  Bound states in the continuum (BICs) are trapped or guided modes with
frequencies in radiation continua. They are associated with high-quality-factor
resonances that give rise to strong local field enhancement and rapid
variations in scattering spectra, and have found many valuable applications. A
guided mode of an optical waveguide can also be a BIC, if there is a lateral
structure 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. In
this paper, we show (analytically and numerically) that a typical BIC in
optical waveguides with a left-right mirror symmetry and a single lateral
leakage channel is robust with respect to any structural perturbation that
preserves the left-right mirror symmetry. Our study improves the theoretical
understanding on BICs and can be useful when applications of BICs in optical
waveguides are explored.
