High-order Accurate Schemes for Maxwell-Bloch Equations with Material Interfaces

Efficient and high-order accurate FDTD schemes are developed for nonlinear dispersive models in active multi-level media with material interfaces in 2D and 3D arbitrary geometry. The considered nonlinear systems are multi-level generalizations of 2-level optical Maxwell-Bloch equations. Arbitrary numbers of atomic levels and macroscopic polarization vectors can be accounted for in the multi-level atomic (MLA) system. The MLA models are suitable for modeling active media with various properties, such as lasing, saturable absorption, reverse saturable absorption, etc. Composite overlapping grids are employed to handle complex geometry with material interfaces, using locally conforming curvilinear grids for curved boundaries and interfaces and Cartesian grids for the rest. The developed high-order schemes allow compact stencils in time integration, and efficient point-wise update of the numerical solutions.