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Spaceplates are novel flat-optic devices that implement the optical response of a free-space volume over a smaller length, effectively "compressing space" for light propagation. Together with flat lenses such as metalenses or diffractive lenses, spaceplates have the potential to enable a drastic miniaturization of any free-space optical system. While the fundamental and practical bounds on the performance metrics of flat lenses have been well studied in recent years, a similar understanding of the ultimate limits of spaceplates is lacking, especially regarding the issue of bandwidth, which remains as a crucial roadblock for the adoption of this platform. In this work, we derive fundamental bounds on the bandwidth of spaceplates as a function of their numerical aperture and compression ratio (ratio by which the free-space pathway is compressed). The general form of these bounds is universal and can be applied and specialized for different broad classes of space-compression devices, regardless of their particular implementation. Our findings also offer relevant insights into the physical mechanism at the origin of generic space-compression effects, and may guide the design of higher performance spaceplates, opening new opportunities for ultra-compact, monolithic, planar optical systems for a variety of applications., Comment: 12 pages, 4 figures

Resonances in optical systems are useful for many applications, such as frequency comb generation, optical filtering, and biosensing. However, many of these applications are difficult to implement in optical metasurfaces because traditional approaches for designing multi-resonant nanostructures require significant computational and fabrication efforts. To address this challenge, we introduce the concept of Fourier lattice resonances (FLRs) in which multiple desired resonances can be chosen a priori and used to dictate the metasurface design. Because each resonance is supported by a distinct surface lattice mode, each can have a high quality factor. Here, we experimentally demonstrate several metasurfaces with arbitrarily placed resonances (e.g., at 1310 and 1550 nm) and Q-factors as high as 800 in a plasmonic platform. This flexible procedure requires only the computation of a single Fourier transform for its design, and is based on standard lithographic fabrication methods, allowing one to design and fabricate a metasurface to fit any specific, optical-cavity-based application. This work represents an important milestone towards the complete control over the transmission spectrum of a metasurface.

Multiresonant metasurfaces could enable many applications in filtering, sensing and nonlinear optics. However, developing a metasurface with more than one high-quality-factor or high-Q resonance at designated resonant wavelengths is challenging. Here, we experimentally demonstrate a plasmonic metasurface exhibiting different, narrow surface lattice resonances by exploiting the polarization degree of freedom where different lattice modes propagate along different dimensions of the lattice. The surface consists of aluminum nanostructures in a rectangular periodic lattice. The resulting surface lattice resonances were measured around 630 nm and 1160 nm with Q-factors of ~50 and ~800, respectively. The latter is a record-high plasmonic Q-factor within the near-infrared type-II window. Such metasurfaces could benefit applications such as frequency conversion and all-optical switching.

The development of metasurfaces has enabled unprecedented portability and functionality in flat optical devices. Spaceplates have recently been introduced as a complementary element to reduce the space between individual metalenses. This will further miniaturize entire imaging devices. However, a spaceplate necessitates a non-local optical response -- one which depends on the transverse spatial frequency component of a light field -- therefore making it challenging both to design them and to assess their ultimate performance and potential. Here, we employ inverse-design techniques to explore the behaviour of general thin-film-based spaceplates. We observe a tradeoff between the compression factor R and the numerical aperture NA of such devices; we obtained a compression factor of R = 5.5 for devices with an NA = 0.42 up to a record R = 340 with NA of 0.017. Our work illustrates that even simple designs consisting of realistic materials (i.e., silicon and glass) permit capable spaceplates for monochromatic applications., Comment: 8 pages, 4 figures

The nonlinear optical response of materials is the foundation upon which applications such as frequency conversion, all-optical signal processing, molecular spectroscopy, and nonlinear microscopy are built. However, the utility of all such parametric nonlinear optical processes is hampered by phase-matching requirements. Quasi-phase-matching, birefringent phase matching, and higher-order-mode phase matching have all been developed to address this constraint, but the methods demonstrated to date suffer from the inconvenience of only being phase-matched for a single, specific arrangement of beams, typically co-propagating, resulting in cumbersome experimental configurations and large footprints for integrated devices. Here, we experimentally demonstrate that these phase-matching requirements may be satisfied in a parametric nonlinear optical process for multiple, if not all, configurations of input and output beams when using low-index media. Our measurement constitutes the first experimental observation of direction-independent phase matching for a medium sufficiently long for phase matching concerns to be relevant. We demonstrate four-wave mixing from spectrally distinct co- and counter-propagating pump and probe beams, the backward-generation of a nonlinear signal, and excitation by an out-of-plane probe beam. These results explicitly show that the unique properties of low-index media relax traditional phase-matching constraints, which can be exploited to facilitate nonlinear interactions and miniaturize nonlinear devices, thus adding to the established exceptional properties of low-index materials., Comment: 17 pages, including supplementary information

Optical materials with vanishing dielectric permittivity, known as epsilon-near-zero (ENZ) materials, have been shown to possess enhanced nonlinear optical responses in their ENZ region. These strong nonlinear optical properties have been firmly established in homogeneous materials; however, it is as of yet unclear whether metamaterials with effective optical parameters can exhibit a similar enhancement. Here, we probe an optical ENZ metamaterial composed of a subwavelength periodic stack of alternating Ag and SiO$_2$ layers and measure a nonlinear refractive index $n_2 = (1.2 \pm 0.1) \times 10^{-12}$ m$^2$/W and nonlinear absorption coefficient $\beta = (-1.5 \pm 0.2) \times 10^{-5}$ m/W at its effective zero-permittivity wavelength. The measured $n_2$ is $10^7$ times larger than $n_2$ of fused silica and four times larger than that the $n_2$ of silver. We observe that the nonlinear enhancement in $n_2$ scales as $1/(n_0 \mathrm{Re}[n_0])$, where $n_0$ is the linear effective refractive index. As opposed to homogeneous ENZ materials, whose optical properties are dictated by their intrinsic material properties and hence are not widely tunable, the zero-permittivity wavelength of the demonstrated metamaterials may be chosen to lie anywhere within the visible spectrum by selecting the right thicknesses of the sub-wavelength layers. Consequently, our results offer the promise of a means to design metamaterials with large nonlinearities for applications in nanophotonics at any specified optical wavelength., Comment: 24 pages, includes supporting information

Plasmonic nanostructures hold promise for the realization of ultra-thin sub-wavelength devices, reducing power operating thresholds and enabling nonlinear optical functionality in metasurfaces. However, this promise is substantially undercut by absorption introduced by resistive losses, causing the metasurface community to turn away from plasmonics in favour of alternative material platforms (e.g., dielectrics) that provide weaker field enhancement, but more tolerable losses. Here, we report a plasmonic metasurface with a quality-factor (Q-factor) of 2340 in the telecommunication C band by exploiting surface lattice resonances (SLRs), exceeding the record by an order of magnitude. Additionally, we show that SLRs retain many of the same benefits as localized plasmonic resonances, such as field enhancement and strong confinement of light along the metal surface. Our results demonstrate that SLRs provide an exciting and unexplored method to tailor incident light fields, and could pave the way to flexible wavelength-scale devices for any optical resonating application., Comment: 15 pages, includes supporting information

Spontaneous emission, stimulated emission and absorption are the three fundamental radiative processes describing light-matter interactions. Here, we theoretically study the behaviour of these fundamental processes inside an unbounded medium exhibiting a vanishingly small refractive index, i.e., a near-zero-index (NZI) host medium. We present a generalized framework to study these processes and find that the spatial dimension of the NZI medium has profound effects on the nature of the fundamental radiative processes. Our formalism highlights the role of the number of available optical modes as well as the ability of an emitter to couple to these modes as a function of the dimension and the class of NZI media. We demonstrate that the fundamental radiative processes are inhibited in 3D homogeneous lossless zero index materials but may be strongly enhanced in a zero index medium of reduced dimensionality. Our findings have implications in thermal, nonlinear and quantum optics as well as in designing quantum metamaterials at optical or microwave frequencies.

On January 13th 2020, the inaugural Photonics Online Meetup (POM) brought together more than 1100 researchers to discuss the latest advances in photonics. Or rather, it didn't, because the meeting was completely delocalized with the speakers, organizers, and attendees scattered across six continents and hundreds of locations, connected via a video-conferencing tool and social media. Despite this "delocalisation," the meeting retained many characteristics of a traditional conference: invited and contributed talks with follow-up questions and discussion, and a poster session. However, unlike with traditional conferences, all attendees avoided air travel, high registration costs (it was completely free), CO2 emission, or visa issues. Surely the impact on families was minimized as well, though participants in inconvenient time zones had to wake up early or stay up late. In this Comment, we highlight the key steps that enabled this event, offering tips and advice, to aid the organisation of similar Online Meetups., Comment: Updated some of the text and added a figure

Centuries of effort to improve imaging has focused on perfecting and combining lenses to obtain better optical performance and new functionalities. The arrival of nanotechnology has brought to this effort engineered surfaces called metalenses, which promise to make imaging devices more compact. However, unaddressed by this promise is the space between the lenses, which is crucial for image formation but takes up by far the most room in imaging systems. Here, we address this issue by presenting the concept of and experimentally demonstrating an optical 'spaceplate', an optic that effectively propagates light for a distance that can be considerably longer than the plate thickness. Such an optic would shrink future imaging systems, opening the possibility for ultra-thin monolithic cameras. More broadly, a spaceplate can be applied to miniaturize important devices that implicitly manipulate the spatial profile of light, for example, solar concentrators, collimators for light sources, integrated optical components, and spectrometers., Comment: 4 figures, 3 videos, includes complete SI

Resonant metasurfaces are devices composed of nanostructured sub-wavelength scatterers that generate narrow optical resonances, enabling applications in filtering, nonlinear optics, and molecular fingerprinting. It is highly desirable for these applications to incorporate such devices with multiple, high-quality-factor resonances; however, it can be challenging to obtain more than a pair of narrow resonances in a single plasmonic surface. Here, we demonstrate a multi-resonant metasurface that operates by extending the functionality of surface lattice resonances, which are the collective responses of arrays of metallic nanoparticles. This device features a series of resonances with high quality factors (Q ~ 40), an order of magnitude larger than what is typically achievable with plasmonic nanoparticles, as well as a narrow free spectral range. This design methodology can be used to better tailor the transmission spectrum of resonant metasurfaces and represents an important step towards the miniaturization of optical devices., Comment: 8 pages, 4 figures, includes MATLAB code in Supplementary Materials

We show that standard approximations in nonlinear optics are violated for situations involving a small value of the linear refractive index. Consequently, the conventional equation for the intensity-dependent refractive index, $n(I) = n_0 + n_2 I$, becomes inapplicable in epsilon-near-zero and low-index media, even in the presence of only third-order effects. For the particular case of indium tin oxide, we find that the $\chi^{(3)}$, $\chi^{(5)}$ and $\chi^{(7)}$ contributions to refraction eclipse the linear term; thus, the nonlinear response can no longer be interpreted as a perturbation in these materials. Although the response is non-perturbative, we find no evidence that the power series expansion of the material polarization diverges., Comment: 4 pages, 3 figures

Propagation losses in micro-ring resonator waveguides can be determined from the shape of individual resonances in their transmission spectrum. The losses are typically extracted by fitting these resonances to an idealized model that is derived using scattering theory. Reflections caused by waveguide boundaries or stitching errors, however, cause the resonances to become asymmetric, resulting in poor fits and unreliable propagation loss coefficients. We derive a model that takes reflections into account and, by performing full-wave simulations, we show that this model accurately describes the asymmetric resonances that result from purely linear effects, yielding accurate propagation loss coefficients., Comment: 8 pages, 4 figures

Zero-index materials exhibit exotic optical properties that can be utilized for integrated-optics applications. However, practical implementation requires compatibility with complementary metallic-oxide-semiconductor (CMOS) technologies. We demonstrate a CMOS-compatible zero-index metamaterial consisting of a square array of air holes in a 220-nm-thick silicon-on-insulator (SOI) wafer. This design is achieved through a Dirac-cone dispersion. The metamaterial is entirely composed of silicon and offers compatibility through low-aspect-ratio structures that can be simply fabricated in a standard device layer. This platform enables mass adoption and exploration of zero-index-based photonic devices at low cost and high fidelity., Comment: 18 pages, 4 figures

Zero-index metamaterials (ZIMs) offer unprecedented ways to manipulate the flow of light, and are of interest for wide range of applications including optical cloaking, super-coupling, and unconventional phase-matching properties in nonlinear optics. Impedance-matched ZIMs can be obtained through a photonic Dirac-cone (PDC) dispersion induced by an accidental degeneracy of two linear bands - typically an electric monopole mode and a transverse magnetic dipole mode - at the center of the Brillouin zone. Consequently, PDC can only be achieved for a particular combination of geometric parameters of the metamaterial, and hence is sensitive to fabrication imperfections. These fabrication imperfections may limit the usefulness in practical applications. In this work we overcome this obstacle and demonstrate robust all-dielectric (AD) ZIM that supports PDC dispersion over wide parameter space. Our structure, consisting of an array of Si pillars on silica substrate, is fabricated in silicon-oninsulator (SOI) platform and operates at telecom wavelengths., Comment: 5 pages, 6 figures