Terahertz (THz) is an innovative form of electromagnetic radiation providing unique spectroscopy capabilities in critical fields, ranging from biology to material science and security. The limited availability of high-resolution imaging devices, however, constitutes a major limitation in this field. In this work, we tackle this challenge by proposing an innovative type of time-space nonlinear Ghost-Imaging (GI) methodology that conceptually outperforms established single-pixel imaging protocols. Our methodology combines nonlinear pattern generation with time-resolved single-pixel measurements, as enabled by the state-of-the-art Time-Domain Spectroscopy (TDS) technique. This approach is potentially applicable to any wave-domain in which the field is a measurable quantity. The full knowledge of the temporal evolution of the transmitted field enables devising a new form of full-wave reconstruction process. This gives access not only to the morphological features of the sample with deeply subwavelength resolution but also to its local spectrum (hyperspectral imaging). As a target application, we consider hyperspectral THz imaging of a disordered inhomogeneous sample.
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