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The recent comment on our previously published article questioned the novelty and computational efficiency of our work. Here we respond by restating the novelty and scientific value of our work as well as showing why the specific alternative methods stated in the comment are unlikely to outperform the methods we compare for metasurface applications involving high refractive index particles near high refractive index substrates. 

Metasurface design tends to be tedious and time-consuming based on sweeping geometric parameters. Common numerical simulation techniques are slow for large areas, ultra-fine grids, and/or three-dimensional simulations. Simulation time can be reduced by combining the principle of the discrete dipole approximation (DDA) with analytical solutions for light scattered by a dipole near a flat surface. The DDA has rarely been used in metasurface design, and comprehensive benchmarking comparisons are lacking. Here, we compare the accuracy and speed of three DDA methods—substrate discretization, two-dimensional Cartesian Green’s functions, and one-dimensional (1D) cylindrical Green’s functions—against the finite difference time domain (FDTD) method. We find that the 1D cylindrical approach performs best. For example, the s-polarized field scattered from a silica-substrate-supported 600 × 180 × 60 nm gold elliptic nanocylinder discretized into 642 dipoles is computed with 0.78 % pattern error and 6.54 % net power error within 294 s, which is 6 times faster than FDTD. Our 1D cylindrical approach takes advantage of parallel processing and also gives transmitted field solutions, which, to the best of our knowledge, is not found in existing tools. We also examine the differences among four polarizability models: Clausius–Mossotti, radiation reaction, lattice dispersion relation, and digitized Green’s function, finding that the radiation reaction dipole model performs best in terms of pattern error, while the digitized Green’s function has the lowest power error. 

Lens-free microscopes can utilize holographic reconstruction techniques to recover the image of an object from the digitally recorded superposition of an unperturbed plane wave and a wave scattered by the object. Image reconstruction most commonly relies on the scalar angular spectrum method (ASM). While fast, the scalar ASM can be inaccurate for nanoscale objects, either because of the scalar approximation, or more generally, because it only models field propagation and not light-matter interaction, including inter-particle coupling. Here we evaluate the accuracy of the scalar ASM when combined with three different light-matter interaction models for computing the far-field light scattered by random arrays of gold and polystyrene nanoparticles. Among the three models—a dipole-matched transmission model, an optical path length model, and a binary amplitude model—we find that which model is most accurate depends on the nanoparticle material and packing density. For polystyrene particles at any packing density, there is always at least one model with error below 20%, while for gold nanoparticles with 40% or 50% surface coverage, there are no models that can provide errors better than 30%. The ASM error is determined in comparison to a discrete dipole approximation model, which is more computationally efficient than other full-wave modeling techniques. The knowledge of when and how the ASM fails can serve as a first step toward improved resolution in lens-free reconstruction and can also be applied to other random nanoparticle array applications such as lens-based super-resolution imaging, sub-diffraction beam focusing, and biomolecular sensing.