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Unprecedented material compatibility and ease of integration, in addition to the unique and diverse optoelectronic properties of layered materials, have generated significant interest in their utilization in nanophotonic devices. While initial nanophotonic experiments with layered materials primarily focused on light sources, modulators, and detectors, recent efforts have included nonlinear optical devices. In this paper, we review the current state of cavity-enhanced nonlinear optics with layered materials. Along with conventional nonlinear optics related to harmonic generation, we report on emerging directions of nonlinear optics, where layered materials can potentially play a significant role.

We report a design method that can generate an array of wavelength-scale spheres to produce specified 3D optical field patterns., Controlling the propagation of optical fields in three dimensions using arrays of discrete dielectric scatterers is an active area of research. These arrays can create optical elements with functionalities unrealizable in conventional optics. Here, we present an inverse design method based on the inverse Mie scattering problem for producing three-dimensional optical field patterns. Using this method, we demonstrate a device that focuses 1.55-μm light into a depth-variant discrete helical pattern. The reported device is fabricated using two-photon lithography and has a footprint of 144 μm by 144 μm, the largest of any inverse-designed photonic structure to date. This inverse design method constitutes an important step toward designer free-space optics, where unique optical elements are produced for user-specified functionalities.

The miniaturization of current image sensors is largely limited by the volume of the optical elements. Using a sub-wavelength patterned quasi-periodic structure, also known as a metasurface, one can build planar optical elements based on the principle of diffraction. However, it was believed that high refractive index materials are required for metasurface optics. Here, we show that one can employ the design principles of a metasurface even with low contrast materials, such as silicon nitride. We validate our theory by fabricating and experimentally characterizing several silicon nitride based lenses and vortex beam generators . The fabricated lenses achieved beam spots of less than 1 {\mu}m with numerical apertures as high as ~ 0.75. A transmission efficiency of 90% and focusing efficiency of 40% in the visible regime was observed. Our results pave the way towards building low-loss metasurface based optical elements at visible frequencies using low contrast materials., Comment: 6 figures

Sub-wavelength diffractive optics, commonly known as metasurfaces, have recently garnered significant attention for their ability to create ultra-thin flat lenses with a high numerical aperture. Several materials with different refractive indices have been used to create metasurface lenses (metalenses). In this paper, we analyze the role of refractive index on the performance of these metalenses. We employ both forward and inverse design methodologies to perform our analysis. We found that, while high-refractive-index materials allow for extreme reduction of the focal length, for moderate focal lengths and numerical aperture (

We design metalenses to capture colored images with white light by combining metasurfaces and computational imaging., Conventional imaging systems comprise large and expensive optical components that successively mitigate aberrations. Metasurface optics offers a route to miniaturize imaging systems by replacing bulky components with flat and compact implementations. The diffractive nature of these devices, however, induces severe chromatic aberrations, and current multiwavelength and narrowband achromatic metasurfaces cannot support full visible spectrum imaging (400 to 700 nm). We combine principles of both computational imaging and metasurface optics to build a system with a single metalens of numerical aperture ~0.45, which generates in-focus images under white light illumination. Our metalens exhibits a spectrally invariant point spread function that enables computational reconstruction of captured images with a single digital filter. This work connects computational imaging and metasurface optics and demonstrates the capabilities of combining these disciplines by simultaneously reducing aberrations and downsizing imaging systems using simpler optics.

Tunable metasurfaces are a promising candidate for the next generation of spatial light modulators which will require higher refresh rates, smaller pixel sizes, and compact form factors. Phase-change memory materials present a unique platform for nonvolatile reconfigurable metasurfaces which could undergo phase transitions at MHz frequencies if actuated electrically, more than three orders of magnitude higher than refresh rates of existing commercial SLMs. While stable intermediate phases of GeSbTe (GST) exist which can be used for imparting differential phase shifts, the stochasticity of the material properties would limit the robustness of such a phase shifter, whereas the fully crystalline and amorphous states exhibit more consistent behavior. To overcome this, we design GST digital metamolecules comprising constituent meta-atoms which individually are in either the SET or RESET state, but which together form a tunable metamolecule with a set of robust phase shifts. We simulate active metasurface lenses based on these metamolecules, showing successful focusing, and demonstrate nano-patterning of a GST film with isolated nanoposts of material which could be electrically actuated, unlike counterparts which must be optically reconfigured.

Freeform optics aims to expand the toolkit of optical elements by allowing for more complex phase geometries beyond rotational symmetry. Complex, asymmetric curvatures are employed to enhance the performance of optical components while minimizing their weight and size. Unfortunately, these asymmetric forms are often difficult to manufacture at the nanoscale with current technologies. Metasurfaces are planar sub-wavelength structures that can control the phase, amplitude, and polarization of incident light, and can thereby mimic complex geometric curvatures on a flat, wavelength-scale thick surface. We present a methodology for designing analogues of freeform optics using a low contrast dielectric metasurface platform for operation at visible wavelengths. We demonstrate a cubic phase plate with a point spread function exhibiting enhanced depth of field over 300 {\mu}m along the optical axis with potential for performing metasurface-based white light imaging, and an Alvarez lens with a tunable focal length range of over 2.5 mm with 100 {\mu}m of total mechanical displacement. The adaptation of freeform optics to a sub-wavelength metasurface platform allows for the ultimate miniaturization of optical components and offers a scalable route toward implementing near-arbitrary geometric curvatures in nanophotonics., Comment: 5 figures

The miniaturization of current image sensors is primarily limited by the volume of optical elements. Using a subwavelength patterned quasi-periodic structure known as a metasurface, we can build planar optical elements based on the principle of diffraction. This platform allows us to mimic complex, asymmetric curvatures with ease and is ideal for the adaptation of freeform optics to the micron scale. The implementation of freeform optics on metasurfaces allows for extreme miniaturization of optical components. In our research we have demonstrated metasurface based optical elements such as lenses, vortex beam generators, and cubic phase plates near visible frequencies. Our fabricated lenses achieved beam spots of less than 1 μm with numerical apertures as high as ~ 0.75. We observed a transmission efficiency of 90% and focusing efficiency of 40% in the visible wavelengths. In addition, we have demonstrated a dynamic metasurface optical system called the Alvarez lens with a tunable focal length range of over 2.5 mm corresponding to a change in optical power of ~1600 diopters with 100 m of total mechanical displacement.

Large-area metasurfaces composed of discrete wavelength-scale scatterers present an extremely large number of degrees of freedom to engineer an optical element. These degrees of freedom provide tremendous design flexibility, and a central challenge in metasurface design is how to optimally leverage these degrees of freedom towards a desired optical function. Inverse design can be used to explore non-intuitive design space for metasurfaces. We report an inverse design method exploiting T-Matrix scattering of ellipsoidal scatterer based metasurfaces. Multifunctional, polarization multiplexed metasurfaces were designed using this approach. Finally, we apply this method to optimize the efficiency of an existing high numerical aperture (0.83)metalens design, and report an increase in efficiency from 26% to 32%

We build a full-color imaging system comprising a single metasurface by designing a wavelength-invariant point spread function across the whole visible band combined with post-capture deconvolution with a single linear filter.

We fabricate nano-patterned films of GeSbTe to make optical metasurfaces of isolated scatterers with the goal of arbitrary electrical reconfigurability, and induce phase changes by heating with a femtosecond pulsed laser.

Metasurface optics is a promising candidate for realizing the next generation of miniaturized optical components. Unlike refractive optics, these devices modify light over a wavelength-scale thickness, changing the phase, amplitude, and polarization. This review details recent developments and state-of-the-art metasurfaces realized using silicon nitride. We emphasize this material as to date it has the lowest refractive index with which metasurfaces have been experimentally demonstrated. The wide band gap of silicon nitride enables reduced absorption over a broad wavelength range relative to its higher index counterparts, providing a CMOS-compatible platform for producing a variety of high efficiency metasurface elements and systems.

Arrays of wavelength scale scatterers are a promising platform for designing optical elements with a compact footprint. The large number of degrees of freedom in this system allows for unique and plentiful functionalities. However, the many variables also create a complex design problem. While intuitive forward design methods work for simple optical elements, they often fail to produce complicated elements, especially those involving multiple elements. We present an inverse design methodology for large arrays of wavelength scale spheres based on both adjoint optimization or sensitivity analysis and generalized multi-sphere Mie theory as a solution to the design problem. We validate our methodology by designing two sets of optical elements with scatterers on sub-wavelength and super-wavelength periodicity grids. Both sets consist of a singlet and a doublet lens, with one and two layers of spheres respectively designed for 1550 nm. The designed NA is ~0.33 (~0.5) for the sub-wavelength (super-wavelength) periodic structure. We find that with the sub-wavelength periodicity, the full width at half maximum of the focal spot produced by the singlet and doublet is smaller than that produced by an ideal lens with the same geometric parameters. Finally, we simulate a realistic experimental scenario for the doublet where the spheres are placed on a substrate with the same refractive index. We find the performance is similar, but with lower intensity at the focal spot and larger spot size. The method described here will simplify the design procedure for complicated multifunctional optical elements and or scatterer array-based volume optics based on a specified figure of merit.

Quantum simulation is a promising approach to understand complex strongly correlated many-body systems using relatively simple and tractable systems. Photon-based quantum simulators have great advantages due to the possibility of direct measurements of multi-particle correlations and ease of simulating non-equilibrium physics. However, interparticle interaction in existing photonic systems is often too weak limiting the potential of quantum simulation. Here we propose an approach to enhance the interparticle interaction using exciton-polaritons in MoS$_2$ monolayer quantum-dots embedded in 2D photonic crystal microcavities. Realistic calculation yields optimal repulsive interaction in the range of $1$-$10$~meV --- more than an order of magnitude greater than the state-of-art value. Such strong repulsive interaction is found to emerge neither in the photon-blockade regime for small quantum dot nor in the polariton-blockade regime for large quantum dot, but in the crossover between the two regimes with a moderate quantum-dot radius around 20~nm. The optimal repulsive interaction is found to be largest in MoS$_2$ among commonly used optoelectronic materials. Quantum simulation of strongly correlated many-body systems in a finite chain of coupled cavities and its experimental signature are studied via exact diagonalization of the many-body Hamiltonian. A method to simulate 1D superlattices for interacting exciton-polariton gases in serially coupled cavities is also proposed. Realistic considerations on experimental realizations reveal advantages of transition metal dichalcogenide monolayer quantum-dots over conventional semiconductor quantum-emitters.

The ease of integration and a large second-order nonlinear coefficient of atomically thin layered two-dimensional (2D) materials presents a unique opportunity to realize second-order nonlinearity in a silicon compatible integrated photonic system. However, the phase-matching requirement for second-order nonlinear optical processes makes the nanophotonic design difficult. We show that by nano-patterning the 2D material, quasi-phase-matching can be achieved. Such patterning-based quasi-phase-matching could potentially compensate for inevitable fabrication errors and significantly simplify the design process of the nonlinear nanophotonic devices.

Using inexpensive and high-throughput stepper lithography, we design and fabricate 1 cm wide tunable metalenses which exhibit a focal length change of 162%, more than 6 cm, with only 2.4 mm lateral actuation.