Efficient FDTD-PML Simulation of Gain Medium Based on Exponential Time Differencing Algorithm

An exponential time differencing (ETD) algorithm is introduced to incorporate the homogeneously broadened Lorentzian oscillator of gain medium in a four-level atomic system into the finite difference time domain (FDTD). Compared with the well known auxiliary differential equation (ADE) method, the proposed algorithm shows the same accuracy but can save one-third of the additional memory space for treating the Lorentzian oscillators, and has simpler formulations. The ETD implementation of the stretched coordinates perfectly matched layer (SC-PML) with the complex frequency shifted (CFS) stretching variable is applied to truncate computational domain with gain media. Simulations involving both TE and TM waves indicate that compared with the modified conventional PMLs and the convolution PML (CPML), the proposed absorbing boundary formulations can lead to a significant improvement of the absorbing performance with a similar memory requirement. Compared with the application of the material dependent PMLs to the gain media in previous studies, the proposed absorbing boundary condition has simpler formulas and can be applied to complex computational domains much more straightforwardly.