We experimentally demonstrate Time-Resolved Nonlinear Ghost Imaging and its ability to perform hyperspectral imaging in difficult-to-access wavelength regions, such as the Terahertz domain. We operate by combining nonlinear quadratic sparse generation and nonlinear detection in the Fourier plane. We demonstrate that traditional time-slice approaches are prone to essential limitations in near-field imaging due to space-time coupling, which is overcome by our technique. As a proof-of-concept of our implementation, we show that we can provide experimental access to hyperspectral images completely unrecoverable through standard fixedtime methods.

In many disciplines, states that emerge in open systems far from equilibrium are determined by a few global parameters1,2. These states can often mimic thermodynamic equilibrium, a classic example being the oscillation threshold of a laser3 that resembles a phase transition in condensed matter. However, many classes of states cannot form spontaneously in dissipative systems, and this is the case for cavity solitons2 that generally need to be induced by external perturbations, as in the case of optical memories4,5. In the past decade, these highly localized states have enabled important advancements in microresonator-based optical frequency combs6,7. However, the very advantages that make cavity solitons attractive for memories—their inability to form spontaneously from noise—have created fundamental challenges. As sources, microcombs require spontaneous and reliable initiation into a desired state that is intrinsically robust8–20. Here we show that the slow non-linearities of a free-running microresonator-filtered fibre laser21 can transform temporal cavity solitons into the system’s dominant attractor. This phenomenon leads to reliable self-starting oscillation of microcavity solitons that are naturally robust to perturbations, recovering spontaneously even after complete disruption. These emerge repeatably and controllably into a large region of the global system parameter space in which specific states, highly stable over long timeframes, can be achieved.

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.

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