We report the polarization, the interference far-filed pattern, the multimodal spectral emission and the power extraction of the emitted beam from a set of electrically-pumped random quantum cascade lasers in the terahertz range. By integrating, on chip, a non-linear multilayer graphene stack with the laser gain medium, we demonstrate self-induced phase-coherence between the naturally incoherent random modes. We then employ the devised random laser in a detectorless near-field imaging system, exploiting the intracavity reinjection of the laser field via self-mixing interferometry in a confocal microscope for speckle-free tomography with nm-size resolution
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