Tackling the phase problem of diffraction for retrieval of photonic structures formed in nanocomposite materials

We experimentally demonstrate how to solve the phase problem of diffraction using multi-wave interference with standard diffraction experimental setups without the need for taking any auxiliary data. In particular, we show that the phases of the Fourier components of a periodic structure can be fully recovered by deliberately choosing a probe wavelength of the diffracting radiation much smaller than the lattice constant. In the course of the demonstration, we accurately determine the refractive index profile of nanocomposite phase gratings by light and neutron diffraction measurements.