Hybrid metal-dielectric guided mode resonance devices have an advantage over the all-dielectric guided mode resonance device for having a thin metal grating conductive layer that can be used as an electrode for tunable applications. In this work, we investigate the coupling between the waveguide mode and surface plasmons of the gold nanoslits grating in the hybrid guided mode resonance filter. It is shown that the coupling between the waveguide mode and surface plasmons can be engineered by increasing either the thickness of the low index of the refraction spacing layer or the thickness of the high index of the refraction waveguide layer. Therefore, a narrow spectral linewidth and a high finesse of hybrid guided mode resonance filters can be obtained by increasing the thickness of the low index of the refraction spacing layer or the thickness of the high index of the refraction waveguide layer. A hybrid guided mode resonance transmission filter with a narrow spectral linewidth of 2.8 nm is designed at the 1660.2 nm center wavelength.

In this work, we propose and implement a machine learning method of using a forward deep learning neural network and Fano function inverse matching to design and optimize hybrid metal-dielectric guided mode resonance narrow linewidth optical filters. First, a forward deep learning neural network is trained with a small design sample set generated with finite difference time domain physical simulations. The trained forward neural network is then used to generate a large sample set of three million designs. In inverse matching process, filter peak wavelength and spectral linewidth are two matching parameters first used for down selecting designs from the large sample set to a small sample set. Because of the asymmetric nature of the guided mode resonance filter spectral line-shape, Fano functions are used to match against the spectra in the small sample set to find the design with narrow filter linewidth. Optical transmission filters with linewidth between 6.8 nm and 8.7 nm are designed in visible spectrum.