**Juan S. Totero Gongora, Luana Olivieri, Luke Peters, Jacob Tunesi, Vittorio Cecconi, Antonio Cutrona, Robyn Tucker, Vivek Kumar, Alessia Pasquazi and Marco Peccianti \***

Emergent Photonics (EP*ic*) Laboratory, Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK; jt420@sussex.ac.uk (J.S.T.G.); l.olivieri@sussex.ac.uk (L.O.); l.peters@sussex.ac.uk (L.P.); jt298@sussex.ac.uk (J.T.); v.cecconi@sussex.ac.uk (V.C.); ac878@sussex.ac.uk (A.C.); rt232@sussex.ac.uk (R.T.); vk230@sussex.ac.uk (V.K.); a.pasquazi@sussex.ac.uk (A.P.)

**\*** Correspondence: m.peccianti@sussex.ac.uk; Tel.: +44-(0)1273-873171

Received: 21 January 2020; Accepted: 17 May 2020; Published: 20 May 2020

**Abstract:** Terahertz (THz) imaging is a rapidly emerging field, thanks to many potential applications in diagnostics, manufacturing, medicine and material characterisation. However, the relatively coarse resolution stemming from the large wavelength limits the deployment of THz imaging in micro- and nano-technologies, keeping its potential benefits out-of-reach in many practical scenarios and devices. In this context, single-pixel techniques are a promising alternative to imaging arrays, in particular when targeting subwavelength resolutions. In this work, we discuss the key advantages and practical challenges in the implementation of time-resolved nonlinear ghost imaging (TIMING), an imaging technique combining nonlinear THz generation with time-resolved time-domain spectroscopy detection. We numerically demonstrate the high-resolution reconstruction of semi-transparent samples, and we show how the Walsh–Hadamard reconstruction scheme can be optimised to significantly reduce the reconstruction time. We also discuss how, in sharp contrast with traditional intensity-based ghost imaging, the field detection at the heart of TIMING enables high-fidelity image reconstruction via low numerical-aperture detection. Even more striking—and to the best of our knowledge, an issue never tackled before—the general concept of "resolution" of the imaging system as the "smallest feature discernible" appears to be not well suited to describing the fidelity limits of nonlinear ghost-imaging systems. Our results suggest that the drop in reconstruction accuracy stemming from non-ideal detection conditions is complex and not driven by the attenuation of high-frequency spatial components (i.e., blurring) as in standard imaging. On the technological side, we further show how achieving efficient optical-to-terahertz conversion in extremely short propagation lengths is crucial regarding imaging performance, and we propose low-bandgap semiconductors as a practical framework to obtain THz emission from quasi-2D structures, i.e., structure in which the interaction occurs on a deeply subwavelength scale. Our results establish a comprehensive theoretical and experimental framework for the development of a new generation of terahertz hyperspectral imaging devices.

**Keywords:** terahertz; nonlinear optical conversion; complex optical systems; adaptive imaging; single-pixel imaging; surface nonlinear photonics
