Terahertz quantum cascade laser sources based on intra-cavity difference frequency generation are currently the only electrically-pumped monolithic semiconductor light sources providing broadly-tunable terahertz output at frequencies up to 6 THz at room temperature. Relying on the active regions with the giant second-order nonlinear susceptibility and the Cherenkov phase matching scheme, these devices demonstrated drastic improvements in performance in the past several years and can now produce narrow-linewidth single-mode terahertz emission that is tunable from below 1 THz to almost 6 THz with power output sufficient for imaging and spectroscopic applications. This chapter provides a comprehensive overview of this device technology

Optical nonlinearity manifests nonlinear interaction of an optical field with a material. The origin of optical nonlinearity is the nonlinear response of electrons in a material to an optical field. Macroscopically, the nonlinear optical response of a material is described by an optical polarization that is a nonlinear function of the optical field. This optical polarization is obtained through density matrix analysis by using the interaction Hamiltonian, which can be approximated with electric dipole interaction in most cases. When the interaction Hamiltonian is small compared to the Hamiltonian of the system, it can be treated as a perturbation to the system by expanding the density matrix in a perturbation series and the total optical polarization in terms of a series of polarizations. In most nonlinear optical processes of interest, the perturbation expansion of the polarization is valid and only the three terms of linear, second-order, and third-order polarizations are significant. The perturbation expansion is not valid in the cases of high-order harmonic generation and optical saturation. Then, a full analysis is required.