  Guided-mode resonances in diffraction gratings are manifested as peaks (dips)
in reflection (transmission) spectra. Smaller resonance line widths (higher
Q-factors) ensure stronger light-matter interactions and are beneficial for
field-dependent physical processes. However, strong angular and spectral
dispersion are inherent to such high-Q resonances. We demonstrate that a class
of high-Q resonant modes (Q-factor >1000) exhibiting extraordinarily weak
dispersion can be excited in crossed gratings simultaneously with the modes
with well-known nearly linear dispersion. Furthermore, we show that the
polarization of the incoming light can be adjusted to engineer the dispersion
of these modes, and strong to near-flat dispersion or vice-versa can be
achieved by switching between two mutually orthogonal linear polarization
states. We introduce a semi-analytical model to explain the underlying physics
behind these observations and perform full-wave numerical simulations and
experiments to support our theoretical conjecture. The results presented here
will benefit all applications that rely on resonances in free-space-coupled
geometries.
