Optically pumped nonlinear metasurfaces (NLMS) of gold split-ring resonators (SRRs) generate broadband single-cycle terahertz (THz) wavepackets by optical rectification and, by spatially varying the SRR orientation, already shape their spatiotemporal structure using a single effective element of the nonlinear response tensor. The source work (Keren-Zur et al., Nature Communications 2019) explicitly poses the unresolved program: further investigation of the full nonlinear-response tensor of the NLMS, adding to the toolbox of THz wavepacket shaping the ability to obtain control over the spatial polarization, amplitude, and continuous phase; and study of the physical mechanism of the nonlinear interaction itself, to shed new light on ways to significantly enhance the THz-generation efficiency. Subsequent work has substantially achieved the wavefront-control goal through geometric-phase and chiral meta-atom designs, and efficiency has gained orders of magnitude through epsilon-near-zero hybridization and resonant dielectric metasurfaces, but no complete tensor-level characterization or predictive microscopic account of absolute efficiency exists, absolute conversion efficiency remains near 1e-6, and systematic collective-effect studies of THz-emitting NLMS are lacking. The problem remains open.

Background

The terahertz (THz) frequency band (roughly 0.1–10 THz) sits between microwave and infrared technologies and supports spectroscopy, imaging, and wireless communication applications, but the lack of compact, efficient, and controllable THz sources is a long-standing bottleneck known as the THz gap. One established generation mechanism is optical rectification (OR): an intense femtosecond optical pulse passing through a medium with a second-order nonlinear susceptibility produces a broadband, single-cycle THz transient. Conventional OR crystals such as ZnTe and GaP are sub-millimeter thick and constrained by phonon absorption and phase matching between the optical pump and the THz output.

A nonlinear metasurface (NLMS) is an optically thin, subwavelength-spaced array of nanoresonators that replaces the bulk crystal: strong local field enhancement at each resonator boosts the effective nonlinear response, and the subwavelength thickness removes phase-matching constraints. The most studied implementation is an array of gold split-ring resonators (SRRs) — U-shaped metallic nanorings with a resonant fundamental mode that concentrates the pump field in the gap. The nonlinear response of the array is described by an effective nonlinear response tensor (the surface-averaged second-order susceptibility, whose independent components are fixed by the SRR symmetry), and the emitted THz field amplitude and polarization are governed by which tensor elements are excited by a given pump polarization. In the source work (Keren-Zur, Tal, Fleischer, Mittleman and Ellenbogen, Nature Communications 10, 1778 (2019)), a 1550 nm femtosecond pump was rectified by an SRR NLMS, and spatially varying the SRR orientation across the array encoded a position-dependent sign of one effective tensor element, experimentally generating spatiotemporally tailored (structured) single-cycle THz wavepackets with binary phase control. The authors emphasize that only a single effective tensor element was used, and that the physical mechanism responsible for the generation efficiency was not established.

Several concepts from adjacent metasurface optics bear on the open directions. The Pancharatnam–Berry (PB) or geometric phase is the position-dependent phase that a circularly polarized nonlinear emission acquires when the meta-atom is rotated, enabling continuous phase profiles without changing the resonator shape. An epsilon-near-zero (ENZ) material is one whose real permittivity passes through zero near the pump wavelength; thin ENZ films (such as indium tin oxide, ITO) enhance the local field and the effective nonlinearity of a coupled plasmonic metasurface. Bound states in the continuum (BIC) and quasi-BIC resonances are high-Q collective modes of dielectric metasurface arrays that confine the pump field and enhance nonlinear generation while avoiding Ohmic loss. Surface lattice resonances arise from collective in-phase dipole oscillations across the array (diffractive coupling) and similarly modify the nonlinear emission. Later work has used each of these levers in isolation; the open question is the quantitative, predictive integration of all of them for THz-emitting NLMS.

Problem Statement

For optically pumped, SRR-based nonlinear metasurfaces that generate broadband single-cycle THz wavepackets by optical rectification — currently designed around a single effective nonlinear tensor element — establish the quantitative, predictive understanding that the source work (Keren-Zur et al., Nature Communications 10, 1778 (2019)) identifies as unresolved. The linked parts, which jointly serve this single objective, are: (1) determine the full nonlinear-response tensor of the SRR-based NLMS (all relevant effective tensor elements, their frequency dependence and spatial distribution), as the quantitative basis for position-resolved control of the generated THz polarization, amplitude, and continuous phase; (2) identify the microscopic physical mechanism(s) — including the roles of meta-atom geometry, near-field enhancement, material choice, hot-electron and carrier dynamics, and substrate or coupled-film response — that set the absolute nonlinear THz-generation efficiency and its bandwidth; (3) identify, on the basis of this understanding, ways to significantly enhance the generation efficiency; and (4) characterize systematically the collective, array-mediated effects on the nonlinear emission in the NLMS. In the literature since the source work, the wavefront-control capability of part (1) has been substantially achieved by geometric-phase and chiral meta-atom designs, so the surviving open core is the quantitative-understanding half of the objective: the complete tensor-level characterization of part (1), the predictive microscopic efficiency account of part (2), and the efficiency-enhancement and collective-effect studies of parts (3) and (4). The four parts form the joint objective, with the following scope: part (1), the complete set of independent effective tensor elements with their pump-frequency dependence; part (2), a microscopic mechanism supported by a predictive model that accounts for the absolute efficiency and its bandwidth; part (3), an enhancement route with a quantified efficiency gain; and part (4), a systematic account of the array-mediated effects on the emission. Parts (3) and (4) are distinct objectives: (3) proposes an enhancement route, which may exploit collective effects, while (4) characterizes those collective effects on the emission; a single collective-effect study may contribute to both.

References

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