Not yet reviewed by Pith; the record is open.

In conventional diffraction theory, a subwavelength period is considered a prerequisite to achieve interesting resonance-assisted physical phenomena, such as bound states in the continuum and diverse zero-order spectral responses with $100\%$ diffraction efficiency. Here, we present modified diffraction equations that provide mechanisms to control light diffraction beyond the subwavelength limit. We show that resonant diffraction phenomena are governed by the superposition of scattering processes, owing to higher Fourier harmonic components. By appropriately engineering the Fourier harmonic components in the grating parameters, unwanted diffraction orders can be suppressed. Moreover, bound states in the continuum and highly efficient zero-order spectral responses can be achieved beyond the subwavelength limit. The concept of engineering Fourier harmonic components in periodic modulations provides new mechanisms to overcome the diffraction limit.