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Waveguiding structures made of anisotropic media support bound states in thecontinuum (BICs) that arise when the radiation channel of otherwise semi-leakymodes is suppressed. Hitherto, only structures with optical axes aligned insymmetric orientations inside the waveguide plane, where BICs appear as linesin the momentum-frequency dispersion diagram, have been considered. Here weaddress settings where such symmetry is broken and unveil a number offundamental new features. Weak and strong symmetry-breaking regimes areidentified, corresponding to azimuthal and polar optical axes orientationasymmetries, respectively. The azimuthal symmetry-breaking is found to stillpreserve the existence loci of BICs in the momentum-frequency dispersiondiagram as lines. However, all possible BICs become interferometric, while thepolarization separable states that occur in symmetric settings cease to exist.The polar symmetry-breaking has stronger effects and transforms the BICs'existence loci from lines to points, which correspond to full-vector statesthat exist at discrete values of the optical axis orientation for a givenwavelength. Such transformation results in fundamental changes in thetopological properties of the radiated field around the BICs.

Topological properties of bound-states-in-the-continuum in geometries with broken anisotropy-symmetry