for TM<sub>z</sub> polarization and
:<math> E_x^{inc}(x,y,t) = \sin\phi \; \exp \left(-\frac{(t-t_0)^2}{\tau^2} \right) \exp(j2\pi f_0 t) \exp(-jk_x x) \exp(-jk_y y)</math>:<math> E_y^{inc}(x,y,t) = -\cos\phi \; \exp \left(-\frac{(t-t_0)^2}{\tau^2} \right) \exp(j2\pi f_0 t) \exp(-jk_x x) \exp(-jk_y y)</math><!--[[Image:FDTD88.png]]-->
for TE<sub>z</sub> polarization. Here, f<sub>0</sub> is the center frequency of the modulated Gaussian pulse waveform, t<sub>0</sub> is the time delay, and τ is the Gaussian pulse width. The choices of the Gaussian waveform parameters are very critical in order to avoid possible resonances. For a fixed value of k<sub>l</sub>, the horizontal resonance occurs at:
:<math> f_{res} = \frac{k_l c}{2 \pi} </math><!--[[Image:FDTD101.png]]-->
For a fixed frequency f<sub>0</sub> and a fixed incidence angle θ<sub>0</sub>, the resonant frequency is reduced to:
<!-- :<math> f_{res} = f_0 \sin \theta_0 </math> -->
[[Image:FDTD102.png]]