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Layered van der Waals (vdW) materials have emerged as a promising platform for nanophotonics due to large refractive indexes and giant optical anisotropy. Unlike conventional dielectrics and semiconductors, the absence of covalent bonds between layers allows for novel degrees of freedom in designing optically resonant nanophotonic structures down to the atomic scale, from the precise stacking of vertical heterostructures to controlling the twist angle between crystallographic axes. Specifically, while transition metal dichalcogenides monolayers exhibit giant second order nonlinear responses, their bulk counterparts with 2H stacking have zero second order response. In this work, we show second harmonic generation (SHG) arising from the interface of WS$_2$/MoS$_2$ hetero-bilayer thin films with an additional SHG enhancement in nanostructured optical antennas mediated by both the excitonic resonances and the anapole condition. When both conditions are met, we observe up to $10^2$ SHG signal enhancement. Our results highlights vdW materials as a platform for designing unique multilayer optical nanostructures and metamaterial, paving the way for advanced applications in nanophotonics and nonlinear optics., Comment: Manuscript + Supplementary (21 pages, 3 Main figures 8 supplementary figures)

Dry synthesis is a highly versatile method for the fabrication of nanoporous metal films, since it enables easy and reproducible deposition of single or multi-layer(s) of nanostructured materials that can find intriguing applications in plasmonics, photochemistry and photocatalysis, to name a few. Here, we extend the use of this methodology to the preparation of copper nanoislands that represent an affordable and versatile example of disordered plasmonic substrate. We perform detailed characterizations of the system using several techniques such as spectroscopic ellipsometry, cathodoluminescence, electron energy loss spectroscopy, ultrafast pump-probe spectroscopy and second-harmonic generation with the aim to investigate the optical properties of these systems in an unprecedented systematic way. Our study represents the starting point for future applications of this new disordered plasmonic system ranging from sensing to photochemistry and photocatalysis.

Digital signal processing is the cornerstone of several modern-day technologies, yet in multiple applications it faces critical bottlenecks related to memory and speed constraints. Thanks to recent advances in metasurface design and fabrication, light-based analog computing has emerged as a viable option to partially replace or augment digital approaches. Several light-based analog computing functionalities have been demonstrated using patterned flat optical elements, with great opportunities for integration in compact nanophotonic systems. So far, however, the available operations have been restricted to the linear regime, limiting the impact of this technology to a compactification of Fourier optics systems. In this paper, we introduce nonlinear operations to the field of metasurface-based analog optical processing, demonstrating that nonlinear optical phenomena, combined with nonlocality in flat optics, can be leveraged to synthesize kernels beyond linear Fourier optics, paving the way to a broad range of new opportunities. As a practical demonstration, we report the experimental synthesis of a class of nonlinear operations that can be used to realize broadband, polarization-selective analog-domain edge detection.

Metasurfaces represent a new frontier in materials science paving for unprecedented methods of controlling electromagnetic waves, with a range of applications spanning from sensing to imaging and communications. For pulsed terahertz generation, metasurfaces offer a gateway to tuneable thin emitters that can be utilised for large-area imaging, microscopy and spectroscopy. In literature THz-emitting metasurfaces generally exhibit high absorption, being based either on metals or on semiconductors excited in highly resonant regimes. Here we propose the use of a fully dielectric semiconductor exploiting morphology-mediated resonances and inherent quadratic nonlinear response. Our system exhibits a remarkable 40-fold efficiency enhancement compared to the unpatterned at the peak of the optimised wavelength range, demonstrating its potential as scalable emitter design.

All-optical modulation yields the promise of high-speed information processing. In this frame, metasurfaces are rapidly gaining traction as ultrathin multifunctional platforms for light management. Among the featured functionalities, they enable light wavefront manipulation and, more recently, demonstrated the ability to perform light-by-light manipulation through nonlinear optical processes. Here, by employing a nonlinear periodic metasurface, we demonstrate all-optical routing of telecom photons upconverted to the visible range. This is achieved via the interference between two frequency-degenerate upconversion processes, namely third-harmonic and sum-frequency generation, stemming from the interaction of a pump pulse with its frequency-doubled replica. By tuning the relative phase and polarization between these two pump beams, and concurrently engineering the nonlinear emission of the individual elements of the metasurfaces (meta-atoms) along with its pitch, we route the upconverted signal among the diffraction orders of the metasurface with a modulation efficiency up to 90%. Thanks to the phase control and the ultrafast dynamics of the underlying nonlinear processes, free-space all-optical routing could be potentially performed at rates close to the employed optical frequencies divided by the quality factor of the optical resonances at play. Our approach adds a further twist to optical interferometry, which is a key-enabling technique in a wide range of applications, such as homodyne detection, radar interferometry, LiDAR technology, gravitational waves detection, and molecular photometry. In particular, the nonlinear character of light upconversion combined with phase sensitivity is extremely appealing for enhanced imaging and biosensing., Comment: 18 pages, 6 figures

The rapid development of metasurfaces - 2D ensembles of engineered nanostructures - is presently fostering a steady drive towards the miniaturization of many optical functionalities and devices to a subwavelength size. The material platforms for optical metasurfaces are rapidly expanding and for the past few years, we are seeing a surge in establishing meta-optical elements from high-index, highly transparent materials with strong nonlinear and electro-optic properties. Crystalline lithium niobate (LN), a prime material of choice in integrated photonics, has shown great promise for future meta-optical components, thanks to its large electro-optical coefficient, second-order nonlinear response and broad transparency window ranging from the visible to the mid-infrared. Recent advances in nanofabrication technology have indeed marked a new milestone in the miniaturization of LN platforms, hence enabling the first demonstrations of LN-based metasurfaces. These seminal works set the first steppingstone towards the realization of ultra-flat monolithic nonlinear light sources with emission ranging from the visible to the infrared, efficient sources of correlated photon pairs, as well as electro-optical devices. Here, we review these recent advances, discussing potential perspectives for applications in light conversion and modulation shaping as well as quantum optics, with a critical eye on the potential setbacks and limitations of this emerging field., Comment: 45 Pages, 6 Figures

Metasurfaces have appeared as a versatile platform for miniaturized functional nonlinear optics due to their design freedom in tailoring wavefronts. The key factor that limits its application in functional devices is the low conversion efficiency. Recently, dielectric metasurfaces governed by either high-quality factor modes (quasi-bound states in the continuum) or Mie modes, enabling strong light-matter interaction, have become a prolific route to achieve high nonlinear efficiency. Here, we demonstrate both numerically and experimentally an effective way of spatial nonlinear phase control by using the Pancharatnam-Berry phase principle with a high third harmonic conversion efficiency of $10^{-4}$ $1/W^2$. We find that the magnetic Mie resonance appears to be the main contributor to the third harmonic response, while the contribution from the quasi-bound states in the continuum is negligible. This is confirmed by a phenomenological model based on coupled anharmonic oscillators. Besides, our metasurface provides experimentally a high diffraction efficiency (80-90%) in both polarization channels. We show a functional application of our approach by experimentally reconstructing an encoded polarization-multiplexed vortex beam array with different topological charges at the third harmonic frequency with high fidelity. Our approach has the potential viability for future on-chip nonlinear signal processing and wavefront control.

Nonlinear light sources are central to a myriad of applications, driving a quest for their miniaturisation down to the nanoscale. In this quest, nonlinear metasurfaces hold a great promise, as they enhance nonlinear effects through their resonant photonic environment and high refractive index, such as in high-index dielectric metasurfaces. However, despite the sub-diffractive operation of dielectric metasurfaces at the fundamental wave, this condition is not fulfilled for the nonlinearly generated harmonic waves, thereby all nonlinear metasurfaces to date emit multiple diffractive beams. Here, we demonstrate the enhanced single-beam second- and third-harmonic generation in a metasurface of crystalline transition-metal-dichalcogenide material, offering the highest refractive index. We show that the interplay between the resonances of the metasurface allows for tuning of the unidirectional second-harmonic radiation in forward or backward direction, not possible in any bulk nonlinear crystal. Our results open new opportunities for metasurface-based nonlinear light-sources, including nonlinear mirrors and entangled-photon generation., Comment: 16 pages, 8 figures

We use numerical simulations to demonstrate third-harmonic generation with near-unity nonlinear circular dichroism (CD) and high conversion efficiency ($ 10^{-2}\ \text{W}^{-2}$) in asymmetric Si-on-SiO$_2$ metasurfaces. The working principle relies on the selective excitation of a quasi-bound state in the continuum, characterized by a very high ($>10^5$) quality-factor. By tuning multi-mode interference with the variation of the metasurface geometrical parameters, we show the possibility of independent control of linear CD and nonlinear CD. Our results pave the way for the development of all-dielectric metasurfaces for nonlinear chiro-optical devices with high conversion efficiency.

Nonlinear metasurfaces have become prominent tools for controlling and engineering light at the nanoscale. Usually, the polarization of the total generated third harmonic is studied. However, diffraction orders may present different polarizations. Here, we design an high quality factor silicon metasurface for third harmonic generation and perform back focal plane imaging of the diffraction orders, which present a rich variety of polarization states. Our results demonstrate the possibility of tailoring the polarization of the generated nonlinear diffraction orders paving the way to a higher degree of wavefront control.

Infrared imaging is a crucial technique in a multitude of applications, including night vision, autonomous vehicles navigation, optical tomography, and food quality control. Conventional infrared imaging technologies, however, require the use of materials like narrow-band gap semiconductors which are sensitive to thermal noise and often require cryogenic cooling. Here, we demonstrate a compact all-optical alternative to perform infrared imaging in a metasurface composed of GaAs semiconductor nanoantennas, using a nonlinear wave-mixing process. We experimentally show the up-conversion of short-wave infrared wavelengths via the coherent parametric process of sum-frequency generation. In this process, an infrared image of a target is mixed inside the metasurface with a strong pump beam, translating the image from infrared to the visible in a nanoscale ultra-thin imaging device. Our results open up new opportunities for the development of compact infrared imaging devices with applications in infrared vision and life sciences., Comment: 32 pages, 13 figures

The full control of the fundamental photophysics of nanosystems at frequencies as high as few THz is key for tunable and ultrafast nano-photonic devices and metamaterials. Here we combine geometrical and ultrafast control of the optical properties of halide perovskite nanoparticles, which constitute a prominent platform for nanophotonics. The pulsed photoinjection of free carriers across the semiconducting gap leads to a sub-picosecond modification of the far-field electromagnetic properties that is fully controlled by the geometry of the system. When the nanoparticle size is tuned so as to achieve the overlap between the narrowband excitons and the geometry-controlled Mie resonances, the ultrafast modulation of the transmittivity is completely reversed with respect to what is usually observed in nanoparticles with different sizes, in bulk systems and in thin films. The interplay between chemical, geometrical and ultrafast tuning offers an additional control parameter with impact on nano-antennas and ultrafast optical switches.

Nonlinear wavefront control is a crucial requirement in realizing nonlinear optical applications with metasurfaces. Numerous aspects of nonlinear frequency conversion and wavefront control have been demonstrated for plasmonic metasurfaces. However, several disadvantages limit their applicability in nonlinear nanophotonics, including high dissipative loss and low optical damage threshold. In contrast, it has been shown that metasurfaces made of high-index dielectrics can provide strong nonlinear responses. Regardless of the recent progress in nonlinear optical processes using all-dielectric nanostructures and metasurfaces, much less advancement has been made in realizing a full wavefront control directly with the generation process. Here, we demonstrate the nonlinear wavefront control for the third-harmonic generation with a silicon metasurface. We use a Pancharatnam-Berry phase approach to encode phase gradients and holographic images on nanostructured silicon metasurfaces. We experimentally demonstrate the polarization-dependent wavefront control and the reconstruction of an encoded hologram at the third-harmonic wavelength with high fidelity. Further, we show that holographic multiplexing is possible by utilizing the polarization states of the third harmonic generation. Our approach eases design and fabrication processes and paves the way to an easy to use toolbox for nonlinear optical wavefront control with all-dielectric metasurfaces.

Optical nanoantennas have shown a great capacity for efficient extraction of photons from the near to the far-field, enabling directional emission from nanoscale single-photon sources. However, their potential for the generation and extraction of multi-photon quantum states remains unexplored. Here we demonstrate experimentally the nanoscale generation of two-photon quantum states at telecommunication wavelengths based on spontaneous parametric down-conversion in an optical nanoantenna. The antenna is a crystalline AlGaAs nanocylinder, possessing Mie-type resonances at both the pump and the bi-photon wavelengths and when excited by a pump beam generates photonpairs with a rate of 35 Hz. Normalized to the pump energy stored by the nanoantenna, this rate corresponds to 1.4 GHz/Wm, being one order of magnitude higher than conventional on-chip or bulk photon-pair sources. Our experiments open the way for multiplexing several antennas for coherent generation of multi-photon quantum states with complex spatial-mode entanglement and applications in free-space quantum communications and sensing., Comment: A new author, Aristide Lema\^itre, has been added to the author list. No change has been made to the main text

Being motivated by the recent prediction of high-$Q$ supercavity modes in subwavelength dielectric resonators, we study the second-harmonic generation from isolated subwavelength AlGaAs nanoantennas pumped by a structured light. We reveal that nonlinear effects at the nanoscale can be enhanced dramatically provided the resonator parameters are tuned to the regime of the bound state in the continuum. We predict a record-high conversion efficiency for nanoscale resonators that exceeds by two orders of magnitude the conversion efficiency observed at the conditions of magnetic dipole Mie resonance, thus opening the way for highly-efficient nonlinear metadevices., Comment: 7 pages, 4 figures, 1 table

The optimization of nonlinear optical processes at the nanoscale is a crucial step for the development of nanoscale photon sources for quantum-optical networks. The development of innovative plasmonic nanoantenna designs and hybrid nanostructures to enhance optical nonlinearities in very small volumes represents one of the most promising routes. In such systems, the upconversion of photons can be achieved with high efficiencies via third-order processes, such as third harmonic generation (THG), thanks to the resonantly-enhanced volume currents. Conversely, second-order processes, such as second harmonic generation (SHG), are often inhibited by the symmetry of metal lattices and of common nanoantenna geometries. SHG and THG processes in plasmonic nanostructures are generally treated independently, since they both represent a small perturbation in the light-matter interaction mechanisms. In this work, we demonstrate that this paradigm does not hold in general, by providing evidence of a cascaded process in THG, which is fueled by SHG and sizably contributes to the overall yield. We address this mechanism by unveiling an anomalous fingerprint in the polarization state of the nonlinear emission from non-centrosymmetric gold nanoantennas and point out that such cascaded processes may also appear for structures that exhibit only moderate SHG yields - signifying its general relevance in plasmon-enhanced nonlinear optics. The presence of this peculiar mechanism in THG from plasmonic nanoantennas at telecommunication wavelengths allows gaining further insight on the physics of plasmon-enhanced nonlinear optical processes. This could be crucial in the realization of nanoscale elements for photon conversion and manipulation operating at room-temperature., Comment: 25 pages, 4 figures

We report on the broadband transient optical response from anisotropic nanobrick amorphous silicon particles, exhibiting Mie-type resonances. A quantitative model is developed to identify and disentangle the three physical processes that govern the ultrafast changes of the nanobrick optical properties, namely two-photon absorption, free-carrier relaxation, and lattice heating. We reveal a set of operating windows where ultrafast all-optical modulation of transmission is achieved with full return to zero in 20 ps. This is made possible due to the interplay between the competing nonlinear processes and despite the slow (nanosecond) internal lattice dynamics. The observed ultrafast switching behavior can be independently engineered for both or- thogonal polarizations using the large anisotropy of nanobricks thus allowing ultrafast anisotropy control. Our results categorically ascertain the potential of all-dielectric resonant nanophotonics as a platform for ultrafast optical devices, and reveal the pos- sibility for ultrafast polarization-multiplexed displays and polarization rotators.

We aim to clarify the role that absorption plays in nonlinear optical processes in a variety of metallic nanostructures and show how it relates to emission and conversion efficiency. We define a figure of merit that establishes the structure's ability to either favor or impede second harmonic generation. Our findings suggest that, despite the best efforts embarked upon to enhance local fields and light coupling via plasmon excitation, nearly always the absorbed harmonic energy far surpasses the harmonic energy emitted in the far field. Qualitative and quantitative understanding of absorption processes is crucial in the evaluation of practical designs of plasmonic nanostructures for the purpose of frequency mixing.

Boosting nonlinear frequency conversion in extremely confined volumes remains a key challenge in nano-optics, nanomedicine, photocatalysis, and background-free biosensing. To this aim, field enhancements in plasmonic nanostructures are often exploited to effectively compensate for the lack of phase-matching at the nanoscale. Second harmonic generation (SHG) is, however, strongly quenched by the high degree of symmetry in plasmonic materials at the atomic scale and in nanoantenna designs. Here, we devise a plasmonic nanoantenna lacking axial symmetry, which exhibits spatial and frequency mode overlap at both the excitation and the SHG wavelengths. The effective combination of these features in a single device allows obtaining unprecedented SHG conversion efficiency. Our results shed new light on the optimization of SHG at the nanoscale, paving the way to new classes of nanoscale coherent light sources and molecular sensing devices based on nonlinear plasmonic platforms., Comment: 14 pages, 4 figures

We demonstrate experimentally the existence of three-wave resonant interaction solitary triplets in quadratic media. Stable velocity-locked bright-dark-bright spatial solitary triplets, determined by the balance between the energy exchange rates and the velocity mismatch between the interacting waves, are excited in a KTP crystal.

We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse bandwidth. Our approach goes beyond the usual coupled wave description of $\chi^{(2)}$ phenomena and provides an accurate modelling of the evolution of ultra-broadband pulses also when the separation into different coupled frequency components is not possible or not profitable.