Subterahertz difference-frequency generation in terahertz quantum cascade lasers

We have detected subterahertz spectral lines in the emission of free-running GaAs/AlGaAs quantum cascade lasers (QCLs) operating around 3 THz. We have found that the power W( fd) of an individual sub-THz line at the frequency fd is directly proportional to a power product W( fi) × W( fk) of the corresponding pair of THz lines having the frequency difference fi − fk =  fd. The established one-to-one correspondence of each sub-THz line to pair combinations of THz lines proves the nonlinear mechanism of difference-frequency generation (DFG) in the QCL active region. The conversion efficiencies W( fi − fk)/[ W( fi) × W( fk)] estimated from the experimental data are about 4 × 10−3 and 5 × 10−5 W−1 for the sub-THz lines found at 132 and 310 GHz, correspondingly. Considering nonlinear polarization of QCL active regions as the reason for DFG, we have evaluated the following values of the second-order nonlinear susceptibility χ(2)(132 GHz) ≅ 7 × 105 pm/V and χ(2)(310 GHz) ≅ 4 × 104 pm/V from the experimental data. The obtained results pave the way for the use of THz QCLs as sources of sub-THz radiation.