Spectral and spatial shaping of Smith Purcell Radiation

The Smith Purcell effect, observed when an electron beam passes in the vicinity of a periodic structure, is a promising platform for the generation of electromagnetic radiation in previously-unreachable spectral ranges. However, most of the studies of this radiation were performed on simple periodic gratings, whose radiation spectrum exhibits a single peak and its higher harmonics predicted by a well-established dispersion relation. Here, we propose a method to shape the spatial and spectral far-field distribution of the radiation using complex periodic and aperiodic gratings. We show, theoretically and experimentally, that engineering multiple peak spectra with controlled widths located at desired wavelengths is achievable using Smith-Purcell radiation. Our method opens the way to free-electron driven sources with tailored angular and spectral response, and gives rise to focusing functionality for spectral ranges where lenses are unavailable or inefficient

Smith-Purcell Radiation from Low-Energy Electrons

Recent advances in the fabrication of nanostructures and nanoscale features in metasurfaces offer a new prospect for generating visible, light emission from low energy electrons. In this paper, we present the experimental observation of visible light emission from low-energy free electrons interacting with nanoscale periodic surfaces through the Smith-Purcell (SP) effect. SP radiation is emitted when electrons pass in close proximity over a periodic structure, inducing collective charge motion or dipole excitations near the surface, thereby giving rise to electromagnetic radiation. We demonstrate a controlled emission of SP light from nanoscale gold gratings with periodicity as small as 50 nm, enabling the observation of visible SP radiation by low energy electrons (1.5 to 6 keV), an order of magnitude lower than previously reported. We study the emission wavelength and intensity dependence on the grating pitch and electron energy, showing agreement between experiment and theory. Further reduction of structure periodicity should enable the production of SP-based devices that operate with even slower electrons that allow an even smaller footprint and facilitate the investigation of quantum effects for light generation in nanoscale devices. A tunable light source integrated in an electron microscope would enable the development of novel electron-optical correlated spectroscopic techniques, with additional applications ranging from biological imaging to solid-state lighting.Comment: 16 pages, 4 figure

Monochromatic X-ray source based on scattering from a magnetic nanoundulator

We present a novel design for an ultra-compact, passive light source capable of generating ultraviolet and X-ray radiation, based on the interaction of free electrons with the magnetic near-field of a ferromagnet. Our design is motivated by recent advances in the fabrication of nanostructures, which allow the confinement of large magnetic fields at the surface of ferromagnetic nanogratings. Using ab initio simulations and a complementary analytical theory, we show that highly directional, tunable, monochromatic radiation at high frequencies could be produced from relatively low-energy electrons within a tabletop design. The output frequency is tunable in the extreme ultraviolet to hard X-ray range via electron kinetic energies from 1 keV-5 MeV and nanograting periods from 1 {\mu}m-5 nm. Our design reduces the scale, cost, and complexity of current free-electron-driven light schemes, bypassing the need for lengthy acceleration stages in conventional synchrotrons and free-electron lasers and driving lasers in other compact designs. Our design could help realize the next generation of tabletop or on-chip X-ray sources.Comment: 8 pages, 4 figure

End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing

We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (i.e. the object can be described by a small number of non-zero values, but the positions of these values are unknown). We nest an iterative, unapproximated compressed sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting in an interpretable, data-efficient method for maximally leveraging metaoptics to exploit object sparsity. We apply our framework to super-resolution imaging and high-resolution depth imaging with a phase-change material: in both situations, our end-to-end framework computationally discovers optimal metasurface structures for compressed sensing recovery, automatically balancing a number of complicated design considerations. The optimized metasurface imaging systems are robust to noise, significantly improving over random scattering surfaces and approaching the ideal compressed sensing performance of a Gaussian matrix, showing how a physical metasurface system can demonstrably approach the mathematical limits of compressed sensing

Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics

Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. Shift-invariance has deep implications for the design and functionality of optical devices, such as the necessity of free space between components (as in compound objectives made of several curved surfaces). We present a method for nanophotonic inverse design of compact imaging systems whose resolution is not constrained by paraxial shift-invariance. Our method is end-to-end, in that it integrates density-based full-Maxwell topology optimization with a fully iterative elastic-net reconstruction algorithm. By the design of nanophotonic structures that scatter light in a non-shift-invariant manner, our optimized nanophotonic imaging system overcomes the limitations of paraxial shift-invariance, achieving accurate, noise-robust image reconstruction beyond shift-invariant resolution

Fullwave Maxwell inverse design of axisymmetric, tunable, and multi-scale multi-wavelength metalenses

We demonstrate new axisymmetric inverse-design techniques that can solve problems radically different from traditional lenses, including \emph{reconfigurable} lenses (that shift a multi-frequency focal spot in response to refractive-index changes) and {\emph{widely separated}} multi-wavelength lenses ($\lambda = 1\,\mu$m and $10\,\mu$m). We also present experimental validation for an axisymmetric inverse-designed monochrome lens in the near-infrared fabricated via two-photon polymerization. Axisymmetry allows fullwave Maxwell solvers to be scaled up to structures hundreds or even thousands of wavelengths in diameter before requiring domain-decomposition approximations, while multilayer topology optimization with $\sim 10^5$ degrees of freedom can tackle challenging design problems even when restricted to axisymmetric structures.Comment: 13 pages, 6 figure

Photonic probabilistic machine learning using quantum vacuum noise

Probabilistic machine learning utilizes controllable sources of randomness to encode uncertainty and enable statistical modeling. Harnessing the pure randomness of quantum vacuum noise, which stems from fluctuating electromagnetic fields, has shown promise for high speed and energy-efficient stochastic photonic elements. Nevertheless, photonic computing hardware which can control these stochastic elements to program probabilistic machine learning algorithms has been limited. Here, we implement a photonic probabilistic computer consisting of a controllable stochastic photonic element - a photonic probabilistic neuron (PPN). Our PPN is implemented in a bistable optical parametric oscillator (OPO) with vacuum-level injected bias fields. We then program a measurement-and-feedback loop for time-multiplexed PPNs with electronic processors (FPGA or GPU) to solve certain probabilistic machine learning tasks. We showcase probabilistic inference and image generation of MNIST-handwritten digits, which are representative examples of discriminative and generative models. In both implementations, quantum vacuum noise is used as a random seed to encode classification uncertainty or probabilistic generation of samples. In addition, we propose a path towards an all-optical probabilistic computing platform, with an estimated sampling rate of ~ 1 Gbps and energy consumption of ~ 5 fJ/MAC. Our work paves the way for scalable, ultrafast, and energy-efficient probabilistic machine learning hardware

Biasing the quantum vacuum to control macroscopic probability distributions

One of the most important insights of quantum field theory is that electromagnetic fields must fluctuate. Even in the vacuum state, the electric and magnetic fields have a nonzero variance, leading to ubiquitous effects such as spontaneous emission, the Lamb shift, the Casimir effect, and more. These "vacuum fluctuations" have also been harnessed as a source of perfect randomness, for example to generate perfectly random photonic bits. Despite these achievements, many potential applications of quantum randomness in fields such as probabilistic computing rely on controllable probability distributions, which have not yet been realized on photonic platforms. In this work, we show that the injection of vacuum-level "bias" fields into a multi-stable optical system enables a controllable source of "biased" quantum randomness. We demonstrate this concept in an optical parametric oscillator (OPO). Ordinarily, an OPO initiated from the ground state develops a signal field in one of two degenerate phase states (0 and $\pi$) with equal probability. By injecting bias pulses which contain less than one photon on average, we control the probabilities associated with the two output states, leading to the first controllable photonic probabilistic bit (p-bit). We shed light on the physics behind this process, showing quantitative agreement between theory and experiment. Finally, we demonstrate the potential of our approach for sensing sub-photon level fields by showing that our system is sensitive to the temporal shape of bias field pulses far below the single photon level. Our results suggest a new platform for the study of stochastic quantum dynamics in nonlinear driven-dissipative systems, and point toward possible applications in ultrafast photonic probabilistic computing, as well as the sensing of extremely weak fields