Integer multi-wavelength gradient phase metagrating for perfect refraction: Phase choice freedom in supercella).

Phase gradient metagratings (PGMs) reshape the impinging wavefront though the interplay between the linear adjacent phase increment inside supercells and the grating diffraction of supercells. However, the adjacent phase increment is elaborately designed by tuning the resonance of each subcell at a certain target frequency, which inevitably confines PGMs to operate only at the single frequency in turn. We notice that there exists a freedom of phase choice with a multi-2π increment in a supercell of PGMs, whereas conventional designs focus on the 2π increment. This freedom can induce a collaborative mechanism of surface impedance matching and multi-wavelength subcells, enabling the design of PGMs at multi-wavelengths. We further design and fabricate a supercell consisting of eight curved pipes to construct the two-wavelengths PGMs. The linear adjacent phase gradient of 0.25π at the fundamental frequency 3430 Hz is achieved, while the almost perfect transmission effect is observed due to the impedance match at the ends of curved pipes. In addition, the transmission field at the double frequency 6860 Hz is measured, whose refraction direction is consistent with that at 3430 Hz. This design strategy originated from phase choice freedom in the supercell and the experimental fabrication might stimulate applications on other multi-wavelength metasurfaces/metagratings.