Optical Extraction Efficiency for External Cavity Quantum Cascade Lasers

Abstract

In this paper, we present a simple method for calculation of optical extraction efficiency of mid-infrared quantum cascade laser coupled to external cavity. The approach is based on the three-level rate equation model describing the variation of the electron number in the states and the photon number present within the Fabry-Perot quantum cascade laser and the external cavity. The system shares the same active region and includes the dependence of the loss on external cavity parameters. We find in particular that the power coupled out through the external mirror varies linearly with current injection and depends strongly on the external cavity reflectivity. Moreover, a considerable increase in the threshold current of external cavity occurs when decreasing the values of the external cavity reflectivity and the slope efficiency decreases with decreasing external cavity reflectivity. We also derive an analytical formula for the optical extraction efficiency of external cavity and analyze the simultaneous effects of the current injection and the external cavity reflectivity on it. Results show that at laser threshold, the optical extraction efficiency is zero and it rises as the current injection increases. For high current injection, extraction efficiency of up to 11 % at Rext = 10 % can be attained. In addition, the equations allowing the determination of the optimum reflectance of external cavity and the maximum optical extraction efficiency are also derived within the premises of our model in the general case.