Bound states in the continuum (BICs) are radiationless localized states embedded in the part of the parameter space that otherwise corresponds to radiative modes. Many decades after their original prediction 1,2 and early observations in acoustic systems 3 , such states have been recently demonstrated in photonic structures with engineered geometries [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . In this paper we put forward a mechanism, based on waveguiding structures containing anisotropic birefringent materials, which affords the existence of BICs that exhibit fundamentally-new properties. In particular, anisotropy-induced BICs may exist in symmetric as well as in asymmetric geometries; they form in tunable angular propagation directions; their polarization may be pure transverse-electric, pure transverse-magnetic or full-vector with tunable polarization-hybridity; and they may be the only possible bound states of properly designed structures, thus appearing as a discrete, isolated bound state embedded in a whole sea of radiative states.
2Bound states in the continuum were originally predicted in 1929 by von Neumann and Wigner as discrete fully-bounded quantum states with energies above the continuum of the corresponding Hamiltonian. Signatures of acoustic BICs were observed experimentally several decades ago 3 , but only after the recent theoretical studies and landmark experiments conducted in classical photonic systems the implications of the almost century-old concept were properly appreciated, stimulating deeper understanding over its origin [9][10][11] and inspiring new schemes 12-14 and applications [15][16][17] .BICs discovered to date are almost-pure transverse-electric (TE) or transversemagnetic (TM) waves 4,[7][8][9][19][20][21] , namely with a negligible fraction of energy being carried by the respective orthogonal polarization. The corresponding trapping mechanism can thus be intuitively viewed as a scalar or spinor potential. In contrast, photonic structures containing anisotropic media can support bound states that, in general, involve the fullvector electric and magnetic field components. This important feature opens up the possibility to search for full-vector BICs that cannot exist in scalar analogies. In this paper we explore the concept and expose its potential.By and large, coupling localized states with a coexisting radiative continuum results in energy being shed away and thus in unbound states that decay and fade away during propagation. Bound states can only exist when such transverse radiative leakage is suppressed by a suitable mechanism. Here we address the existence of such mechanism in optical waveguiding structures fabricated in anisotropic media. We restrict ourselves to the simplest structures fabricated in birefringent uniaxial natural materials, the optical axes of the crystals are set to lie on the waveguide plane forming an angle θ with the wave propagation direction, θ is set to be equal for all materials, and we set the cladding to be an isotropic medium (Fig. ...