Origin of bound states in the continuum in a grating waveguide: Parity symmetry breaking due to mode crossing

A mechanism leading to the formation of bound states in the continuum (BICs) in a planar grating waveguide is revealed. BICs appear when dispersion curves of the leaking even-parity and non-leaking odd-parity infinite-grating eigenmodes intersect. These intersections engender a parity symmetry break of the leaking eigenmode, causing it to decouple from a spatial Fourier harmonic that is emitted out of the waveguide. As a result, the otherwise low-Q waveguide eigenmode, comprised of those two aforementioned and some other infinite-grating eigenmodes, acquires a very high quality factor in a narrow vicinity of the mode-crossing frequency. Implementation of such a mechanism can be instructive for designing BICs in other photonic crystals and structures.