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We consider a discrete non-linear Schrödinger equation on Z and show that, after adding a small potential localized in the time-frequency space, one can construct a three-parametric family of non-decaying spacetime quasiperiodic solutions to this equation. The proof is based on the Craig–Wayne–Bourgain method combined with recent techniques of dealing with Anderson localization for two-dimensional quasiperiodic operators with degenerate frequencies.

Water-based coherent detection of broadband terahertz (THz) wave has been recently proposed with superior performances, which can alleviate the limited detection bandwidth and high probe laser energy requirement in the solid- and air-based detection schemes, respectively. Here, we demonstrate that the water-based detection method can be extended to the aqueous salt solutions and the sensitivity can be significantly enhanced. The THz coherent detection signal intensity scales linearly with the third-order nonlinear susceptibilityχ⁽³⁾or quadratically with the linear refractive indexη₀of the aqueous salt solutions, while the incoherent detection signal intensity scales quadratically withχ⁽³⁾or quartically withη₀, proving the underlying mechanism is the four-wave mixing. Both the coherent and incoherent detection signal intensities appear positive correlation with the solution concentration. These results imply that the liquid-based THz detection scheme could provide a new technique to measureχ⁽³⁾and further investigate the physicochemical properties in the THz band for various liquids.