Numerical Dispersion Relation for the 2D LOD-FDTD Method in Lossy Media

A closedform expression is derived for the numerical dispersion relation of the 2D locally onedimensional finitedifference timedomain (LODFDTD) method in lossy media. In contrast to the lossless formulation, we found that transverseelectric (TE ) and transversemagnetic (TM ) waves in lossy media exhibit different numerical dispersion relations. Moreover, when the material relaxationtime constant is not well resolved by the integration timestep the TM case shows much worse accuracy than the TE case. To remove this limitation, a splitfield LODFDTD formulation for TM waves is then considered which exhibits the same dispersion relation as the LODFDTD method for TE waves. The validity of the theoretical results is illustrated through numerical simulations.