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We explain the origin of bound states in the continuum (BICs) in a planargrating waveguide, in particular, a mechanism for formation of degenerate BICs,via the analytical theory of the infinite-grating eigenmodes. Conventionalsymmetry-protected BICs are formed at normal incidence mainly by a singleinfinite-grating eigenmode that has an odd spatial parity on both sides of theBIC resonance. The odd parity is the reason for a cutoff from theradiation-loss channel and appearance of such BICs. The mechanism of emergenceof a degenerate BIC in a vicinity of a degenerate frequency of twoinfinite-grating eigenmodes is different. The degenerate BIC is formed by ananti-phased coherent superposition of two crossing infinite-grating eigenmodesboth of which possess a mixed parity and experience parity symmetry breaking asthe frequency scans through the degeneracy point. In this case a cutoff fromthe radiation-loss channel and extremely high-Q narrow resonance is achieveddue to the destructive interference of the two crossing eigenmodes.Implementation of such a mechanism can be instructive for designing BICs inother photonic crystals and structures.

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