## 2 THz DFG-QCL Design and Characterization  
The DAU active region structure is used for the present DFG-QCL, in which the inter-sub-band transitions for laser action occur from two anti-crossed upper sub-bands to lower miniband and these many transitions result in a broad-gain spectrum. In the active region designs, almost equal dipole matrix elements are designed for the inter-sub-band transitions from the two upper states to lower laser states in order to achieve the flat-top broad electroluminescence emission spectrum. In the DAU active region, several sets of states contribute to resonant \(\chi^{(2)}\) for DFG. These energy states relevant to the optical resonance were engineered to attain the second order optical nonlinearity in the DAU active region. For the active region of a THz-DFG device emitting around 3 THz, the estimated module of the nonlinear susceptibility is \(\mid\chi^{(2)}\mid\) = 7.8 nm/V. The waveguide core in our CW devices consists of 40-staege active regions (sheet doping density in each active region stage: 1.0 \(\times\) 10\({}^{11}\) cm\({}^{-2}\)). The growth of all the semiconductor layer structures were done by metal organic vapor phase epitaxy method on an undoped InP substrate [50,51]. The waveguide structure was designed to achieve optical mode confinement for mid-infrared, and THz DFG emission at a Cherenkov phase matching angle of \(\sim\) 20 degrees into the undoped InP device substrate. A schematic of the device structure is shown in Figure 1a. The growth initiates with a 200 nm thick In\({}_{0.53}\)Ga\({}_{0.47}\)As current injection layer (Si, 1.0 \(\times\) 10\({}^{18}\) cm\({}^{-3}\)) and then a 5 \(\upmu\)m thick n-InP (Si, 1.5 \(\times\) 10\({}^{16}\) cm\({}^{-3}\)) is formed as a lower cladding layer. The strain compensated InGaAs/InAlAs active region layers are sandwiched between n-In\({}_{0.53}\)Ga\({}_{0.47}\)As guide layers (Si, 1.5 \(\times\) 10\({}^{16}\) cm\({}^{-3}\)) where the thicknesses of 250 nm and 450 nm are used for lower and upper layers. A buried DFB grating (single-period) was defined by nanoimprint lithography for the single-mode laser emission and etched into upper n-In\({}_{0.53}\)Ga\({}_{0.47}\)As guide layers. A first-order grating period was \(\Lambda\) = 1.04 \(\upmu\)m for the single mode DFB emission. The coupling coefficient \(\kappa\) was estimated to be \(\sim\)7 cm\({}^{-1}\). The wafer was processed into 12-\(\upmu\)m-wide ridge structures and buried with a semi-insulating Fe doped InP layer. Subsequently, the upper cladding layer was grown with a 5 \(\upmu\)m thick n-InP (Si, 1.5 \(\times\) 10\({}^{16}\) cm\({}^{-3}\)) and then followed by a 15 nm thick n\({}^{+}\)- InP (Si, \(\sim\)10\({}^{19}\) cm\({}^{-3}\)) cap contact layer. Finally, the top contacts (Ti/Au) was evaporated and followed by electroplating of a thick 5 \(\upmu\)m Au layer on top of the laser structure. The laser bars were equipped in an epitaxial side-up mounting configuration on a copper block and then cooled in open-loop liquid nitrogen cryostats for the initial device characterization, which was performed in the Hamamatsu laboratories in Japan. Figure 1b,c show the measured emission results for a THz DFG-QCL with 3-mm-long, 12-\(\upmu\)m-wide buried-heterostructure waveguide, operated in CW mode at 78 K. Figure 1b shows the mid-infrared emission spectra, in which the rapid-scan measurements (a spectral resolution of 0.2 cm\({}^{-1}\)) were performed for the two mid-infrared pumps as well as the generated THz emission from the DFG-QCL. In this device, we adopted the DFB/FP pumping for generating broadband THz emission via nonlinear frequency mixing between a single mode due to the DFB grating and broadband multi-modes due to the FP cavity, as shown in Figure 1b. The position of DFB emission was considerably detuned (\(\sim\)90 cm\({}^{-1}\)) from the peak gain; it is important not to suppress the broadband emission due to FP cavity. Consequently, wide bandwidth of the FP modes and high mid-infrared output power are expected to generate broadband THz frequency.