Hexagonal diffraction gratings generated by convolutional neural network-based deep learning for suppressing high-order diffractions.

The $\pm 1$st order diffraction of gratings is widely used in spectral analysis. However, when the incident light is non-monochromatic, the higher-order diffractions generated by traditional diffraction gratings are always superimposed on the useful first-order diffraction, complicating subsequent spectral decoding. In this paper, single-order diffraction gratings with a sinusoidal transmittance, called hexagonal diffraction gratings (HDGs), are designed using a convolutional neural network based on deep learning algorithm. The trained convolutional neural network can accurately retrieve the structural parameters of the HDGs. Simulation and experimental results confirm that the HDGs can effectively suppress higher-order diffractions above the third order. The intensity of third-order diffraction is reduced from 20% of the first-order diffraction to less than that of the background. This higher-order diffraction suppression property of the HDGs is promising for applications in fields such as synchrotron radiation, astrophysics, and soft x-ray lasers.