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We theoretically and numerically investigate resonant optical properties ofcomposite structures consisting of several subwavelength resonant diffractiongratings separated by homogeneous layers. Using the scattering matrixformalism, we demonstrate that the composite structure comprising N gratingshas a multiple transmittance zero of the order N. We show that at the distancebetween the gratings satisfying the Fabry-P\'erot resonance condition, an(N-1)-degenerate bound state in the continuum (BIC) is formed. The results ofrigorous numerical simulations fully confirm the theoretically predictedformation of multiple zeros and BICs in the composite structures. Near theBICs, an effect very similar to the electromagnetically induced transparency isobserved. We show that by proper choice of the thicknesses of the layersseparating the gratings, nearly rectangular reflectance or transmittance peakswith steep slopes and virtually no sidelobes can be obtained. In particular,one of the presented examples demonstrates the possibility of obtaining anapproximately rectangular transmittance peak having a significantlysubnanometer width. The presented results may find application in the design ofoptical filters, sensors and devices for optical differentiation andtransformation of optical signals.

Resonant properties of composite structures consisting of several resonant diffraction gratings