Effects of off-diagonal permittivity terms on polarization singularities in anisotropic grating system

The evolutions of polarization singularities, including bound states in the continuum (BICs) and circularly polarized states (C points), are usually realized by tuning the geometric parameters of photonic crystal slabs. Here, we use the off-diagonal terms of permittivity tensor to manipulate polarization singularities without breaking the structural symmetry in an anisotropic grating system. By controlling the optical axis of anisotropic media, BICs can be shifted to different positions or split into C points, meanwhile, the creation and annihilation of multiple C points are also observed during the evolution process for both TE and TM modes, respectively. Remarkably, two different splitting directions of BICs can be achieved by tuning the off-diagonal terms of permittivity tensor for the two modes. This work illustrates the important role of off-diagonal terms on the far-field polarization singularities and provide an alternative way to precisely manipulate optical singularities