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It has recently been realised that illumination by intensely powerful radiation is not the only path to a nonlinear optical response by a given material. As demonstrated for a layer of indium tin oxide (ITO), strong nonlinear effects can be observed in a material for illuminating fields of quite moderate strength in a neighbourhood of the wavelengths which render it an epsilon-near-zero (ENZ) material. Inspired by these observations we introduce, discuss and analyse a rather different formulation of the governing equations for the Capretti experiment with a view towards robust and highly accurate numerical simulation. By contrast to volumetric algorithms which are greatly disadvantaged for the piecewise homogeneous geometries we consider, surface methods provide optimal performance as they only consider interfacial unknowns. In this contribution, we study an interfacial approach which is based upon Dirichlet–Neumann operators (DNOs). We show that, for a layer of nonlinear Kerr medium, the DNO is not only well-defined, but also analytic with respect to all of its independent variables. Our method of proof is perturbative in nature and suggests several new avenues of investigation, including stable numerical simulation, and how one would include the effects of periodic deformations of the layer interfaces into both theory and numerical simulation of the resulting DNOs. This article is part of the theme issue ‘Analytically grounded full-wave methods for advances in computational electromagnetics’. 

Recently, there has been an explosion of activity in the fields of optics and photonics with the advent of fabrication techniques which enable the design of metamaterials which possess properties not encountered in the natural world. In this work, we are concerned with zero permittivity materials and a new scheme to design metamaterials for which all components of the dielectric tensor are approximately zero. Our approach involves the alternate layering of many, very thin, slices of two constituent metamaterials, a uniaxial layered medium and a uniaxial nanowire array. With a simple optimization strategy we demonstrate a candidate configuration which very nearly satisfies our design goal of zero permittivity. 

We present an efficient numerical method for simulating the scattering of electromagnetic fields by a multilayered medium with random interfaces. The elements of this algorithm, the Monte Carlo–transformed field expansion method, are (i) an interfacial problem formulation in terms of impedance-impedance operators, (ii) simulation by a high-order perturbation of surfaces approach (the transformed field expansions method), and (iii) efficient computation of the wave field for each random sample by forward and backward substitutions. Our perturbative formulation permits us to solve a sequence of linear problems featuring an operator that isdeterministic, and its LU decomposition matrices can be reused, leading to significant savings in computational effort. With an extensive set of numerical examples, we demonstrate not only the robust and high-order accuracy of our scheme for small to moderate interface deformations, but also how Padé summation can be used to address large deviations. 

A deep learning aided optimization algorithm for the design of flat thin-film multilayer optical systems is developed. The authors introduce a deep generative neural network, based on a variational autoencoder, to perform the optimization of photonic devices. This algorithm allows one to find a near-optimal solution to the inverse design problem of creating an anti-reflective grating, a fundamental problem in material science. As a proof of concept, the authors demonstrate the method’s capabilities for designing an anti-reflective flat thin-film stack consisting of multiple material types. We designed and constructed a dielectric stack on silicon that exhibits an average reflection of 1.52 %, which is lower than other recently published experiments in the engineering and physics literature. In addition to its superior performance, the computational cost of our algorithm based on the deep generative model is much lower than traditional nonlinear optimization algorithms. These results demonstrate that advanced concepts in deep learning can drive the capabilities of inverse design algorithms for photonics. In addition, the authors develop an accurate regression model using deep active learning to predict the total reflectivity for a given optical system. The surrogate model of the governing partial differential equations can then be broadly used in the design of optical systems and to rapidly evaluate their behavior.