By using the equivalent eigenvalue equation of a waveguide grating, the mirror effect $(\Delta \lambda ∕\lambda >15\%)$ with very high reflectivity $(R>99\%)$ based on guided-mode resonance (GMR) effects in a poly-Si subwavelength periodic membrane is obtained, and the reflection performance of the poly-Si subwavelength periodic membrane is systematically studied. It is shown that the equivalent eigenvalue equation of a waveguide grating can provide a solid starting point for designing the broadband grating with very high reflectivity. The physical mechanisms of broadband reflection of the strongly modulated waveguide grating structures are investigated theoretically and the important role of multiple GMRs for a broad reflection band is discussed in detail. By using the overlap of a resonance pair in which leaky waveguide modes ${\mathrm{TE}}_0$ and ${\mathrm{TE}}_1$ are excited by the strong first diffraction order, enhanced reflection occurs and a flat reflection band with high reflectivity can be achieved by adding a poly-Si thin film under the grating. The grating period, the grating thickness, and the layer thickness do not change the mirror effect except for the incident angle and the filling factor. A flat band with high reflectivity centered near $1.55\mu \mathrm{m}$ is designed to demonstrate this concept.