**4. Conclusions**

In summary, we have proposed an effective way to achieve multifunctional polarization manipulation by a metagrating consisting of periodically arranged meta-atoms inside dielectric gratings. As a proof-of-concept experiment, we have designed and fabricated a sub-wavelength metagrating that consists of wheel-like meta-atoms. The metagrating works in both transmission and reflection modes efficiently. The phase differences between the two principal axes are monotonically altering with the frequencies in transmission mode covering a large dynamic range from 0 to 2π, while they are approximately kept at about π in a broad bandwidth region in reflective mode. Our measurements show that the metagrating can work as a dual-mode, high-efficiency, and multifunctional wave plate to realize various functions including linear-to-circular polarization conversion, linear or circular cross-polarization conversion, and chirality preserving mirror in different frequency bands simultaneously accompanied by a large angular invariance. Such versatile functionalities provide grea<sup>t</sup> flexibilities for optical polarization control devices. The design of metagrating can be extended to other frequency ranges as a compact optical polarization controller in the applications of telecommunications, radar detections, and optical devices.

**Author Contributions:** Conceptualization and methodology, K.S., R.J., J.Z. and X.Z.; data analysis, K.S., R.J., W.Z. and J.Z.; investigation, C.D., W.H., H.L., Y.G., Y.T. and Y.L.; software, K.S., R.J., D.S., C.D. and W.Z.; writing—original draft preparation, K.S., R.J. and J.Z.; writing—review and editing, K.S., R.J., J.Z. and X.Z.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grant Nos. 61601375, 61805204, 11874301, 11674267 and 61701303); Natural Science Basic Research Plan in Shaanxi Province of China (Grant Nos. 2018JQ1036 and 2017JM1009); Fundamental Research Funds for the Central Universities (Grant Nos. 3102016ZY029, 3102017OQD076, 3102017jghk02004 and 3102017zy015); KRISS gran<sup>t</sup> GP2018-0023; AOARD gran<sup>t</sup> FA2386-18-1-4104 funded by the U.S. governmen<sup>t</sup> (AFOSR/AOARD).

**Conflicts of Interest:** The authors declare no conflict of interest.
