Angle-Optimized FDTD Algorithms

The principal concept of this efficient dispersion-reduction method, developed in [53, 54], originates from the necessity to annihilate lattice reflection errors around a preassigned angular span. Such a need is particularly present in electrically large waveguides or high-directivity antenna problems. 

Considering the 2-D TE case first, the semidiscrete equations for Ex, Ey, and Hz may be written as 

Concerning the stability of the previous schemes, von Neumann analysis leads to the Courant criterion 

If a monochromatic wave is substituted in (2.80) and the other FDTD equations, the dispersion relation is 

It is apparent that for a given set of 9 and y, the phase-velocity error can be zeroed if a, b are appropriately selected. This implies that one may solve for a, b from (2.82) or define the dispersion error 

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