ) , 𝑇 is the operating temperature of the absorber, 𝑇 0 is the atmospheric temperature which is agreed to be 273K. When C=1 and T=300K, the solar-thermal conversion efficiency 𝜂 of the proposed absorber is calculated to be 93.92%.…”

“…In addition to the basic performance of the traditional broadband absorber, solar absorber, as a kind of broadband absorber, is also required to have excellent spectral selectivity which is important to high absorption in solar spectra and low loss of thermal radiation emissivity in the mid-infrared band. With the deep research on metamaterial and surface plasmon, wideband absorbers with excellent spectral selectivity and insensitivity to polarization and incidence angle have been proposed one by one [3][4][5][6][7], which is expected to be applied in the design of solar absorbers. Further, kinds of solar spectrally selective absorber structures such as multilayer metal/insulator/metal structure [8][9][10][11][12], fishnet gratings [13][14][15][16], moth eye [17][18][19], and ring structure [20][21][22][23] have been studied for solar thermal absorption.…”