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In the field of optics, bound state in the continuum (BIC) has beenresearched in many photonic crystals and periodic structures due to a strongresonance and an ultrahigh Q factor. Some designs of narrowband transmissionfilters, lasers, and sensors were proposed based on excellent opticalproperties of BIC. In this paper, we consider symmetrical rectangular gratingstructure firstly, then cut off the corner of one of the gratings, the Fanopeak of quasi-BIC can be observed in the spectrum. After that, we furtherchange the tilt parameter of the other grating, which minimizes the Fano linewidth. In the momentum space, the process of structural change corresponds totopological charges split from q=1 into two half charges q=1/2.We analyzeguided mode resonance (GMR) excitation of the grating structure, and discussthe dispersion relations in the waveguide layer with the position of BIC inenergy bands. In addition, the reflectance spectrum is found to exhibitasymmetric line-shapes with different values of the asymmetry parameters, M1and M2. BIC is transformed into quasi-BIC as the symmetry of the structure isbroken. This work demonstrates a double trapezoid structure with strongresonance properties, which has significant implications for exploring thephenomenon of BIC.

Formation of bound states in the continuum in double trapezoidal grating