Rate equations model and optical external efficiency of optically pumped electrically driven terahertz quantum cascade lasers

•A four level rate equations model for a terahertz optically pumped electrically driven quantum cascade laser is introduced and used to model the system both analytically and numerically.•A closed form expressions for the levels occupation, population inversion, midinfrared pump threshold intensity as well as the terahertz field intensity in terms of the device parameters have been obtained.•We also derive an analytical formula for the optical external efficiency and analyze the simultaneous effects of the cavity length and pump intensity on it.

A four level rate equations model for a terahertz optically pumped electrically driven quantum cascade laser is here introduced and used to model the system both analytically and numerically. In the steady state, both in the presence and absence of the terahertz optical field, we solve the resulting nonlinear system of equations and obtain closed form expressions for the levels occupation, population inversion as well as the mid-infrared pump threshold intensity in terms of the device parameters. We also derive, for the first time for this system, an analytical formula for the optical external efficiency and analyze the simultaneous effects of the cavity length and pump intensity on it. At moderate to high pump intensities, we find that the optical external efficiency scales roughly as the reciprocal of the cavity length.