Implementation of perfectly matched layer boundary condition for finite-difference time-domain simulation truncated with gain medium

Boundary condition for the finite-difference-time-domain (FDTD) photonic simulation truncated with a gain medium is studied. Reflection occurs when applying the perfectly matched layer (PML) due to the impedance mismatch. The implementation of PML for the simulation truncated with gain medium is presented including both the un-split and split-field formulation, respectively. Numerical validation through simulating the light propagating in an active semiconductor waveguide containing gain medium indicates that the boundary formulation derived can effectively absorb the out-going light under different carrier densities.