TY - JOUR
T1 - BAND STRUCTURE CALCULATIONS OF THREE-DIMENSIONAL ANISOTROPIC PHOTONIC CRYSTALS IN THE OBLIQUE COORDINATE SYSTEM
AU - Tian, Heng
AU - Li, Tiexiang
AU - Lyu, Xing Long
AU - Lin, Wen Wei
N1 - Publisher Copyright:
© 2023 by SIAM.
PY - 2023/8
Y1 - 2023/8
N2 - 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.
AB - 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.
KW - fast Fourier transform
KW - null-space free method
KW - oblique Yee's scheme
KW - photonic band structure
KW - three-dimensional anisotropic photonic crystals
UR - http://www.scopus.com/inward/record.url?scp=85164592579&partnerID=8YFLogxK
U2 - 10.1137/22M1507863
DO - 10.1137/22M1507863
M3 - Article
AN - SCOPUS:85164592579
SN - 1064-8275
VL - 45
SP - B440-B466
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 4
ER -