  We theoretically and numerically investigate resonant optical properties of
composite structures consisting of several subwavelength resonant diffraction
gratings separated by homogeneous layers. Using the scattering matrix
formalism, we demonstrate that the composite structure comprising N gratings
has a multiple transmittance zero of the order N. We show that at the distance
between the gratings satisfying the Fabry-P\'erot resonance condition, an
(N-1)-degenerate bound state in the continuum (BIC) is formed. The results of
rigorous numerical simulations fully confirm the theoretically predicted
formation of multiple zeros and BICs in the composite structures. Near the
BICs, an effect very similar to the electromagnetically induced transparency is
observed. We show that by proper choice of the thicknesses of the layers
separating the gratings, nearly rectangular reflectance or transmittance peaks
with steep slopes and virtually no sidelobes can be obtained. In particular,
one of the presented examples demonstrates the possibility of obtaining an
approximately rectangular transmittance peak having a significantly
subnanometer width. The presented results may find application in the design of
optical filters, sensors and devices for optical differentiation and
transformation of optical signals.
