Inverse design of optical elements based on arrays of dielectric spheres

Large area optimization of meta-lens via data-free machine learning

Sub-wavelength diffractive optics, commonly known as meta-optics, present a complex numerical simulation challenge, due to their multi-scale nature. The behavior of constituent sub-wavelength scatterers, or meta-atoms, needs to be modeled by full-wave electromagnetic simulations, whereas the whole meta-optical system can be modeled using ray/ Fourier optics. Most simulation techniques for large-scale meta-optics rely on the local phase approximation (LPA), where the coupling between dissimilar meta-atoms is neglected. Here we introduce a physics-informed neural network, coupled with the overlapping boundary method, which can efficiently model the meta-optics while still incorporating all of the coupling between meta-atoms. We demonstrate the efficacy of our technique by designing 1mm aperture cylindrical meta-lenses exhibiting higher efficiency than the ones designed under LPA. We experimentally validated the maximum intensity improvement (up to 53%) of the inverse-designed meta-lens. Our reported method can design large aperture ( ~ 104 − 105λ ) meta-optics in a reasonable time (approximately 15 minutes on a graphics processing unit) without relying on the LPA.

Zhelyeznyakov and coworkers present a data-free physics-informed neural network to model and optimize the electromagnetic field distribution of large-scale ( ~ 1 mm in diameter) optical meta-lenses. This simplified method can speed up the design of large aperture meta-optics.

Meta-atom library generation via an efficient multi-objective shape optimization method

Optimizing the shape of metasurface unit cells can lead to tremendous performance gains in several critically important areas. This paper presents a method of generating and optimizing freeform shapes to improve efficiency and achieve multiple metasurface functionalities (e.g., different polarization responses). The designs are generated using a three-dimensional surface contour method, which can produce an extensive range of nearly arbitrary shapes using only a few variables. Unlike gradient-based topology optimization, the proposed method is compatible with existing global optimization techniques that have been shown to significantly outperform local optimization algorithms, especially in complex and multimodal design spaces.

Computational inverse design for cascaded systems of metasurface optics

Metasurfaces are an emerging technology that may supplant many of the conventional optics found in imaging devices, displays, and precision scientific instruments. Here, we develop a method for designing optical systems composed of multiple unique metasurfaces aligned in sequence and separated by distances much larger than the design wavelengths. Our approach is based on computational inverse design, also known as the adjoint-gradient method. This technique enables thousands or millions of independent design variables (e.g., the shapes of individual meta-atoms) to be optimized in parallel, with little or no intervention required by the user. The assumptions underlying our method are as follows: we use the local periodic approximation to determine the phase-response of a given meta-atom, we use the scalar wave approximation to propagate light fields between metasurface layers, and we do not consider multiple reflections between metasurface layers (analogous to a sequential-optics ray-tracer). To demonstrate the broad applicability of our method, we use it to design an achromatic doublet metasurface lens, a spectrally-multiplexed holographic element, and an ultra-compact optical neural network for classifying handwritten digits.

Controlling three-dimensional optical fields via inverse Mie scattering

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.

Multifunctional metaoptics based on bilayer metasurfaces

Optical metasurfaces have become versatile platforms for manipulating the phase, amplitude, and polarization of light. A platform for achieving independent control over each of these properties, however, remains elusive due to the limited engineering space available when using a single-layer metasurface. For instance, multiwavelength metasurfaces suffer from performance limitations due to space filling constraints, while control over phase and amplitude can be achieved, but only for a single polarization. Here, we explore bilayer dielectric metasurfaces to expand the design space for metaoptics. The ability to independently control the geometry and function of each layer enables the development of multifunctional metaoptics in which two or more optical properties are independently designed. As a proof of concept, we demonstrate multiwavelength holograms, multiwavelength waveplates, and polarization-insensitive 3D holograms based on phase and amplitude masks. The proposed architecture opens a new avenue for designing complex flat optics with a wide variety of functionalities.

Approach to analysis of all-dielectric free-form antenna systems

The analytical model is proposed for simulation of the near-field and far-field characteristics of an all-dielectric free-form antenna system. The antenna system is constructed of an array of high-refractive-index dielectric resonators. The model relies on the coupled mode theory and the perturbation theory for the Maxwell's equations. The model is validated against numerical simulations performed by the ANSYS HFSS electromagnetic solver and microwave experiments. Three designs of the free-form antenna systems are proposed, studied and experimentally tested. The mechanisms of the multiple beam generation and beam steering are demonstrated.

Design and analysis of thin optical lens composed of low-index subwavelength structures

We design a polarization-insensitive subwavelength optical lens capable of focusing plane waves of visible wavelength using traditional optical materials such as glass. Using analytical effective medium theory and finite difference time domain (FDTD) method, the phase of transmission of arrayed subwavelength inclusions is studied with respect to their size and shape. It is shown that the phase relations can be accurately predicted using an analytical method, simplifying the design process. A guideline is established for selecting a set of subwavelength inclusions so that complete phase coverage can be achieved. Analytical calculation of focal length using diffraction equations (Fresnel or Rayleigh-Sommerfeld) along with effective medium approximation is done and compared with FDTD and experimental results, showing high accuracy. Large-scale optical lenses with subwavelength thickness are designed and their performance analyzed using an analytical approach. The optical lenses show high focusing efficiency at small numerical apertures, insensitivity to polarization angle, and robustness to uncertainty in their structural parameters. This work shows that using an analytical method, thin optical lenses with subwavelength structure can be designed and studied.

Role of refractive index in metalens performance

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 (<0.6), there is no appreciable difference in the focal spot size and focusing efficiency for metalenses made of different materials with refractive indices ranging between 1.2 and 3.43 in forward design, and 1.25 and 3.5 in inverse design.

Inverse design of large-area metasurfaces

We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength/multi-angle optimizations, and demultiplexers. To optimize surfaces that can be thousands of wavelengths in diameter, with thousands (or millions) of parameters, the key is a fast approximate solver for the scattered field. We employ a "locally periodic" approximation in which the scattering problem is approximated by a composition of periodic scattering problems from each unit cell of the surface, and validate it against brute-force Maxwell solutions. This is an extension of ideas in previous metasurface designs, but with greatly increased flexibility, e.g. to automatically balance tradeoffs between multiple frequencies or to optimize a photonic device given only partial information about the desired field. Our approach even extends beyond the metasurface regime to non-subwavelength structures where additional diffracted orders must be included (but the period is not large enough to apply scalar diffraction theory).