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Bound states in the continuum (BICs) are trapped or guided modes withfrequencies in radiation continua. They are associated with high-quality-factorresonances that give rise to strong local field enhancement and rapidvariations in scattering spectra, and have found many valuable applications. Aguided mode of an optical waveguide can also be a BIC, if there is a lateralstructure supporting compatible waves propagating in the lateral direction,i.e., there is a channel for lateral leakage. A BIC is typically destroyed(becomes a resonant or a leaky mode) if the structure is slightly perturbed,but some BICs are robust with respect to a large family of perturbations. Inthis paper, we show (analytically and numerically) that a typical BIC inoptical waveguides with a left-right mirror symmetry and a single lateralleakage channel is robust with respect to any structural perturbation thatpreserves the left-right mirror symmetry. Our study improves the theoreticalunderstanding on BICs and can be useful when applications of BICs in opticalwaveguides are explored.

On the robustness of bound states in the continuum in waveguides with lateral leakage channels