Inference in artificial intelligence with deep optics and photonics.

Artificial intelligence tasks across numerous applications require accelerators for fast and low-power execution. Optical computing systems may be able to meet these domain-specific needs but, despite half a century of research, general-purpose optical computing systems have yet to mature into a practical technology. Artificial intelligence inference, however, especially for visual computing applications, may offer opportunities for inference based on optical and photonic systems. In this Perspective, we review recent work on optical computing for artificial intelligence applications and discuss its promise and challenges.

Transverse energy flow in an optical Skyrmionic Hopfion.

The energy flow of light represents a natural way of investigating complex light fields with respect to their applicability. With the generation of a three-dimensional Skyrmionic Hopfion structure in light, which is a topological 3D field configuration with particle-like nature, we paved the way to employ optical, topological constructs. In this work, we present an analysis of the transverse energy flow in the optical Skyrmionic Hopfion, showing the transfer of the topological properties to the mechanical attributes such as the optical angular momentum (OAM). Our findings thus prepare topological structures to be applied in optical traps and data storage or communication.

Caustic networks with customized intensity statistics.

Controlling random light is a key enabling technology that pioneered statistical imaging methods like speckle microscopy. Such low-intensity illumination is especially useful for bio-medical applications where photobleaching is crucial. Since the Rayleigh intensity statistics of speckles do not always meet the requirements of applications, considerable effort has been dedicated to tailoring their intensity statistics. A special random light distribution that naturally comes with radically different intensity structures to speckles are caustic networks. Their intensity statistics support low intensities while allowing sample illumination with rare rouge-wave-like intensity spikes. However, the control over such light structures is often very limited, resulting in patterns with inadequate ratios of bright and dark areas. Here, we show how to generate light fields with desired intensity statistics based on caustic networks. We develop an algorithm to calculate initial phase fronts for light fields so that they smoothly evolve into caustic networks with the desired intensity statistics during propagation. In an experimental demonstration, we exemplarily realize various networks with a constant, linearly decreasing and mono-exponential probability density function.

Fabrication and mechanical characterization of hydrogel-based 3D cell-like structures.

In this article, we demonstrate the fabrication of 3D cell-like structures using a femtosecond laser-based two-photon polymerization technique. By employing poly(ethylene glycol) diacrylate monomers as a precursor solution, we fabricate 3D hemispheres that resemble morphological and biomechanical characteristics of natural cells. We employ an optical tweezers-based microrheology technique to measure the viscoelastic properties of the precursor solutions inside and outside the structures. In addition, we demonstrate the interchangeability of the precursor solution within fabricated structures without impairing the microstructures. The combination of two-photon polymerization and microrheological measurements by optical tweezers demonstrated here represents a powerful toolbox for future investigations into cell mimic and artificial cell studies.

Understanding the formation of surface relief gratings in azopolymers: A combined molecular dynamics and experimental study.

The formation of surface relief gratings in thin azopolymeric films is investigated using atomistic molecular dynamics simulations and compared to experimental results for the specific case of poly-disperse-orange3-methyl-methacrylate. For this purpose, the film is illuminated with a light pattern of alternating bright and dark stripes in both cases. The simulations use a molecular mechanics switching potential to explicitly describe the photoisomerization dynamics between the E and Z isomers of the azo-units and take into account the orientation of the transition dipole moment with respect to the light polarization. Local heating and elevation of the illuminated regions with the subsequent movement of molecules into the neighboring dark regions are observed. This leads to the formation of valleys in the bright areas after re-cooling and is independent of the polarization direction. To verify these observations experimentally, the azopolymer film is illuminated with bright stripes of varying width using a spatial light modulator. Atomic force microscopy images confirm that the elevated areas correspond to the previously dark areas. In the experiment, the polarization of the incident light makes only a small difference since tiny grain-like structures form in the valleys only when the polarization is parallel to the stripes.

Analyzing light-structuring features of droplet lenses on liquid-repelling surfaces.

The complete understanding of the formation of seemingly levitating droplets on liquid-repelling surfaces provides the basis for further development of applications requiring friction-free liquid transport. For the investigation of these droplets and, thereby, the underlying surface properties, standard techniques typically only reveal a fraction of droplet or surface information. Here, we propose to exploit the light-shaping features of liquid droplets when interpreted as thick biconvex elliptical lenses. This approach has the potential to decode a plethora of droplet information from a passing laser beam, by transforming the information into a structured light field. Here, we explore this potential by analyzing the three-dimensional intensity structures sculpted by the droplet lenses, revealing the transfer of the characteristics of the underlying liquid-repelling effect onto the light field. As illustrative complementary examples, we study droplet lenses formed on a non-wetting Taro (Colocasia esculenta) leaf surface and by the Leidenfrost effect on a heated plate. Our approach may reveal even typically "invisible" droplet properties as the refractive index or internal flow dynamics and, hence, will be of interest to augment conventional tools for droplet and surface investigation.

Dual projectile beams.

Accelerating beams, of which the Airy beam is an important representative, are characterized by intensity maxima that propagate along curved trajectories. In this work we present a simple approach to directly generate accelerating beams with controllable trajectories by means of binary phase structures that consist of only a π phase step modulation in comparison to previous studies where two-dimensional cubic phase modulations for example are required, and which have practical limitations due to their challenging fabrication with phase plates or diffractive optical elements (DOEs), or the spatially extended system needed for their generation at the Fourier plane. In our approach, two intensity maxima are formed that propagate along root parabolic trajectories in contrast to Airy and higher order caustic beams that propagate along a parabolic curve, hence we call these beams Dual Projectile Beams (DPBs). By tailoring a step or slit phase patterns with additional Fresnel lenses, we either generate hollow-core or abruptly focusing beams and control their curvatures. Moreover, using DPBs as a simpler complement to complex structured light fields, we demonstrate their versatility at the example of their interaction with nonlinear matter, namely the formation of a spatial soliton in a photorefractive material. We show that the formed solitary state propagates almost unchanged for a distance of several Rayleigh lengths. This light matter interaction can be regarded as a light beam deceleration. The simplicity of this approach makes these beams suitable for integrated optics and high-power laser applications using DOEs or meta-surfaces.

Thermally assisted fabrication of nonlinear photonic structures in lithium niobate with femtosecond laser pulses.

Engineered domain structures play an essential role in nonlinear optics for quasi-phase-matched parametric processes. Pyroelectric field-assisted domain inversion with focused femtosecond laser pulses is a promising approach to create arbitrary two-dimensional nonlinear photonic structures in a large volume without externally applied electrical fields. We fabricate lattices of ferroelectric domains by patterning lithium niobate crystals with femtosecond laser pulses and then heating them to elevated temperatures. After cooling to room temperature, domains form below and above the laser-induced seeds. We investigate the effect of temperature and seed spacing on the number and size of inverted domains. In a temperature range of 220 °C-300 °C all domains are inverted in a two-dimensional lattice with periods of 15 µm × 6.3 µm. Smaller lattice periods result in a smaller fraction of inverted domains. Measurements with conducting, nonconducting, and short-circuited crystal surfaces reveal the influence of surface charges during the domain formation process. From the obtained domain widths and spacings, we calculate the effective nonlinear coefficient of quasi-phase-matched second-harmonic generation in two-dimensional nonlinear photonic structures.

Light transport and localization in disordered aperiodic Mathieu lattices.

Complex optical systems such as deterministic aperiodic Mathieu lattices are known to hinder light diffraction in a manner comparable to randomized optical systems. We systematically incorporate randomness in our complex optical system, measuring its relative contribution of randomness, to understand the relationship between randomness and complexity. We introduce an experimental method for the realization of disordered aperiodic Mathieu lattices with numerically controlled disorder degree. Added disorder always enhances light transport. For lower disorder degrees, we observe diffusive-like transport, and in the range of highest light transport, we detect Anderson localization. With further increase of disorder degree, light transport is slowly decreasing and localization length decreases indicating more pronounced Anderson localization. Numerical investigation at longer propagation distances indicates that the threshold of Anderson localization detection is shifted to lower disorder degrees.

Optical grinder: sorting of trapped particles by orbital angular momentum.

We customize a transversely structured, tunable light landscape on the basis of orbital angular momentum (OAM)-carrying beams for the purpose of advanced optical manipulation. Combining Laguerre-Gaussian (LG) modes with helical phase fronts of opposite OAM handedness, counter-rotating transfer of OAM is enabled in a concentric intensity structure, creating a dynamic "grinding" scenario on dielectric microparticles. We demonstrate the ability to trap and rotate silica spheres of various sizes and exploit the light fields' feature to spatially separate trapped objects by their size. We show the adaptability of the light field depending on the chosen LG mode indices, allowing on-demand tuning of the trapping potential and sorting criteria. The versatility of our approach for biomedical application is examined by spatial discriminating yeast cells and silica spheres of distinct diameter.

Nonlinear Optics: feature issue introduction.

This joint issue of Optics Express and Optical Materials Express features 18 state-of-the art articles that witness actual developments in nonlinear optics, including those by authors who participated in the international conference Nonlinear Optics held in Waikoloa, Hawaii from July 15 to 19, 2019. As an introduction, the editors provide a summary of these articles that cover all aspects of nonlinear optics, from basic nonlinear effects and novel frequency windows to innovative nonlinear materials and devices, thereby paving the way for new nonlinear optical concepts and forthcoming applications.

Optical singularities and Möbius strip arrays in tailored non-paraxial light fields.

A major current challenge in the field of structured light represents the development from three- (3d) to four-dimensional (4d) electric field structures, in which one exploits the transverse as well as longitudinal field components in 3d space. For this purpose, non-paraxial fields are required in order to be able to access visionary 3d topological structures as optical cones, ribbons and Möbius strips formed by 3d polarization states. We numerically demonstrate the customization of such complex topological structures by controlling generic polarization singularities in non-paraxial light fields. Our approach is based on tightly focusing tailored higher-order vector beams in combination with phase vortices. Besides demonstrating the appearance of cones and ribbons around the optical axis, we evince sculpting arrays of Möbius strips realized around off-axis generic singularities.

Morphing discrete diffraction in nonlinear Mathieu lattices.

Discrete optical gratings are essential components to customize structured light waves, determined by the band structure of the periodic potential. Beyond fabricating static devices, light-driven diffraction management requires nonlinear materials. Up to now, nonlinear self-action has been limited mainly to discrete spatial solitons. Discrete solitons, however, are restricted to the eigenstates of the photonic lattice. Here, we control light formation by nonlinear discrete diffraction, allowing for versatile output diffraction states. We observe morphing of diffraction structures for discrete Mathieu beams propagating nonlinearly in photosensitive media. The self-action of a zero-order Mathieu beam in a nonlinear medium shows characteristics similar to discrete diffraction in one-dimensional waveguide arrays. Mathieu beams of higher orders show discrete diffraction along curved paths, showing the fingerprint of respective two-dimensional photonic lattices.

Self-healing high-dimensional quantum key distribution using hybrid spin-orbit Bessel states.

Using spatial modes for quantum key distribution (QKD) has become highly topical due to their infinite dimensionality, promising high information capacity per photon. However, spatial distortions reduce the feasible secret key rates and compromise the security of a quantum channel. In an extreme form such a distortion might be a physical obstacle, impeding line-of-sight for free-space channels. Here, by controlling the radial degree of freedom of a photon's spatial mode, we are able to demonstrate hybrid high-dimensional QKD through obstacles with self-reconstructing single photons. We construct high-dimensional mutually unbiased bases using spin-orbit hybrid states that are radially modulated with a non-diffracting Bessel-Gaussian (BG) profile, and show secure transmission through partially obstructed quantum links. Using a prepare-measure protocol we report higher quantum state self-reconstruction and information retention for the non-diffracting BG modes as compared to Laguerre-Gaussian modes, obtaining a quantum bit error rate (QBER) that is up to 3× lower. This work highlights the importance of controlling the radial mode of single photons in quantum information processing and communication as well as the advantages of QKD with hybrid states.

Introduction: Nonlinear Optics (NLO) 2017 feature issue.

The editors introduce the feature issue on "Nonlinear Optics 2017," based on the topics presented at the NLO 2017 conference, which was held in Waikoloa, Hawaii, USA from July 17-21, 2017. This feature issue is jointly published by Optics Express and Optical Materials Express.

Sculpting complex polarization singularity networks.

Polarization singularities in vectorial light fields have become an important tool for different cutting-edge applications such as information processing with integer information units. However, even though vectorial singularities naturally form configurations of multiple singular points, up to now only rather simple, mostly cylindrical vector beams including single central singularities, have been considered. Here we demonstrate the customization of extended singularity networks embedded in a class of complex polarization structures based on general Ince-Gaussian modes, namely, Ince-Gaussian vector modes. Contributing to fundamental singular optics, our investigations evince the conservation of tailored singularity arrangements upon 3D propagation, whereby respective modes enlarge the range of stable vectorial fields, paving the way to information technologies with a significantly enhanced number of degrees of freedom.

Massive ordering and alignment of cylindrical micro-objects by photovoltaic optoelectronic tweezers.

Optical tools for manipulation and trapping of micro- and nano-objects are a fundamental issue for many applications in nano- and biotechnology. This work reports on the use of one such method, known as photovoltaic optoelectronics tweezers, to orientate and organize cylindrical microcrystals, specifically elongated zeolite L, on the surface of Fe-doped LiNbO3 crystal plates. Patterns of aligned zeolites have been achieved through the forces and torques generated by the bulk photovoltaic effect. The alignment patterns with zeolites parallel or perpendicular to the substrate surface are highly dependent on the features of light distribution and crystal configuration. Moreover, dielectrophoretic chains of zeolites with lengths up to 100 µm have often been observed. The experimental results of zeolite trapping and alignment have been discussed and compared together with theoretical simulations of the evanescent photovoltaic electric field and the dielectrophoretic potential. They demonstrate the remarkable capabilities of the optoelectronic photovoltaic method to orientate and pattern anisotropic microcrystals. The combined action of patterning and alignment offers a unique tool to prepare functional nanostructures with potential applications in a variety of fields such as nonlinear optics or plasmonics.

Synchronization in pairs of rotating active biomotors.

Although synchronization is a well-known physical phenomenon, experimental studies of its emergence in living bacterial cells are still scarce. The difficulty in generating a controlled scenario to detect synchronization has limited the experimental outcomes so far. We present a realization based on holographic optical tweezers in which adhered pairs of self-propelled bacteria rotate in a plane. The separation distance between the bacteria determines the strength of the hydrodynamic coupling. Despite the noisy environment and autonomous dynamics of the living bacteria, we find evidence of phase locking and frequency entrainment in their rotation. The observation of higher order frequency synchronization is also discussed.

Biolens behavior of RBCs under optically-induced mechanical stress.

In this work, the optical behavior of Red Blood Cells (RBCs) under an optically-induced mechanical stress was studied. Exploiting the new findings concerning the optical lens-like behavior of RBCs, the variations of the wavefront refracted by optically-deformed RBCs were further investigated. Experimental analysis have been performed through the combination of digital holography and numerical analysis based on Zernike polynomials, while the biological lens is deformed under the action of multiple dynamic optical tweezers. Detailed wavefront analysis provides comprehensive information about the aberrations induced by the applied mechanical stress. By this approach it was shown that the optical properties of RBCs in their discocyte form can be affected in a different way depending on the geometry of the deformation. In analogy to classical optical testing procedures, optical parameters can be correlated to a particular mechanical deformation. This could open new routes for analyzing cell elasticity by examining optical parameters instead of direct but with low resolution strain analysis, thanks to the high sensitivity of the interferometric tool. Future application of this approach could lead to early detection and diagnosis of blood diseases through a single-step wavefront analysis for evaluating different cells elasticity. © 2017 International Society for Advancement of Cytometry.

Tailored intensity landscapes by tight focusing of singular vector beams.

Vector beams are of major importance to tailor tightly focused fields by creating an additional z-polarization component. Till now, mainly focusing properties of fundamental vector beams have been investigated, whereas the knowledge of focused higher-order singular vector fields is still missing. We fill this gap by numerical analysis of these fields, applying their attractive characteristics as including a spatially adjustable amount of radial and azimuthal components. We demonstrate the realization of three-dimensional polarization structures whose total intensity resembles dark stars and bright flowers. Further, we tailor these focal intensity landscapes by modulating the order of incident vector fields. This in turn allows shaping the focus of a light field for specific applications as e.g. advanced microscopy.