Highly efficient finite‐difference schemes for structures of nonrectangular cross‐section

Djurdjevic, D.Z.; Sewell, P.; Benson, T.M.; Vuković, Ana

doi:10.1002/mop.10335

Cited by 3 publications

(2 citation statements)

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“…In the finite difference approaches of (4) (the standard FDM) and (3), (5) (frequency domain FD-BPM), the main research interests are: developing of socalled improved FD schemes with more accurate treatment of the dielectric interfaces, [9][10][11][12], and extending the range of FD-BPM applicability to the waveguide structures changing in the direction of propagation, [5,6,13,14].…”

Section: Outline Of the Methods 21 Basic Theoretical Conceptmentioning

confidence: 99%

“…FD treatment and discretization of structures with constant cross-section with the refractive transverse index step at the interface between two dielectric regions suffer from reduced accuracy due to the necessary staircase approximation employed by most algorithms, [1,4]. Improved FD-schemes, [8][9][10][11][12]15], enable better accuracy. However, the error introduced at a dielectric interface in all FD implementations is of the order n − 1, assuming the order of the uniform region discretization is given by n. Dielectric corner points truncate the overall accuracy to the order of n − 2, [16].…”

Section: Outline Of the Methods 21 Basic Theoretical Conceptmentioning

confidence: 99%

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New finite-difference formulas for dielectric interfaces

Djurdjevic

2010

FACTA U EE

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The finite difference method is often-used numerical simulation method in electromagnetics. In this paper a new methodology is presented that allows the derivation of finite difference formulas near dielectric interfaces with high accuracy. Derived finite difference formulas have been used in the electric field computations in electrostatics (the two-dimensional Laplace's equation is employed) and in full-vectorial waveguide simulations in photonics (the three-dimensional Helmholtz's equation and the beam propagation simulation technique in frequency domain are employed). The finite difference formulas derivation is made under a power series expansion of the transverse field components in the case for uniform rectangular discretization mesh. The resulting finite difference formulas provide highly accurate solutions, both for electrostatic and waveguide propagation problems even on coarse grids and thus enable a very cost-effective and rapid numerical field simulations. Reported methodology and derived formulas have not been used in finite difference method formulations in literature. Some results for the electric field computation and dielectric waveguide eigenmode and propagation analysis are presented. .

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