Full-wave analysis of photonic-crystal structures with multi quantum well active region

In this paper, a semi-classical formulation for modeling photonic-crystal (PC) structures with a four-layer multi quantum well (MQW) active region is presented. The formulation treats the electromagnetic fields as a classical entity, while employing the quantum-mechanically derived rate equations to analyze the active medium. Using the Poynting theorem, we interrelate the two sets of equations, namely the MQW rate equations and Maxwell's equations. The formulation involves the stimulately emitted photon density in the former and a virtual volume current density representing the generated photons in the latter. With the help of this formulation, we then model a PC optical amplifier as well as a PC hexagonal-defect cavity laser and solve the obtained equations after replacing the involved spatial and temporal derivatives by pseudo-spectral and Runge-Kutta's formulations, respectively. The formulation also takes the effect related to gain saturation and frequency broadening into account.