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We obtain, for the first time to our knowledge, the room-temperature intracavity difference-frequency generation in the mid-infrared range (around 10 mum wavelength) in a butt-joint GaAs/InGaAs/InGaP quantum-well dual-wavelength laser diode which supports lasing at two closely spaced wavelengths in the near-infrared range close to 1 mum. We employ a special asymmetric waveguide design (which makes it possible the different-order transverse-mode lasing) and a low-doped substrate that minimize mid-infrared losses and phase mismatch for the difference-frequency nonlinear-mixing process. We explain qualitatively the physics of the intracavity mode mixing and describe in detail the design of the butt-joint diode laser. We show how to scale the effect into the far-infrared (terahertz) range, to improve the phase-matching conditions, and to enhance further the difference-frequency generation efficiency (the latter is about 1 W/(kW)2 in our first experiment).