  Conventional photonic lattices, such as metamaterials and photonic crystals,
exhibit various interesting physical properties that are attributed to periodic
modulations in lattice parameters. In this study, we introduce novel types of
photonic lattices, namely Fourier-component-engineered metasurfaces, that do
not possess the first Fourier harmonic component in the lattice parameters. We
demonstrate that these metasurfaces support the continuous high-$Q$ bound
states near second stop bands. The concept of engineering Fourier harmonic
components in periodic modulations provides a new method to manipulate
electromagnetic waves in artificial periodic structures.
