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There are two alternative approaches in construction of laser-driven terahertz (THz) wave generators and detectors, one based on frequency conversion in nonlinear crystals, and the other one utilizing laser-excited currents in photoconductive materials. Recent progress in the both directions is stimulated by important applications of THz electromagnetic waves in communications, spectroscopy, biomedicine, tomography and other fields. Concerning nonlinear processes, our last work is devoted to generation of THz fields with particular quantum properties. We show that effect of spontaneous parametric down-conversion (SPDC), well known in the modern quantum optics and quantum information, can be used as a source of quantum-correlated pairs of photons of extremely different frequency ranges, the so-called “optical-terahertz biphotons”. This opens attractive perspectives to move the quantum information and quantum photometry technologies to the terahertz range. High levels of correlation are achieved when the strongly frequency non-degenerate SPDC proceeds in the low-gain limit. The possibility of detecting the weakest terahertz photon fluxes has been demonstrated recently by using a superconductive hot-electron bolometer. The photoconductive antennas based on low-temperature grown InGaAs semiconductors are perspective devices for classical schemes of THz-wave detection and generation. The relatively large band-gap (1.4 eV) of GaAs restricts the set of appropriate laser sources capable of exciting carriers in antennas based on this material. This circumstance stimulated the search of semiconducting materials having the advantages of GaAs, but with smaller band-gaps, allowing absorption of radiation from lasers that are used in optical communications. We studied the THz wave generation by the time-domain spectroscopy method in the spiral antennas fabricated on the low-temperature grown InGaAs layers on GaAs substrates with crystallographic orientations (100) and (111). It was found that the THz wave generation is 3-4 times more effective in the case of (111)A GaAs substrates as compared to the (100) substrates. By analyzing results of the pump-probe measurements, the characteristic carrier relaxation times were obtained for LT-InGaAs samples on GaAs substrates with (111) A and (100) orientations. These results are in a good correspondence with the literature data and qualitatively confirm the results of experiments on the THz generation. We have studied the emission of THz radiation by samples of topological insulators Bi2-xSbxTe3-eSey (BSTS) with various thicknesses and chemical compositions, pumped by 2.5 ps laser pulses of 1.56 μm wavelength. Rhombohedral BSTS films were grown on (0001) sapphire substrates. It was found that the electric field of the THz signal from the island film of TI is 5 times higher than the same of TI samples with a thickness of hundreds of nanometers. The effect of THz radiation amplification in an external electric field in a topological insulator has been demonstrated for the first time