Do dielectric bilayer metasurfaces behave as a stack of decoupled single-layer metasurfaces?

Flat optics or metasurfaces have opened new frontiers in wavefront shaping and its applications. Polarization optics is one prominent area which has greatly benefited from the shape-birefringence of metasurfaces. However, flat optics comprising a single layer of meta-atoms can only perform a subset of polarization transformations, constrained by a symmetric Jones matrix. This limitation can be tackled using metasurfaces composed of bilayer meta-atoms but exhausting all possible combinations of geometries to build a bilayer metasurface library is a very daunting task. Consequently, bilayer metasurfaces have been widely treated as a cascade (product) of two decoupled single-layer metasurfaces. Here, we test the validity of this assumption for dielectric metasurfaces by considering a metasurface made of titanium dioxide on fused silica substrate at a design wavelength of 532 nm. We explore regions in the design space where the coupling between the top and bottom layers can be neglected, i.e., producing a far-field response which approximates that of two decoupled single-layer metasurfaces. We complement this picture with the near-field analysis to explore the underlying physics in regions where both layers are strongly coupled. We also show the generality of our analysis by applying it to silicon metasurfaces at telecom wavelengths. Our unified approach allows the designer to efficiently build a multi-layer dielectric metasurface, either in transmission or reflection, by only running one full-wave simulation for a single-layer metasurface.

Deep learning-assisted light sheet holography.

In a novel approach to layer-based holography, we propose a machine learning-assisted light sheet holography-an optimized holography technique which projects a target scene onto sheets of light along the longitudinal planes (i.e. planes perpendicular to the plane of the hologram). Using a convolutional neural network in conjunction with superposition of Bessel beams, we generate high-definition images which can be stacked in parallel onto longitudinal planes with very high fidelity. Our holography system provides high axial resolution and excellent control over the light intensity along the optical path, which is suitable for augmented reality and/or virtual reality applications.

Point singularity array with metasurfaces.

Phase singularities are loci of darkness surrounded by monochromatic light in a scalar field, with applications in optical trapping, super-resolution imaging, and structured light-matter interactions. Although 1D singular structures, like optical vortices, are common due to their robust topological properties, uncommon 0D (point) and 2D (sheet) singularities can be generated by wavefront-shaping devices like metasurfaces. With the design flexibility of metasurfaces, we deterministically position ten identical point singularities using a single illumination source. The phasefront is inverse-designed using phase-gradient maximization with an automatically-differentiable propagator and produces tight longitudinal intensity confinement. The array is experimentally realized with a TiO2 metasurface. One possible application is blue-detuned neutral atom trap arrays, for which this field would enforce 3D confinement and a potential depth around 0.22 mK per watt of incident laser power. We show that metasurface-enabled point singularity engineering may significantly simplify and miniaturize the optical architecture for super-resolution microscopes and dark traps.

Tunable structured light with flat optics.

Flat optics has emerged as a key player in the area of structured light and its applications, owing to its subwavelength resolution, ease of integration, and compact footprint. Although its first generation has revolutionized conventional lenses and enabled anomalous refraction, new classes of meta-optics can now shape light and dark features of an optical field with an unprecedented level of complexity and multifunctionality. Here, we review these efforts with a focus on metasurfaces that use different properties of input light-angle of incidence and direction, polarization, phase distribution, wavelength, and nonlinear behavior-as optical knobs for tuning the output response. We discuss ongoing advances in this area as well as future challenges and prospects. These recent developments indicate that optically tunable flat optics is poised to advance adaptive camera systems, microscopes, holograms, and portable and wearable devices and may suggest new possibilities in optical communications and sensing.

Generalized polarization transformations with metasurfaces.

Metasurfaces are arrays of sub-wavelength spaced nanostructures, which can be designed to control the many degrees-of-freedom of light on an unprecedented scale. In this work, we design meta-gratings where the diffraction orders can perform general, arbitrarily specified, polarization transformation without any reliance on conventional polarization components, such as waveplates and polarizers. We use matrix Fourier optics to design our devices and introduce a novel approach for their optimization. We implement the designs using form-birefringent metasurfaces and quantify their behavior - retardance and diattenuation. Our work is of importance in applications, such as polarization abberation correction in imaging systems, and in experiments requiring novel and compact polarization detection and control.

Structuring total angular momentum of light along the propagation direction with polarization-controlled meta-optics.

Recent advances in wavefront shaping have enabled complex classes of Structured Light which carry spin and orbital angular momentum, offering new tools for light-matter interaction, communications, and imaging. Controlling both components of angular momentum along the propagation direction can potentially extend such applications to 3D. However, beams of this kind have previously been realized using bench-top setups, requiring multiple interaction with light of a fixed input polarization, thus impeding their widespread applications. Here, we introduce two classes of metasurfaces that lift these constraints, namely: i) polarization-switchable plates that couple any pair of orthogonal polarizations to two vortices in which the magnitude and/or sense of vorticity vary locally with propagation, and ii) versatile plates that can structure both components of angular momentum, spin and orbital, independently, along the optical path while operating on incident light of any polarization. Compact and integrated devices of this type can advance light-matter interaction and imaging and may enable applications that are not accessible via other wavefront shaping tools.

Jones matrix holography with metasurfaces.

We propose a new class of computer-generated holograms whose far-fields have designer-specified polarization response. We dub these Jones matrix holograms. We provide a simple procedure for their implementation using form-birefringent metasurfaces. Jones matrix holography generalizes a wide body of past work with a consistent mathematical framework, particularly in the field of metasurfaces, and suggests previously unrealized devices, examples of which are demonstrated here. In particular, we demonstrate holograms whose far-fields implement parallel polarization analysis and custom waveplate-like behavior.

Engineering phase and polarization singularity sheets.

Optical phase singularities are zeros of a scalar light field. The most systematically studied class of singular fields is vortices: beams with helical wavefronts and a linear (1D) singularity along the optical axis. Beyond these common and stable 1D topologies, we show that a broader family of zero-dimensional (point) and two-dimensional (sheet) singularities can be engineered. We realize sheet singularities by maximizing the field phase gradient at the desired positions. These sheets, owning to their precise alignment requirements, would otherwise only be observed in rare scenarios with high symmetry. Furthermore, by applying an analogous procedure to the full vectorial electric field, we can engineer paraxial transverse polarization singularity sheets. As validation, we experimentally realize phase and polarization singularity sheets with heart-shaped cross-sections using metasurfaces. Singularity engineering of the dark enables new degrees of freedom for light-matter interaction and can inspire similar field topologies beyond optics, from electron beams to acoustics.

Designing the phase and amplitude of scalar optical fields in three dimensions.

The ability to generate any arbitrarily chosen optical field in a three-dimensional (3D) space, in the absence of any sources, without modifying the index of refraction, remains an elusive but much-desired capability with applications in various fields such as optical micromanipulation, imaging, and data communications, to name a few. In this work, we show analytically that it is possible to generate any desired scalar optical field with predefined amplitude and phase in 3D space, where the generated field is an exact duplicate of the desired field in case it is a solution of Helmholtz wave equation, or if the existence of such field is strictly forbidden, the generated field is the closest possible rendition of the desired field in amplitude and phase. The developed analytical approach is further supported via experimental demonstration of optical beams with exotic trajectories and can have a significant impact on the aforementioned application areas.

Experimental demonstration of tunable refractometer based on orbital angular momentum of longitudinally structured light.

The index of refraction plays a decisive role in the design and classification of optical materials and devices; therefore, its proper and accurate determination is essential. In most refractive index (RI) sensing schemes, however, there is a trade-off between providing high-resolution measurements and covering a wide range of RIs. We propose and experimentally demonstrate a novel mechanism for sensing the index of refraction of a medium by utilizing the orbital angular momentum (OAM) of structured light. Using a superposition of co-propagating monochromatic higher-order Bessel beams with equally spaced longitudinal wavenumbers, in a comb-like setting, we generate non-diffracting rotating light structures in which the orientation of the beam's intensity profile is sensitive to the RI of the medium (here, a fluid). In principle, the sensitivity of this scheme can exceed ~2700°/RI unit (RIU) with a resolution of ~ 1 0 - 5 RIU. Furthermore, we show how the unbounded degrees of freedom associated with OAM can be deployed to offer a wide dynamic range by generating structured light that evolves into different patterns based on the change in RI. The rotating light structures are generated by a programmable spatial light modulator. This provides dynamic control over the sensitivity, which can be tuned to perform coarse or fine measurements of the RI in real time. This, in turn, allows high sensitivity and resolution to be achieved simultaneously over a very wide dynamic range, which is a typical trade-off in all RI sensing schemes. We thus envision that this method will open new directions in refractometry and remote sensing.

Structuring light under different polarization states within micrometer domains: exact analysis from the Maxwell equations.

We show the possibility of arbitrary longitudinal spatial modeling of non-diffracting light beams over micrometric regions. The resulting beams, which are highly non-paraxial, possess subwavelength spots and can acquire multiple intensity peaks at predefined locations over regions that are few times larger than the wavelength. The formulation we present here provides exact solutions to the Maxwell's equations where the linear, radial, and azimuthal beam polarizations are all considered. Modeling the longitudinal intensity pattern at small scale can address many challenges in three-dimensional optical trapping and micromanipulation.

Generating attenuation-resistant frozen waves in absorbing fluid.

We demonstrate a class of nondiffracting beams, called frozen waves, with a central spot that can be made to maintain a predefined intensity profile while propagating in an absorbing fluid. Frozen waves are composed of Bessel beams with different transverse and longitudinal wavenumbers, and are generated using a programmable spatial light modulator. The attenuation-resistant frozen waves demonstrated here address the problem of propagation losses in absorbing media. This development can be beneficial for many applications in particle micro-manipulation, data communications, remote sensing, and imaging.

Time-frequency dynamics of superluminal pulse transition to the subluminal regime.

Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.