FDTD Maxwell's equations models for nonlinear electrodynamics and optics

This paper summarizes algorithms which extend the finite-difference time-domain (FDTD) solution of Maxwell's equations to nonlinear optics. The use of the FDTD in this field is novel. Previous modeling approaches were aimed at modeling optical-wave propagation in electrically long structures such as fibers and directional couplers, wherein the primary flow of energy is along a single principal direction. However, the FDTD is aimed at modeling compact structures having energy flow in arbitrary directions. Relative to previous methods, the FDTD achieves robustness by directly solving, for fundamental quantities, the optical E and H fields in space and time rather than performing asymptotic analyses or assuming paraxial propagation and nonphysical envelope functions. As a result, it is almost completely general. It permits accurate modeling of a broad variety of dispersive and nonlinear media used in emerging technologies such as micron-sized lasers and optical switches.