FDTD Modeling
3-D cross-section of a 1.2 N.A. glass lens (5 µm diameter) focusing 800 nm light.
The FDTD method belongs to a general class of differential time domain numerical modeling methods. Maxwell’s (differential form) equations are modified into central-difference equations and discritized. Discritization of space and time makes implementation into software very simple.

The modeling space is defined as a collection of cells which are named Yee Cells. The equations are solved in a leap-frog fashion; that is, the electric field is solved at a given instant in time, then the magnetic field is solved at the next instant in time, and the process is repeated over and over again, and from cell to cell in the direction of propagation.

The modeling uses the Drude free electron model in the form of a modified Debye model formalism. The classical Drude model assumes that the conduction electrons are the transport mechanism for the thermal current. In the modified Debye model the electrons are treated as free electrons and a relaxation time is used to describe the electrons collision frequency within the phonon lattice of the metal.