References

Photonic crystals (PhCs) are periodic structures that exhibit frequency intervals (i.e., bandgaps) in which light cannot propagate. For practical applications, it is highly desirable to dynamically change the bandgaps. Liquid crystals (LCs) can achieve this goal due to their electro-optic effects. Existing numerical methods for computing band structures of PhCs with LCs, such as the finite element [1] and the plane wave expansion methods, require a full discretization of the unit cell, and they give rise to eigenvalue problems of large matrices. For isotropic materials, the band structures can also be calculated using the Dirichlet-to-Neumann (DtN) maps of the unit cells [2]. The DtN-map method is efficient, since the eigenvalue problem is formulated on the boundary of a unit cell, so that the resulting matrices are much smaller. In this paper, we extend the DtN-map method to anisotropic PhCs, such as those involving LCs, with arbitrary 3D anisotropy. We demonstrate the method for both uncoupled and coupled mode cases