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Register a new userDesign and Optimization of Ellipsoid Scatterer-based Metasurfaces via the Inverse T-Matrix Method
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Added by
Maksym Zhelyeznyakov
Publication date
2019
fields
Physics
and research's language is
English
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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%
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The classical adjoint-based topology optimization (TO) method, based on the use of a random continuous dielectric function as an adjoint variable distribution, is known to be one of the most efficient optimization methods that enable the design of optical devices with outstanding performances. However, the strategy for selecting the optimal solution requires a very fine pixelation of the permittivity function of the profile under optimization. Typically, at least 28 pixels are needed while optimizing a one wavelength wide 1D metagrating. This makes it very difficult to extend TO methods to large-scale optimization problems. In this paper, we introduce a new concept of adjoint-based topology optimization that enables fast and efficient geometry based design of both periodic and aperiodic metasurfaces. The structures are built from nano-rods whose widths and positions are to be adjusted. Our new approach requires a very low number of design parameters, thus leading to a drastic reduction in the computational time: about an order of magnitude. Hence, this concept makes it possible to address the optimization of large-scale structures in record time. As a proof-of-concept we apply this method to the design of (i) a periodic metagrating, optimized to have a specific response into a particular direction, and (ii) a dielectric metalens (aperiodic metasurface), enabling a high energy focusing into a well-defined focal spot.
Predicting the optical response of macroscopic arrangements of individual scatterers is a computational challenge, as the problem involves length scales across multiple orders of magnitude. We present a full-wave optical method to highly efficiently compute the scattering of light at objects that are arranged in bi-periodic arrays. Multiple arrays or homogeneous thin-films can be stacked to build up an entire multicomposite material in the third dimension. The scattering properties of the individual objects in each array are described by the T-matrix formalism. Therefore, arbitrarily shaped objects and even molecules can be the basic constituent of the arrays. Taking the T-matrix of the individual scatterer as the point of departure allows to explain the optical properties of the bulk material from the scattering properties of its constituents. We use solutions of Maxwells equations with well defined helicity. Therefore, chiral media are particularly easy to consider as materials for both scatterers or embedding media. We exemplify the efficiency of the algorithm with an exhaustive parametric study of anti-reflective coatings for solar cells made from cylinders with a high degree of helicity preservation. The example shows a speed-up of about 500 with respect to finite-element computations. A second example specifically exploits the use helicity modes to investigate the enhancement of the circular dichroism signal in a chiral material.
Inverse design of large-area metasurfaces can potentially exploit the full parameter space that such devices offer and achieve highly efficient multifunctional flat optical elements. However, since practically useful flat optics elements are large in the linear dimension, an accurate simulation of their scattering properties is challenging. Here, we demonstrate a method to compute accurate simulations and gradients of large-area metasurfaces. Our approach relies on two key ingredients - a simulation distribution strategy that allows a linear reduction in the simulation time with number of compute (GPU) nodes and an efficient single-node computation using the Transition-matrix (T-matrix) method. We demonstrate ability to perform a distributed simulation of large-area, while accurately accounting for scatterer-scatterer interactions significantly beyond the locally periodic approximation, and efficiently compute gradients with respect to the metasurface design parameters. This scalable and accurate metasurface simulation method opens the door to gradient-based optimization of full large-area metasurfaces.
The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, non-intuitive structures with superior performance. Among various methods, large-scale, gradient-based optimization techniques have been one of the most important ways to design a structure containing a vast number of degrees of freedom. These techniques are made possible by the adjoint method, in which the gradient of an objective function with respect to all design degrees of freedom can be computed using only two full-field simulations. However, this approach has so far mostly been applied to linear photonic devices. Here, we present an extension of this method to modeling nonlinear devices in the frequency domain, with the nonlinear response directly included in the gradient computation. As illustrations, we use the method to devise compact photonic switches in a Kerr nonlinear material, in which low-power and high-power pulses are routed in different directions. Our technique may lead to the development of novel compact nonlinear photonic devices.
We present a digitized adjoint method for realizing efficient inverse design of digital subwavelength nanophotonic devices. We design a single-mode 3-dB power divider and a dual-mode demultiplexer to demonstrate the digitized adjoint method for single-object and dual-object optimizations, respectively. The optimization comprises three stages, a first stage of continuous variation for an analog pattern, a second stage of forced permittivity biasing for a quasi-digital pattern, and a third stage for a multi-level digital pattern. Compared with conventional brute-force method, the proposed digitized adjoint method can improve the design efficiency by about 5 times, and the performance optimization can reach approximately the same level using the ternary pattern. The digitized adjoint method takes the advantages of adjoint sensitivity analysis and digital subwavelength structure and creates a new way for efficient and high-performance design of compact digital subwavelength nanophotonic devices. This method could overcome the efficiency bottleneck of the brute-force method that is restricted by the number of pixels of a digital pattern and improve the device performance by extending a conventional binary pattern to a multi-level one, which may be attractive for inverse design of large-scale digital nanophotonic devices.
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