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Multimode bright squeezed vacuum is a non-classical state of light hosting a macroscopic photon number while offering promising capacity for encoding quantum information in its spectral degree of freedom. Here, we employ an accurate model for parametric downconversion in the high-gain regime and use nonlinear holography to design quantum correlations of bright squeezed vacuum in the frequency domain. We propose the design of quantum correlations over two-dimensional lattice geometries that are all-optically controlled, paving the way toward continuous-variable cluster state generation on an ultrafast timescale. Specifically, we investigate the generation of a square cluster state in the frequency domain and calculate its covariance matrix and the quantum nullifier uncertainties, that exhibit squeezing below the vacuum noise level., 11 pages, 5 figures

Nonlinear holography shapes the amplitude and phase of generated new harmonics using nonlinear processes. Classical nonlinear holography influenced many fields in optics, from information storage, demultiplexing of spatial information, and all-optical control of accelerating beams. Here, we extend the concept of nonlinear holography to the quantum regime. We directly shape the spatial quantum correlations of entangled photon pairs in two-dimensional patterned nonlinear photonic crystals using spontaneous parametric down conversion, without any pump shaping. The generated signal-idler pair obeys a parity conservation law that is governed by the nonlinear crystal. Furthermore, the quantum states exhibit quantum correlations and violate the Clauser-Horne-Shimony-Holt inequality, thus enabling entanglement-based quantum key distribution. Our demonstration paves the way for controllable on-chip quantum optics schemes using the high-dimensional spatial degree of freedom.

Strong coupling in light-matter systems is a central concept in cavity quantum electrodynamics and is essential for many quantum technologies. Especially in the optical range, full control of highly connected multi-qubit systems necessitates quantum coherent probes with nanometric spatial resolution, which are currently inaccessible. Here, we propose the use of free electrons as high-resolution quantum sensors for strongly coupled light-matter systems. Shaping the free-electron wave packet enables the measurement of the quantum state of the entire hybrid systems. We specifically show how quantum interference of the free-electron wave packet gives rise to a quantum-enhanced sensing protocol for the position and dipole orientation of a subnanometer emitter inside a cavity. Our results showcase the great versatility and applicability of quantum interactions between free electrons and strongly coupled cavities, relying on the unique properties of free electrons as strongly interacting flying qubits with miniscule dimensions.

We report on the experimental realization and a systematic study of optical frequency comb generation in doubly resonant intracavity second harmonic generation (SHG). The efficiency of intracavity nonlinear processes usually benefits from the increasing number of resonating fields. Yet, achieving the simultaneous resonance of different fields may be technically complicated, all the more when a phase matching condition must be fulfilled as well. In our cavity we can separately control the resonance condition for the fundamental and its second harmonic, by simultaneously acting on an intracavity dispersive element and on a piezo-mounted cavity mirror, without affecting the quasi-phase matching condition. In addition, by finely adjusting the laser-to-cavity detuning, we are able to observe steady comb emission across the whole resonance profile, revealing the multiplicity of comb structures, and the substantial role of thermal effects on their dynamics. Lastly, we report the results of numerical simulations of comb dynamics, which include photothermal effects, finding a good agreement with the experimental observations. Our system provides a framework for exploring the richness of comb dynamics in doubly resonant SHG systems, assisting the design of chip-scale quadratic comb generators. Funding Agencies|PON Ricerca e Innovazione 2014/2020 FESR/FSC (ARS01_00734, QUANCOM); Agenzia Spaziale Italiana(NIHL); Horizon 2020 Framework Programme (820419, FET Flagship on Quantum Technologies, Qombs Project);Ministero degli Affari Esteri e della Cooperazione Internazional (NOICE Joint Laboratory).

We design, fabricate, and characterize integrated mode sorters for multimode fibers that guide well-separated vortex modes. We use 3D direct laser printing to print a collimator and a Cartesian to a log-polar mode transformer on the tip of the fiber. This polarization insensitive device can send different modes into different exit angles and is therefore useful for space division multiplexed optical communication. Two types of fibers with two corresponding sorters are used, enabling the sorting of either four or eight different modes in a compact and robust manner. The integration of the vortex fiber and multiplexer opens the door for widespread exploitation of orbital angular momentum (OAM) for data multiplexing in fiber networks.

We study here the intensity distribution and formation of optical polarization Möbius strips by tightly focusing of C-point singularity beams. These beams are characterized by a central circular polarization point (C-point) surrounded by a spatially varying elliptic polarization. Under tight focusing conditions, the different polarization components of the beam interfere and exhibit clear difference between left-handed and right handed input beams. The transverse polarization distribution at the focal plane is similar to the input distribution for left-handed lemon beam, but exhibits 180° rotation for right handed lemon beam. Moreover, the longitudinal polarization component exhibits spiral phase distribution, owing to spin-orbit angular momentum conversion at the focal plane, with opposite winding directions for the left-handed and right-handed input beams. We show that the shape of the resulting Möbius strip is determined by the helicity of the C-point and by the polarization singularity index, which is the contour integral of polarization ellipse angle around the singularity. It is found that inverting the helicity leads to 180° rotation in the focal plane intensity distribution, accompanied by handedness inversion for the polarization ellipses. The number of separatrices in the input polarization distribution is equivalent to the number of twist points of the Möbius strip in the focal plane, as well as to the number of intensity zeros in the z-component of the focused field. These phenomena are observed for beams with a bright C-point, but also for dark C-point, in which the electric field is zero at the center of the beam.

In 1952 David Bohm proposed an interpretation of quantum mechanics, in which the evolution of states results from trajectories governed by classical equations of motion but with an additional potential determined by the wave function. There exist only a few experiments that test this concept and they employed weak measurement of non-classical light. In contrast, we reconstruct the Bohm trajectories in a classical hydrodynamic system of surface gravity water waves, by a direct measurement of the wave packet. Our system is governed by a wave equation that is analogous to the Schrödinger equation which enables us to transfer the Bohm formalism to classical waves. In contrast to a quantum system, we can measure simultaneously their amplitude and phase. In our experiments, we employ three characteristic types of surface gravity water wave packets: two and three Gaussian temporal slits and temporal Airy wave packets. The Bohm trajectories and their energy flows follow the valleys and bounce off the hills in the corresponding quantum potential landscapes.

Exploring material magnetization led to countless fundamental discoveries and applications, culminating in the field of spintronics. Recently, research effort in this field focused on magnetic skyrmions – topologically robust chiral magnetization textures, capable of storing information and routing spin currents via the topological Hall effect. In this article, we propose an optical system emulating any 2D spin transport phenomena with unprecedented controllability, by employing three-wave mixing in 3D nonlinear photonic crystals. Precise photonic crystal engineering, as well as active all-optical control, enable the realization of effective magnetization textures beyond the limits of thermodynamic stability in current materials. As a proof-of-concept, we theoretically design skyrmionic nonlinear photonic crystals with arbitrary topologies and propose an optical system exhibiting the topological Hall effect. Our work paves the way towards quantum spintronics simulations and novel optoelectronic applications inspired by spintronics, for both classical and quantum optical information processing., Control of effective magnetization textures like skyrmions is limited by the thermodynamic stability in current materials. Here, the authors propose a 3D nonlinear photonic crystal to emulate 2D spin transport phenomena with excellent controllability.

We study theoretically and observe experimentally the evolution of periodic wave trains by utilizing surface gravity water wave packets. Our experimental system enables us to observe both the amplitude and the phase of these wave packets. For low steepness waves, the propagation dynamics is in the linear regime, and these waves unfold a Talbot carpet. By increasing the steepness of the waves and the corresponding nonlinear response, the waves follow the Akhmediev breather solution, where the higher frequency periodic patterns at the fractional Talbot distance disappear. Further increase in the wave steepness leads to deviations from the Akhmediev breather solution and to asymmetric breaking of the wave function. Unlike the periodic revival that occurs in the linear regime, here the wave crests exhibit self acceleration, followed by self deceleration at half the Talbot distance, thus completing a smooth transition of the periodic pulse train by half a period. Such phenomena can be theoretically modeled by using the Dysthe equation.

We investigate bright and dark diffractive focusing emerging in the free propagation of specific wave profiles. These general wave phenomena manifest themselves in matter, water, and classical waves. In this article, we lay the foundations for these effects and illustrate their origin in Wigner phase space. Our theoretical studies are supported by experimental demonstrations of dark focusing in water waves. Moreover, by using different phase slits we analyze several aspects of bright and dark focusing for classical and matter waves., publishedVersion

We propose to use free-electrons as quantum probes of strongly coupled light-matter systems. Interactions with such systems are distinctly imprinted on the electron energy spectrum, allowing for quantum detection and new photon blockade mechanisms.

Spatial modes of light can be used as carriers of information in classical optical communication or as an alphabet in quantum optical communication. In order to exploit the spatial domain, it is required to (de)multiplex different modes from a shared input channel into different output ports. Mode sorters have been employed in free-space and fiber systems but to date have not been realized for planar guided waves. Here we present a general method for compact on-chip sorting of different planar beams with a micrometric footprint and nanometric thickness. The designs were generated using a linkage-tree-based genetic algorithm and were experimentally demonstrated on a surface plasmon polariton platform by sorting of Hermite-Gaussian beams. The method used here can be readily applied to optimize complex, large-scale optical devices involving beam propagation methods.

We experimentally shape the quantum correlations of spatially entangled photon pairs in a two-dimensionally patterned KTiOPO4 crystal using nonlinear holography. Our method enables multi-dimensional engineering of quantum states directly using patterned nonlinear photonic crystals.

Dielectric laser accelerators (DLAs) are fundamentally based on the interaction of photons with free electrons, where energy and momentum conservation are satisfied by mediation of a nanostructure. In this scheme, the photonic nanostructure induces near-fields which transfer energy from the photon to the electron, similar to the inverse-Smith–Purcell effect described in metallic gratings. This, in turn, may provide ground-breaking applications, as it is a technology promising to miniaturize particle accelerators down to the chip scale. This fundamental interaction can also be used to study and demonstrate quantum photon-electron phenomena. The spontaneous and stimulated Smith–Purcell effect and the photon-induced near-field electron-microscopy (PINEM) effect have evolved to be a fruitful ground for observing quantum effects. In particular, the energy spectrum of the free electron has been shown to have discrete energy peaks, spaced with the interacting photon energy. This energy spectrum is correlated to the photon statistics and number of photon exchanges that took place during the interaction. We give an overview of DLA and PINEM physics with a focus on electron phase-space manipulation.

The geometric phase of light has been demonstrated in various platforms of the linear optical regime, raising interest both for fundamental science as well as applications, such as flat optical elements. Recently, the concept of geometric phases has been extended to nonlinear optics, following advances in engineering both bulk nonlinear photonic crystals and nonlinear metasurfaces. These new technologies offer a great promise of applications for nonlinear manipulation of light. In this review, we cover the recent theoretical and experimental advances in the field of geometric phases accompanying nonlinear frequency conversion. We first consider the case of bulk nonlinear photonic crystals, in which the interaction between propagating waves is quasi-phase-matched, with an engineerable geometric phase accumulated by the light. Nonlinear photonic crystals can offer efficient and robust frequency conversion in both the linearized and fully-nonlinear regimes of interaction, and allow for several applications including adiabatic mode conversion, electromagnetic nonreciprocity and novel topological effects for light. We then cover the rapidly-growing field of nonlinear Pancharatnam-Berry metasurfaces, which allow the simultaneous nonlinear generation and shaping of light by using ultrathin optical elements with subwavelength phase and amplitude resolution. We discuss the macroscopic selection rules that depend on the rotational symmetry of the constituent meta-atoms, the order of the harmonic generations, and the change in circular polarization. Continuous geometric phase gradients allow the steering of light beams and shaping of their spatial modes. More complex designs perform nonlinear imaging and multiplex nonlinear holograms, where the functionality is varied according to the generated harmonic order and polarization. Recent advancements in the fabrication of three dimensional nonlinear photonic crystals, as well as the pursuit of quantum light sources based on nonlinear metasurfaces, offer exciting new possibilities for novel nonlinear optical applications based on geometric phases.

The fundamental interaction between free electrons and light stands at the base of both classical and quantum physics, with applications in free-electron acceleration, radiation sources, and electron microscopy. Yet, to this day, all experiments involving free-electron light interactions are fully explained by describing the light as a classical wave, disregarding its quantum nature. Here, we observe quantum statistics effects of photons on free-electron-light interactions. We demonstrate interactions passing continuously from Poissonian to super-Poissonian and up to thermal statistics, unveiling a surprising manifestation of Bohr's Correspondence Principle: the transition from quantum walk to classical random walk on the free-electron energy ladder. The electron walker serves as the probe in non-destructive quantum detection, measuring the photon-correlation ${g^{(2)} (0)}$ and higher-orders ${g^{(n)} (0)}$. Unlike conventional quantum-optical detectors, the electron can perform both quantum weak measurements and projective measurements by evolving into an entangled joint-state with the photons. Our findings suggest free-electron-based non-destructive quantum tomography of light, and constitute an important step towards combined attosecond-temporal and sub-A-spatial resolution microscopy.

Transverse second-harmonic generation, in which the emission angles of the second harmonic are determined by the spatial modulation of the quadratic nonlinearity, has important applications in nonlinear optical imaging, holography, and beam shaping. Here we study the role of the local duty cycle of the nonlinearity on the light intensity distribution in transverse second-harmonic generation, taking the generation of perfect vortices in periodically poled ferroelectric crystal as an example. We show, theoretically and experimentally, that spatial variations of the nonlinearity modulation must be accompanied by the corresponding changes of the width of inverted ferroelectric domains, to ensure uniformity of the light intensity distribution in the generated second harmonic. This work provides a fundamental way to achieve high-quality transverse second-harmonic generation and, hence, opens more possibilities in applications based on harmonic generation and its control.

Spontaneous parametric downconversion (SPDC) in quantum optics is an invaluable resource for the realization of high-dimensional qudits with spatial modes of light. One of the main open challenges is how to directly generate a desirable qudit state in the SPDC process. This problem can be addressed through advanced computational learning methods; however, due to difficulties in modeling the SPDC process by a fully differentiable algorithm, progress has been limited. Here, we overcome these limitations and introduce a physically constrained and differentiable model, validated against experimental results for shaped pump beams and structured crystals, capable of learning the relevant interaction parameters in the process. We avoid any restrictions induced by the stochastic nature of our physical model and integrate the dynamic equations governing the evolution under the SPDC Hamiltonian. We solve the inverse problem of designing a nonlinear quantum optical system that achieves the desired quantum state of downconverted photon pairs. The desired states are defined using either the second-order correlations between different spatial modes or by specifying the required density matrix. By learning nonlinear photonic crystal structures as well as different pump shapes, we successfully show how to generate maximally entangled states. Furthermore, we simulate all-optical coherent control over the generated quantum state by actively changing the profile of the pump beam. Our work can be useful for applications such as novel designs of high-dimensional quantum key distribution and quantum information processing protocols. In addition, our method can be readily applied for controlling other degrees of freedom of light in the SPDC process, such as spectral and temporal properties, and may even be used in condensed-matter systems having a similar interaction Hamiltonian.

Optical N00N states are N-photon path entangled states with important applications in quantum metrology. However, their use was limited till now owing to the difficulties of generating them in an efficient and robust manner. Here we propose and experimentally demonstrate two new simple, compact and robust schemes to generate path entangled N00N states with N = 2 that emerge directly from the nonlinear interaction. The first scheme is based on shaping the pump beam, and the second scheme is based on modulating the nonlinear coefficient of the crystal. These new methods exhibit high coincidence count rates for the detection of a N00N state, reaching record value of 2 × 105 coincidences per second. We observe super-resolution by measuring the second order correlation on the generated N = 2 state in an interferometric setup, showing the distinct fringe periodicity at half of the optical wavelength. Our findings may pave the way towards scalable and efficient sources for super-resolved quantum metrology applications and for the generation of bright squeezed vacuum states.

This comment on the Phys. Rev. A paper "Nonlinear quantum effects in electromagnetic radiation of a vortex electron" by Karlovets and Pupasov-Maximov [Phys. Rev. A 103, 12214 (2021)] addresses their criticism of the combined experimental and theoretical study "Observing the quantum wave nature of free electrons through spontaneous emission" by Remez et al, published in Phys. Rev. Lett. [Phys. Rev. Lett. 123, 060401 (2019)]. We show, by means of simple optical arguments as well as numerical simulations, that the criticism raised by Karlovets and Pupasov-Maximov regarding the experimental regime reported by Remez et al is false. Further, we discuss a necessary clarification for the theoretical derivations presented by Karlovets and Pupasov-Maximov, as they only hold for a certain experimental situation where the final state of the emitting electron is observed in coincidence with the emitted photon - which is not the common scenario in cathodoluminescence. Upon lifting the concerns regarding the experimental regime reported by Remez et al, and explicitly clarifying the electron post-selection, we believe that the paper by Karlovets and Pupasov-Maximov may constitute a valuable contribution to the problem of spontaneous emission by shaped electron wavefunctions, as it presents new expressions for the emission rates beyond the ubiquitous paraxial approximation.

We show that in order to guide waves, it is sufficient to periodically truncate their edges. The modes supported by this type of wave guide propagate freely between the slits, and the propagation pattern repeats itself. We experimentally demonstrate this general wave phenomenon for two types of waves: (i) plasmonic waves propagating on a metal-air interface that are periodically blocked by nanometric metallic walls, and (ii) surface gravity water waves whose evolution is recorded, the packet is truncated, and generated again to show repeated patterns. This guiding concept is applicable for a wide variety of waves., 5 pages, 4 figures

We study phase contributions of wave functions that occur in the evolution of Gaussian surface gravity water wave packets with nonzero initial momenta propagating in the presence and absence of an effective external linear potential. Our approach takes advantage of the fact that in contrast to matter waves, water waves allow us to measure both their amplitudes and phases., 6 pages, 1 table, 2 figures. Accepted to EPJ-ST, not published yet

We introduce a systematic approach for designing 3D nonlinear photonic crystals and pump beams for generating desired quantum correlations between structured photon-pairs. Our model is fully differentiable, allowing accurate and efficient learning and discovery of novel designs., Comment: A supporting code will be published shortly

Investigating light emission by free charged particles through the prism of quantum optics can unveil the emitter wave function., Coherent emission of light by free charged particles is believed to be successfully captured by classical electromagnetism in all experimental settings. However, recent advances triggered fundamental questions regarding the role of the particle wave function in these processes. Here, we find that even in seemingly classical experimental regimes, light emission is fundamentally tied to the quantum coherence and correlations of the emitting particle. We use quantum electrodynamics to show how the particle’s momentum uncertainty determines the optical coherence of the emitted light. We find that the temporal duration of Cherenkov radiation, envisioned for almost a century as a shock wave of light, is limited by underlying entanglement between the particle and light. Our findings enable new capabilities in electron microscopy for measuring quantum correlations of shaped electrons. Last, we propose new Cherenkov detection schemes, whereby measuring spectral photon autocorrelations can unveil the wave function structure of any charged high-energy particle.

We demonstrate focused emission of visible and near-infrared Smith-Purcell radiation by a free-electron-driven metasurface lens emitter. Our findings pave the way for free-electron light sources focusing at wavelengths lacking efficient optics.

The optical analogue of the Stern Gerlach effect is experimentally demonstrated, using the sum frequency generation process, whereby a light beam is deflected into two distinct angles owing to a gradient in the nonlinear coupling.

We show how quantum correlations such as entanglement give rise to a new quantum regime of superradaince and subradiance from free-electrons, demonstrating that light emission can be sensitive to the quantum state of many-body wavefunctions.

ACS photonics 8(12), 3394-3405 (2021). doi:10.1021/acsphotonics.1c00951, Published by American Chemical Society, Washington, DC

We propose nonlinear optical systems that are analogous to spin-transport in magnetic materials. We find a topological Hall effect for light in skyrmionic nonlinear photonic crystals, and spin-Anderson localization in optical spin-glass.

A new photonic N00N state source is presented, where the two entangled photons are directly generated at a spatially shaped periodically poled nonlinear crystal. An interference experiment shows the super resolution that characterize such states.

We study the evolution of linear and nonlinear Talbot carpets emerging in surface gravity water waves. In our measurements, we are able to record both amplitude and phase of the Temporal Talbot effect.

We study theoretically and observe experimentally the evolution of solitary surface gravity water wavepackets propagating in homogeneous and time-dependent flow created by a computer-controlled water pump, resulting in an effective linear potential. Unlike a potential free soliton, in this case the wavepacket envelope accelerates, while its phase is proportional to the cubic power of the position in the water tank. For increased wave steepness, we observe the emergence of asymmetry in the envelope, and hence it no longer retains its soliton shape. Furthermore, we study a case of ballistic dynamics of solitary surface gravity water wavepackets with initial nonzero momentum and demonstrate that their trajectory is similar to that of a projectile pulled by gravity. Nevertheless, their envelope shape is preserved during propagation, and the envelope phase is identical to that measured without an initial momentum.

We report on the experimental realization of optical frequency comb (OFC) generation in a doubly-resonant cavity second harmonic generation (SHG) system. OFCs continue to attract significant interest, offering a wealth of potential applications beyond frequency metrology. Continuously-driven Kerr microresonators, whose nonlinear response is dominated by the third-order nonlinearity, have proven to be viable alternatives to comb sources based on femtosecond mode-locked lasers. Recently, OFCs have also been directly generated through second-order nonlinear interactions in cw-pumped resonators namely, a singly-resonant cavity SHG system and a nearly-degenerate optical parametric oscillator. Theoretical studies have also predicted OFCs in doubly-resonant cavity SHG systems with a much lower threshold with respect to the singly-resonant configurations. Here we report on the first observations of OFCs in such a doubly-resonant system. The experiment is based on a periodically poled lithium niobate crystal, placed in a traveling-wave optical cavity, pumped by a cw Nd:YAG laser emitting 0.5 W at 1064 nm. The cavity is resonant for frequencies around both the fundamental pump and its second harmonic at 532 nm, and an intracavity adjustable silica window is used to separately set the detunings of the pump and its second harmonic. Stable cavity locking to the pump laser is achieved via the Pound-Drever-Hall offset locking technique, thanks to a counterpropagating orthogonally polarized auxiliary beam. We measured a power threshold for comb formation as low as 5 mW, reduced by more than one order of magnitude with respect to singly-resonant configurations. The locking system permitted to explore frequency detunings up to several cavity linewidths, and to correspondingly observe a large variety of comb regimes, with different teeth spacing and spectral span, as well as the contribution of photothermal effect to the whole dynamics. In this regard, we developed an extended theoretical model that includes thermo-optical nonlinearities.

In a nonlinear three-wave mixing process, the interacting waves can accumulate an adiabatic geometric phase (AGP) if the nonlinear coefficient of the crystal is modulated in a proper manner along the nonlinear crystal. This concept was studied so far only for the case in which the pump wave is much stronger than the two other waves, hence can be assumed to be constant. Here we extend this analysis for the fully nonlinear process, in which all three waves can be depleted and we show that the sign and magnitude of the AGP can be controlled by the period, phase and duty cycle of the nonlinear modulation pattern. In this fully nonlinear interaction, all the states of the system can be mapped onto a closed surface. Specifically, we study a process in which the eigenstate of the system follows a circular rotation on the surface. Our analysis reveals that the AGP equals to the difference between the total phase accumulated along the circular trajectory and that along its vertical projection, which is universal for the undepleted (linear) and depleted (nonlinear) cases. Moreover, the analysis reveals that the AGPs in the processes of sum-frequency generation and difference-frequency generation have opposite chirality. Finally, we utilize the AGP in the fully nonlinear case for splitting the beam into different diffraction orders in the far field., 9 pages, 36 references, 7 figures. Published on Physical Review A

We sttudy the fundamental influence of an emitter's wavefunction on the coherence of its electromagnetic radiation. Our findings allow for a new method to measure the wavefunction dimensions of charged quanttum particles.

We introduce an efficient, nonperturbative method for calculating the first and second order quantum correlations of down converted photons that recovers experimental results. Our algorithm paves the way towards engineering arbitrarily structured nonclassical light.

We present and numerically study the dynamics of a spatial quadratic soliton near an interface that is changing adiabatically. We demonstrate the applicability of this design for an all optical passive isolator.

We construct skyrmion textures in a synthetic spin-1/2 dimension using nonlinear photonic crystals, giving rise to artificial gauge fields: a magnetic field, mimicking the topological Hall effect, and an electric field unique to our system.

Superoscillating function is a band-limited function that is locally oscillating faster than its highest Fourier component. In this work, we study and implement methods to generate multi-lobe optical superoscillating beams, with nearly constant intensity and constant local frequency. We generated superoscillating patterns having up to 12 sub-wavelength oscillations, with local frequency of 20% to 40% above the band-limit. We then test the potential application of these beams to super-resolution structured illumination microscopy. By utilizing the Moire effect on a fluorescent grating, we have demonstrated experimentally resolution improvement over the conventional sinusoidal illumination. Our simulations show that structured illumination microscopy with super oscillating multi-lobe beams can provide more than twofold improvement in resolution, with respect to the classical diffraction limit and for coherent or incoherent modalities.

Custom plasmonic beams are advantageous for numerous scientific and technological aspects. While plasmonic wavefront shaping had traditionally been a truly planar process, taking place on a single surface, here we explore a new method for plasmonic shaping by selectively coupling plasmonic waves between different surfaces of an insulator–metal–insulator structure. In contrast to most previous shaping techniques that rely on free-space illumination, here the plasmonic beam in the buried surface acts as the light source. We demonstrate, both experimentally and numerically, a way to tailor the amplitude and phase of the wavefront using this new technique. The proposed method can be used to efficiently shape the plasmonic beam, for potential applications in sensing, interferometry, and communications.