Finite element simulation of microphotonic lasing system

We present a method for performing time domain simulations of a microphotonic system containing a four level gain medium based on the finite element method. This method includes an approximation that involves expanding the pump and probe electromagnetic fields around their respective carrier frequencies, providing a dramatic speedup of the time evolution. Finally, we present a two dimensional example of this model, simulating a cylindrical spaser array consisting of a four level gain medium inside of a metal shell.