  In the field of optics, bound state in the continuum (BIC) has been
researched in many photonic crystals and periodic structures due to a strong
resonance and an ultrahigh Q factor. Some designs of narrowband transmission
filters, lasers, and sensors were proposed based on excellent optical
properties of BIC. In this paper, we consider symmetrical rectangular grating
structure firstly, then cut off the corner of one of the gratings, the Fano
peak of quasi-BIC can be observed in the spectrum. After that, we further
change the tilt parameter of the other grating, which minimizes the Fano line
width. In the momentum space, the process of structural change corresponds to
topological charges split from q=1 into two half charges q=1/2.We analyze
guided mode resonance (GMR) excitation of the grating structure, and discuss
the dispersion relations in the waveguide layer with the position of BIC in
energy bands. In addition, the reflectance spectrum is found to exhibit
asymmetric line-shapes with different values of the asymmetry parameters, M1
and M2. BIC is transformed into quasi-BIC as the symmetry of the structure is
broken. This work demonstrates a double trapezoid structure with strong
resonance properties, which has significant implications for exploring the
phenomenon of BIC.
