Most optical systems involve a combination of lenses separated by free-space regions where light acquires the required angle-dependent phase delay for a certain functionality. Very recently, flat-optics structures have been proposed to compress these large free-space volumes and miniaturize the overall optical system. However, these early designs can only replace freespace volumes of limited length, or operate in a very narrow angular range, or require a high-index background. These issues raise questions about the applicability of these devices in practical scenarios. Here, we first derive a fundamental trade-off between the length of compressed free space and the operating angular range, which explains some of the limitations of earlier designs, and we then propose a solution to relax this trade-off using nonlocal metasurface structures composed of suitably coupled resonant layers. This strategy, inspired by coupled-resonator-based band-pass microwave filters, allows replacing free-space volumes of arbitrary length over wide angular ranges, and with very high transmittance. Finally, we theoretically demonstrate, for the first time, the potential of combining local and nonlocal metasurfaces to realize compact, fully solid-state, planar structures for focusing, imaging, and magnification, in which the focal length of the lens (and, hence, its magnifying power) does not dictate the actual distance at which focusing is achieved. Our findings are expected to extend the reach of the field of metasurfaces and open new unexplored opportunities.
Causality -the principle stating that the output of a system cannot precede the input -is a universal property of nature. Here, we extend the concept of causality, and its implications, from the temporal to the spectral domain, leveraging the peculiar properties of time-modulated non-Hermitian wave-physics systems, with particular emphasis on photonic systems. Specifically, we uncover the existence of a broad class of complex time-modulated metamaterials which obey the time-domain equivalent of the well-established frequency-domain Kramers-Kronig relations. We find that, in the scattering response of such time-modulated systems, the output frequencies are inherently prohibited from spectrally preceding the input frequencies, hence we refer to these systems as 'spectrally causal'. We explore the consequences of this newly introduced concept for several relevant applications, including broadband perfect absorption, temporal cloaking of an 'event', and truly unidirectional propagation along a synthetic dimension. By extending the concept of causality into the spectral domain and providing new tools to extend the field of temporally modulated metamaterials ("chrono-metamaterials") into the complex realm, our findings not only deepen our understanding of spectral scattering dynamics, but may also open unexplored opportunities and enable relevant technological advances in various areas of photonics and, more broadly, of wave physics and engineering.Significance Statement -The causality principle -an effect cannot temporally precede its cause -is a fundamental property of nature and underlies several constraints on the properties of physical materials. Here, we extend the notion of causality from the temporal to the spectral domain in temporally modulated wave-physics systems. Specifically, we uncover the existence of a broad class of time-modulated photonic systems that are "spectrally causal" in the sense that the output wave cannot contain oscillations with frequencies (colors) lower than the frequencies of the input wave oscillations. As an important consequence, wave reflections are then automatically minimized. This new class of timemodulated metamaterials has relevant implications for broadband perfect absorption, invisibility, unidirectional propagation, and may open unexplored opportunities in wave physics and engineering.
Oxidative carbonylation of methane is an appealing approach to the synthesis of acetic acid but is limited by the demand for additional reagents. Here, we report a direct synthesis of CH3COOH solely from CH4 via photochemical conversion without additional reagents. This is made possible through the construction of the PdO/Pd–WO3 heterointerface nanocomposite containing active sites for CH4 activation and C–C coupling. In situ characterizations reveal that CH4 is dissociated into methyl groups on Pd sites while oxygen from PdO is the responsible for carbonyl formation. The cascade reaction between the methyl and carbonyl groups generates an acetyl precursor which is subsequently converted to CH3COOH. Remarkably, a production rate of 1.5 mmol gPd–1 h–1 and selectivity of 91.6% toward CH3COOH is achieved in a photochemical flow reactor. This work provides insights into intermediate control via material design, and opens an avenue to conversion of CH4 to oxygenates.
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