The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulations

We are developing full-wave vector Maxwell equation solvers for use in studying the physics and engineering of linear and nonlinear integrated photonics systems. Particular emphasis has been given to the interaction of ultrafast optical pulses with nonresonant and resonant optical materials and structures. Results are reviewed that simulate the interaction of ultrafast optical pulses with structures (e.g., gratings of finite length) filled with materials exhibiting resonant loss or gain. In particular, we consider structures loaded with atomic media resonant at or near the frequency of the incident optical radiation. Interest in these problems follows from our desire to design micron-sized linear and nonlinear guided-wave couplers, modulators, and switches. These resonant problems pose interesting FDTD modeling issues because of the many time and length scales involved. To understand the physics underlying the small-distance scale and short-time scale interactions, particularly in the resonance regime of the materials and the associated device structures, a first principles approach is desirable. Thus, the results presented are based upon a quantum mechanical two-level atom model for the materials. The resulting Maxwell-Bloch model requires a careful marriage between microscopic (quantum mechanical) material models of the resonant material systems and the multidimensional, macroscopic Maxwell´s equations solver. The FDTD numerical issues are discussed. Examples are given to illustrate the design and control of these resonant large-scale optical structures. An optical triode is designed and characterized with the FDTD Maxwell-Bloch simulator