BAND STRUCTURE CALCULATIONS OF THREE-DIMENSIONAL ANISOTROPIC PHOTONIC CRYSTALS IN THE OBLIQUE COORDINATE SYSTEM

In this article, we consider the band structure calculations of three-dimensional (3D) anisotropic photonic crystals (PhCs), especially those with nonorthogonal Bravais lattices. By directly working with the intrinsic coordinate system with {a ℓ} 3 ℓ =1 as the basis and the covariant formulation of Maxwell's equations, the approach proposed here treats nonorthogonal and orthogonal Bravais lattices in an equal and unified manner and trivially incorporates the Bloch condition in the discretization. Yee's scheme does not require the coordinate system or mesh to be orthogonal, and assisted by linear interpolation, this scheme can handle anisotropic media, by which the frequency domain Maxwell's equations are discretized into a standard eigenvalue problem (SEP). With an alternative understanding of null-space deflation techniques, this SEP is transformed into several equivalent null-space free SEPs, whose smallest few positive eigenvalues and associated eigenvectors are calculated by an iterative eigensolver of the inner-outer type. Comparison with other methods for band structure calculations of 3D anisotropic and isotropic PhCs is made to demonstrate the effectiveness and strength of our present approach.