Nonstandard Finite-Difference Time-Domain Methodology for Light Propagation in 3rd Order Nonlinear Materials

The finite-difference time-domain (FDTD) methodology is widely used in computational electromagnetics, but unless a fine space-time mesh is used its accuracy is low. We have shown how to greatly improve the accuracy on a coarse mesh by employing what is called nonstandard (NS) FDTD. In this paper we extend our methodology to compute light propagation in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3^{\text{rd}}$</tex> order nonlinear dielectrics. We have demonstrated its accuracy and stability.