Energy Stable SBP-FDTD Methods for Maxwell–Duffing Models in Nonlinear Photonics

We consider electromagnetic models that describe nonlinear optical phenomenon in which the nonlinear polarization is driven by the electric field and modeled as anharmonic oscillator(s). These models are given by Duffing equations and incorporate both nonlinearity and dispersion. Using the auxiliary differential equation approach, our discretizations of the coupled Maxwell-Duffing models are high-order and energy-stable finite-difference time-domain (FDTD) methods of so-called summation by parts (SBP) type. Boundary and interface conditions are handled by the simultaneous approximation technique (SAT).