# Optical Realization of Wave-Based Analog Computing with Metamaterials
## 4 Conclusions and Outlook  
In this review, we have presented some of the most exciting developments in the field of analogous optical computing taking advantage of metamaterials, offering an integrated and miniaturized platform for image processing and edge detection to overcome the limitations of digital electronic computers. With continuous exploitation, tremendous novel approaches have been proposed based on different physical mechanisms, including Brewster effect, surface plasmonic, photonic spin Hall effect, local/excitation mode coupling to implement mathematical operations. Despite the promising unprecedent advances of meta-structures over traditional optical system for analog computing, to date, it is still extremely challenging to further improve the performance which is limited by spatial resolution, efficiency, operating bandwidth, strong polarization/angle/symmetry dependence. In general, computational metamaterials can be divided into two major categories: plasmonics and dielectrics. Leveraging highly confined surface plasmonic modes, plasmonic spatial differentiators process advantages of simplicity and ultracompact size. However, they suffer from some fundamental limitations, for instance, the critical coupling condition limits the incident angles, the presence of higher-order Taylor coefficients lead to a narrow spatial bandwidth and further effect the resolution of the computational system. In addition, the conversion efficiency is restricted by intrinsic material loss. To improve the efficiency and achieve high-resolution edge detection, all-dielectric metasurface is emerging as an alternative platform, which is a promising candidate for further broadening of the operational spatial bandwidth and reducing the absorption losses. It should be mentioned that dielectric metasurfaces also have some drawbacks--some of them only work for one polarization while the energy of other polarized waves is completely wasted, which may lead to relatively low signal-to-noise ratio. Moreover, determining how to balance the features of numerical aperture, efficiency and spatial resolution requires an elaborate design [157].  
Although some limitations exist in this emerging field, we are pleased to see that many achievements have been proposed and demonstrated to overcome these drawbacks. [PERSON] et al. [158] proposed a photonic crystal differentiator with improved robustness with incoherent light. [PERSON] et al. [145] designed a nonlocal metasurface by engineering nonlocality in momentum space that can perform both even- and odd-order differentiations. This study provides a high-quality, efficient and polarization-insensitive image processing platform for 2D edge detection. We believe that as it continuously evolves, the metamaterial-based analogous optical computing will be extensively applied in signal and image processing.  
[PERSON] conceived the review; [PERSON], [PERSON] wrote the manuscript; [PERSON], [PERSON], [PERSON], [PERSON] revised the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (No. 11774057, 12074314, 11674266), This research was funded by Funds for Equipment Advance Research during the 13 th Five-Year Plan under Grant 61400030305.  
Data Availability StatementData sharing not applicable.  
The authors declare no conflict of interest.