Mechanism study of all-dielectric metamaterial wideband reflector based on quasi-canonical mode*

All-dielectric metamaterial broadband reflectors have the advantages of low loss, high reflection efficiency, and compact structure. An in-depth understanding of the formation mechanism of their reflection bands is of great significance in optimizing metamaterial structure and performance, and in further designing novel photonic devices as well. In this work, two all-dielectric metamaterial broadband reflectors are constructed by using discrete silicon nanopillar array and silicon nanopillar array connected with a silicon sublayer. The quasi -normal modes of the metamaterial reflectors are solved. Combining the quasi-normal modes with the scattering matrix theory, we obtain the fitted reflection spectra of the metamaterial, and then reveal that the zero -frequency quasi-normal mode has a substantial influence on the accuracy of the fitting results. A dispersion relation analysis method is proposed to accurately solve the zero-frequency quasi-normal mode. Furthermore, the fitted resonance reflection spectrum and background reflection spectrum are obtained by using high -Q-value quasi-normal mode and low -Q-value quasi-normal mode, respectively. Our results show that the broadband reflection of the considered metamaterial reflectors should be attributed to the background reflection induced by the low -Q quasi-normal modes. The research method proposed in this paper can also be used for discussing quasi bound states in the continuum, Mie resonances, and other resonance phenomena, which provides a new way for interpreting the spectral characteristics of metamaterials.