Conventions

The following are the conventions of FDTD++.

Units

• Distances are measured in meters
• Time is measured in seconds
• Material parameters are relative to the vacuum (e.g., relative permittivities), and the parameters entering these models are in units of eV ($\omega$, etc.). See the materials file section.
• Spectra are in eV
• Conductivity ($\sigma$) is in S/m.

Temporal Staggering

\begin{eqnarray} {\bf{E}}^{t-1/2} \rightarrow {\bf{E}}^{t+1/2} \\ {\bf{H}}^{t} \rightarrow {\bf{H}}^{t+1} \\ {\bf{J}}^{t-1/2} \rightarrow {\bf{J}}^{t+1/2} \\ \end{eqnarray}

Spatial Staggering

\begin{eqnarray} {E_x}_{i+1/2, j, k} \\ {E_y}_{i, j+1/2, k} \\ {E_z}_{i, j, k+1/2} \\ \end{eqnarray}

\begin{eqnarray} {H_x}_{i, j+1/2, k+1/2} \\ {H_y}_{i+1/2, j, k+1/2} \\ {H_z}_{i+1/2, j+1/2, k} \\ \end{eqnarray}