FDTD Maxwell's equations models for nonlinear electrodynamics and optics

A. Taflove is with the Department of Electrical and Computer Engineering, McCormick School of Engineering, Northwestern University, Evanston, IL 60208 USA. This paper summarizes algorithms which extend the finite-difference time-domain (FDTD) solution of Maxwell's equations to nonlinear optics. The use of FDTD in this field is novel. Previous modeling approaches were aimed at modeling opticalwave propagation in electrically long structures such as fibers and directional couplers, wherein the primary flow of energy is along a single principal direction. However, FDTD is aimed at modeling compact structures having energy flow in arbitrary directions. Relative to previous methods, 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.